CBSE 11th Standard Maths Subject Probability Value Based Questions 2 Marks Questions With Solution 2022 - by Rupa Das - Bhubaneswar - May 31, 2021 - View & Read

• 1)

  Three coins are tossed. Find the probability of exactly 2 heads.

• 2)

  Three coins are tossed. Find the probability of atleast 2 heads.

• 3)

  Three coins are tossed. Find the probability of almost 2 heads.

• 4)

  Three coins are tossed. Find the probability of no head.

• 5)

  Three coins are tossed. Find the probability of What is the significance of tossing a coin in cricket?

CBSE 11th Standard Maths Subject Probability Value Based Questions 2 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 31, 2021 - View & Read

• 1)

  Three coins are tossed. Find the probability of all heads

• 2)

  Three coins are tossed. Find the probability of exactly 2 heads.

• 3)

  Three coins are tossed. Find the probability of atleast 2 heads.

• 4)

  Three coins are tossed. Find the probability of almost 2 heads.

• 5)

  Three coins are tossed. Find the probability of no head.

CBSE 11th Standard Maths Subject Statistics Value Based Questions 2 Marks Questions With Solutions 2021 - by Rupa Das - Bhubaneswar - May 31, 2021 - View & Read

• 1)

  An analysis of monthly wages paid to workers in two firms A and B belonging to the same industry, give the following result.

  	Firm A	Firm B
  Number of wages earners	586	648
  Mean of monthly wages	Rs. 5253	Rs. 5253
  Variance of distribution of wages	100	121

  Which value is addressed by the firms by paying out larger wages to employees?

• 2)

  A school conducted an intelligence test for the students and the winner of the test was to be awarded with a cash prize of Rs. 5000.
  The scores of 48 children in an intelligence test are shown in the following frequency table.

  Score	Frequency	Score	Frequency
  71	4	97	4
  76	3	101	3
  79	4	103	3
  83	5	107	3
  86	6	110	2
  89	5	114	2
  90	4

  Calculate the variance \({ \sigma }^{ 2 }\) and find out the percentage of children, whose scores lies between \(\overline { x } -\sigma \) and \(\overline { x } +\sigma \).

• 3)

  A school conducted an intelligence test for the students and the winner of the test was to be awarded with a cash prize of Rs. 5000.
  The scores of 48 children in an intelligence test are shown in the following frequency table.

  Score	Frequency	Score	Frequency
  71	4	97	4
  76	3	101	3
  79	4	103	3
  83	5	107	3
  86	6	110	2
  89	5	114	2
  90	4

  What value is shown in this question?

• 4)

  In a survey of 44 villages of a state, about the use of LGP as a cooking mode, the following information about the families using LPG was obtained.

  Number of families	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60
  Number of villages	6	8	16	8	4	2

  Find the mean deviation about median for the following data.

• 5)

  In a survey of 44 villages of a state, about the use of LGP as a cooking mode, the following information about the families using LPG was obtained.

  Number of families	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60
  Number of villages	6	8	16	8	4	2

  Do you think more awareness was needed for the villagers to use LPG as a mode of cooking?

CBSE 11th Standard Maths Subject Statistics Value Based Questions 2 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 31, 2021 - View & Read

• 1)

  An analysis of monthly wages paid to workers in two firms A and B belonging to the same industry, give the following result.

  	Firm A	Firm B
  Number of wages earners	586	648
  Mean of monthly wages	Rs. 5253	Rs. 5253
  Variance of distribution of wages	100	121

  Which firm A or B pays out larger amount as monthly wages?

• 2)

  An analysis of monthly wages paid to workers in two firms A and B belonging to the same industry, give the following result.

  	Firm A	Firm B
  Number of wages earners	586	648
  Mean of monthly wages	Rs. 5253	Rs. 5253
  Variance of distribution of wages	100	121

  Which firm A or B, shows greater variability in individual wages?

• 3)

  An analysis of monthly wages paid to workers in two firms A and B belonging to the same industry, give the following result.

  	Firm A	Firm B
  Number of wages earners	586	648
  Mean of monthly wages	Rs. 5253	Rs. 5253
  Variance of distribution of wages	100	121

  Which value is addressed by the firms by paying out larger wages to employees?

• 4)

  A school conducted an intelligence test for the students and the winner of the test was to be awarded with a cash prize of Rs. 5000.
  The scores of 48 children in an intelligence test are shown in the following frequency table.

  Score	Frequency	Score	Frequency
  71	4	97	4
  76	3	101	3
  79	4	103	3
  83	5	107	3
  86	6	110	2
  89	5	114	2
  90	4

  Calculate the variance \({ \sigma }^{ 2 }\) and find out the percentage of children, whose scores lies between \(\overline { x } -\sigma \) and \(\overline { x } +\sigma \).

• 5)

  A school conducted an intelligence test for the students and the winner of the test was to be awarded with a cash prize of Rs. 5000.
  The scores of 48 children in an intelligence test are shown in the following frequency table.

  Score	Frequency	Score	Frequency
  71	4	97	4
  76	3	101	3
  79	4	103	3
  83	5	107	3
  86	6	110	2
  89	5	114	2
  90	4

  What value is shown in this question?

CBSE 11th Standard Maths Subject Probability HOT Questions 6 Mark Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  A box contains 200 bolts and 70 nuts. It is given that 60% bolts and 40% nuts are rusted.Two objects are selected at random from the box.Find the probability that either both are bolts or both are rusted.

• 2)

  If 4-digit numbers greater than 5,000 are randomly formed from the digits 0, 1, 3, 5, and 7, what is the probability of forming a number divisible by 5 when, (i) the digits are repeated? (ii) the repetition of digits is not allowed?

• 3)

  If 4digit numbers greater than 5000 are randomly formed the digits 0,1,3,5 and 7.What is the probability of forming a number divisible by 5 when the repetition of digits are not allowed?

CBSE 11th Standard Maths Subject Relations and Functions HOT Questions 6 Mark Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  If f(x) = \(\begin{cases} 1+x,-1 \leq x<0 \\ x^{2}-1, \quad 0\end{cases}\)
  Then, find f(3), f(-2), f(0), \(f(\frac { 1 }{ 2 } )\), f(2-h) and f(-1+h), where h > 0 is very small.

• 2)

  Let A = {8, 11, 12, 15, 18, 23} and f is a function from \(A\rightarrow N\) such that f(x) = highest prime factor of x, find f  and its range. 

• 3)

  Find the domain of the function \(f(x)=\frac { { x }^{ 2 }+2x+1 }{ { x }^{ 2 }-8x+12 } \)

CBSE 11th Standard Maths Subject Complex Numbers and Quadratic Equations HOT Questions 4 Mark Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  If z is a complex number such that \(|z-1|=|z+1|\)  then show that Re(z) = 0.

• 2)

  Find the modulus and argument of \(z=\frac { (1+i)^{ 13 } }{ (1+i)^{ 7 } }\)

• 3)

  If (1+i)(1+2i)(1+3i)...(1+ni)=(x+iy), then show that 2.5.10....(1+n²)=x²+y²

• 4)

  Find the value of x and y, if \(\frac { \left( 1+i \right) x-2i }{ 3+i } +\frac { \left( 2-3i \right) y+i }{ 3-i } =i\)

• 5)

  Find the value of \({ 2x }^{ 4 }+{ 5x }^{ 3 }+{ 7x }^{ 2 }-x+41,when\ x=-2-\sqrt { 3i } \)

CBSE 11th Standard Maths Subject Trigonometric Functions HOT Questions 4 Mark Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  If \(cos\left( \alpha +\beta \right) =\frac { 4 }{ 5 } ,\quad sin(\alpha -\beta )=\frac { 5 }{ 13 } \) and \(\alpha , \beta \) lie between 0 and \(\frac { \pi }{ 4 } \) then prove that \(tan 2\alpha =\frac { 56 }{ 33 } .\)

• 2)

  If \(\theta +\phi =\alpha \) and \(tan \theta =k\) \(tan\quad \phi ,\) then prove that \(sin\left( \theta -\phi \right) =\frac { k-1 }{ k+1 } sin\alpha .\)

• 3)

  If tan(πcosθ)=cot(πsinθ)  then prove that  \(cos\left( \theta -\frac { \pi }{ 4 } \right) =\pm \frac { 1 }{ 2\sqrt { 2 } } .\)

• 4)

  If \(cos \left( \theta +\phi \right) = m\quad cos\quad \left( \theta -\phi \right) \)then find the value of \(\frac { 1-m }{ 1+m } cot\quad \phi .\)

• 5)

  Two trees A and B are on the same side of a river. From a point C in the river the distance of trees A and B are 250m and 300m, respectively of the angle C is 45⁰, find the distance between the trees.[use \(\sqrt { 2 } =1.44\)]

CBSE 11th Standard Maths Subject Sets HOT Questions 4 Mark Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  In a survey of 400 movie viewers, 150 were listed as liking 'Veer Zaara', 100 were listed as liking 'Aitraaz' and 75 were listed both liking 'Aitraaz' as well as 'Veer zaara'.Find how many people liking neither 'Aitraaz' nor 'Veer Zaara'?

• 2)

  Out of 100 students, 15 passed in English, 12 passed in Mathematics, 8 in Science, 4 in English and Science, 4 in all the three.Find how many students passed in  English and Mathematics but not in Science?

• 3)

  Out of 100 students, 15 passed in English, 12 passed in Mathematics, 8 in Science, 4 in English and Science, 4 in all the three.Find how many students passed in Mathematics and Science but not in English?

• 4)

  Prove that  \(A-(B\cap C)=(A-B)\cup (A-C).\)

CBSE 11th Standard Maths Subject Statistics HOT Questions 2 Mark Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  Find the standard deviation and the variance of first n natural numbers.

• 2)

  If \(\bar { x } \) is mean and \(MD\left( \bar { x } \right) \) is the mean deviation from mean then find the number of observations lying between \(\bar { x } -MD\left( \bar { x } \right) \) and \(\bar { x } +MD\left( \bar { x } \right) \) . Use the data 22,24,30,27,29,31,25,28,41,42.

• 3)

  Calculate the mean deviation about median for the age distribution of 100 persons given below.

  Age	16-20	21-25	26-30	31-35	36-40	41-45	46-50	51-55
  Number	5	6	12	14	26	12	16	9

  First, make the class intervals are of uniform length and then use the following formula.
  \(Median\left( M \right) =l+\frac { \frac { N }{ 2 } -cf }{ f } \times h\quad and\quad MD\left( M \right) =\frac { \Sigma fi|{ x }_{ i }-M| }{ \Sigma fi } \)

CBSE 11th Standard Maths Subject Limits and Derivatives HOT Questions 2 Mark Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  Evaluate \(\lim_ { h\rightarrow 0 } \frac { (a+h)^{ 2 }sin(a+h)-a^{ 2 }sin\quad a }{ h } \)

• 2)

  Evaluate \(\lim _{x \rightarrow \pi / 6} \frac{\cot ^{2} x-3}{\operatorname{cosec} x-2}\)

• 3)

  Evaluate \(\lim _{x \rightarrow 2} \frac{x^{2}-x \log x+2 \log x-4}{x-2}\)

• 4)

  Evaluate \(\lim_ { x\rightarrow 0 }{ lim } \frac { x\quad tan4x }{ 1-cos4x } \)

• 5)

  Evaluate \(\lim_ { x\rightarrow 0 }{ lim } \frac { sin\quad x-2sin\quad 3x+sin\quad 5x }{ x } \)

CBSE 11th Standard Maths Subject Trigonometric Functions HOT Questions 2 Mark Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  If m sin\(\theta \) = n sin (\(\theta \) + 2\(\alpha \)), then prove that tan (\(\theta \) + \(\alpha \)) cot \(\alpha \) = \(\frac { m+n }{ m-n } \)

• 2)

  In \(\triangle \)ABC, if a cos A=b cos B, show that the triangle is either isosceles or right angled.

• 3)

  In a ΔABC, \(\frac { { a }^{ 2 }-{ b }^{ 2 } }{ { a }^{ 2 }+{ b }^{ 2 } } =\frac { \sin { \left( A-B \right) } }{ \sin { A+B } } \) , prove that it is either a right angled or an isosceles triangle.

• 4)

  Prove that
  \(tan\quad \theta \quad tan\quad ({ 60 }^{ o }-\theta )tan\quad ({ 60 }^{ o }+\theta )\quad =\quad tan\quad 3\theta .\)

• 5)

  If cos \(\alpha \) +cos \(\beta\) = 0 = sin \(\alpha \) +sin\(\beta\), then find the value of cos2\(\alpha \)+cos 2\(\beta\)

CBSE 11th Standard Maths Subject Probability HOT Questions 2 Mark Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  The number lock of a suitcase has four wheels, each labelled with 10 digits.i.e., from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?

• 2)

  A single letter is selected at random from the word 'PROBABILITY', then find the probability that letter is vowel. 

• 3)

  Check whether the following probabilities P(A)=0.3, P(B)=0.65 and \(P(A\cup B)=7\) are consistently defined.

• 4)

  If  A and B are two events such that P(A) = \(\frac { 1 }{ 4 } \)  P(B) = \(\frac { 1 }{ 2 } \) and \(P(A\cap B)=\frac { 1 }{ 8 } \) .Then , find P ( not A and not B).

• 5)

  An experiiment consists of rolling a die and then tossing a coin, once, if the number on the die is even. If the number in the die is odd, then coin is tossed twice. Write the sample space for this experiment.

CBSE 11th Standard Maths Subject Probability HOT Questions 2 Mark Questions 2021 - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  A and B are two events that P(A) = 0.54, P(B) = 0.69 and \(P(A\cap B)\) = 0.35. Find \(P(A\cap B')\)

• 2)

  6 boys and 6 girls sit in a row randomly, Find tha probability that all 6 girls sit together

• 3)

  The number lock of a suitcase has four wheels, each labelled with 10 digits.i.e., from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?

• 4)

  A single letter is selected at random from the word 'PROBABILITY', then find the probability that letter is vowel. 

• 5)

  Check whether the following probabilities P(A)=0.3, P(B)=0.65 and \(P(A\cup B)=7\) are consistently defined.

CBSE 11th Standard Maths Subject Sets HOT Questions 2 Mark Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  If f: R \(\rightarrow\) R be defined as follows
  \(f(x)=\begin{cases} 1,\quad \quad x\quad \in \quad Q \\ -1,\quad x\quad \notin \quad Q \end{cases}\)
  Find  \(f\left( \frac { 1 }{ 2 } \right) ,f\left( \pi \right) \)

• 2)

  Show that n {P [P (P ( \(\phi\) ))]}=4

• 3)

  Let  B be a subset of an A and let P(A: B) = { X \(\in\) P(A): X \(\supset\) B}.
  If A = (1,2,3,4} and B ={1,2}. List all the members of the set P(A :B).

• 4)

  Let A = {1,2,3,4}, B= {1,2,3} and c= (2,4). Find all sets X satisfying each pair of conditions.
  X  \(\subseteq\) B and X  \(\nsubseteq\) C

• 5)

  Let A = {1,2,3,4}, B= {1,2,3} and c= (2,4). Find all sets X satisfying each pair of conditions
  X \(\subseteq\) B, X \(\neq\)B and X \(\nsubseteq\) C

CBSE 11th Standard Maths Subject Sets HOT Questions 2 Mark Questions 2021 - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  In a class of 60 students, 25 students play cricket, 20 students play Tennis and 10 students play both the gmes. Then, find the number of students who play neither games.

• 2)

  Let F₁ be the set of parallelograms, F₂ be the set of rectangles, F₃ be the set of rhombus and F₄ be the set of squares. Then, show that F₁ is equal to the union of all sets.

• 3)

  In a town of 840 persons read Hindi, 300 read English and 200 read both newspapers. Then, find the number of persons who read neither of the newspapers

• 4)

  Each students in a class of 40 students study atlest one of the subjects English,Mathematics and Economics. 16 students study English, 22 Economics and 26 Mathematics, 5 study English and Economics, 14 Mathematics and Economics and 2 English, Economics and Mathematics. Find the number of students who study English and Mathematics

CBSE 11th Standard Maths Subject Sets HOT Questions 1 Mark Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  In a class of 140 students, 60 play Football, 48 play Hockey and 75 play Cricket, 30 play Hockey and Cricket, 18 play Football and Cricket, 42 play Football and Hockey and 8 play all the three games.Use diagram to find, Students who play Football and Hockey,but not Cricket.

• 2)

  In a group of children, 35 play football out of which 20 play football only, 22 play hockey, 25 play cricket out of which 11 play cricket only. Out of these, 7play cricket and football but not hockey, 3 play football and hockey but not cricket and 12 play football and cricket both?How many play all the three games?

• 3)

  In a group of children, 35 play football out of which 20 play football only, 22 play hockey, 25 play cricket out of which 11 play cricket only. Out of these, 7play cricket and football but not hockey, 3 play football and hockey but not cricket and 12 play football and cricket both?How many play cricket and hockey but not football?

• 4)

  In a group of children, 35 play football out of which 20 play football only, 22 play hockey, 25 play cricket out of which 11 play cricket only. Out of these, 7play cricket and football but not hockey, 3 play football and hockey but not cricket and 12 play football and cricket both?How many play hockey only?

• 5)

  In a group of children, 35 play football out of which 20 play football only, 22 play hockey, 25 play cricket out of which 11 play cricket only. Out of these, 7play cricket and football but not hockey, 3 play football and hockey but not cricket and 12 play football and cricket both?What is the total number of children in the group?

CBSE 11th Standard Maths Subject Sets HOT Questions 1 Mark Questions 2021 - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  In a class of 140 students, 60 play Football, 48 play Hockey and 75 play Cricket, 30 play Hockey and Cricket, 18 play Football and Cricket, 42 play Football and Hockey and 8 play all the three games.Use diagram to find, Students who do not play any of these three games.

• 2)

  In a class of 140 students, 60 play Football, 48 play Hockey and 75 play Cricket, 30 play Hockey and Cricket, 18 play Football and Cricket, 42 play Football and Hockey and 8 play all the three games.Use diagram to find, Students who play only Cricket.

• 3)

  In a class of 140 students, 60 play Football, 48 play Hockey and 75 play Cricket, 30 play Hockey and Cricket, 18 play Football and Cricket, 42 play Football and Hockey and 8 play all the three games.Use diagram to find, Students who play Football and Hockey,but not Cricket.

• 4)

  In a group of children, 35 play football out of which 20 play football only, 22 play hockey, 25 play cricket out of which 11 play cricket only. Out of these, 7play cricket and football but not hockey, 3 play football and hockey but not cricket and 12 play football and cricket both?How many play all the three games?

• 5)

  In a group of children, 35 play football out of which 20 play football only, 22 play hockey, 25 play cricket out of which 11 play cricket only. Out of these, 7play cricket and football but not hockey, 3 play football and hockey but not cricket and 12 play football and cricket both?How many play cricket and hockey but not football?

CBSE 11th Standard Maths Subject HOT Questions 6 Mark Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  If f(x) = \(\begin{cases} 1+x,-1 \leq x<0 \\ x^{2}-1, \quad 0\end{cases}\)
  Then, find f(3), f(-2), f(0), \(f(\frac { 1 }{ 2 } )\), f(2-h) and f(-1+h), where h > 0 is very small.

• 2)

  Find the domain of the function \(f(x)=\frac { { x }^{ 2 }+2x+1 }{ { x }^{ 2 }-8x+12 } \)

• 3)

  If ⁿC_r-1 = 36. ⁿC_r = 84 and ⁿC_r+1 = 126 then find ^rC₂

• 4)

  Find  \(\lim _{x \rightarrow 0} f(x) \text { and } \lim _{x \rightarrow 1} f(x), \text { where }\)
  \(f(x)=\left\{\begin{array}{ll} 2 x+3, & x \leq 0 \\ 3(x+1), & x>0 \end{array}\right.\)

• 5)

  If 4digit numbers greater than 5000 are randomly formed the digits 0,1,3,5 and 7.What is the probability of forming a number divisible by 5 when the repetition of digits are not allowed?

CBSE 11th Standard Maths Subject HOT Questions 6 Mark Questions 2021 Part - II - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  Solve the equation z² =\(\overset { \_ }{ z } \) , where z = x + iy.

• 2)

  If ⁿC_r-1 = 36. ⁿC_r = 84 and ⁿC_r+1 = 126 then find ^rC₂

• 3)

  Find  \(\lim _{x \rightarrow 0} f(x) \text { and } \lim _{x \rightarrow 1} f(x), \text { where }\)
  \(f(x)=\left\{\begin{array}{ll} 2 x+3, & x \leq 0 \\ 3(x+1), & x>0 \end{array}\right.\)

• 4)

  A box contains 200 bolts and 70 nuts. It is given that 60% bolts and 40% nuts are rusted.Two objects are selected at random from the box.Find the probability that either both are bolts or both are rusted.

• 5)

  If 4-digit numbers greater than 5,000 are randomly formed from the digits 0, 1, 3, 5, and 7, what is the probability of forming a number divisible by 5 when, (i) the digits are repeated? (ii) the repetition of digits is not allowed?

CBSE 11th Standard Maths Subject HOT Questions 6 Mark Questions 2021 Part - I - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  Let A = {8, 11, 12, 15, 18, 23} and f is a function from \(A\rightarrow N\) such that f(x) = highest prime factor of x, find f  and its range. 

• 2)

  Find the real numbers x and y, if (x-iy) (3+5i) is the conjugate of -6 -24i.

• 3)

  If ⁿC_r-1 = 36. ⁿC_r = 84 and ⁿC_r+1 = 126 then find ^rC₂

• 4)

  If lines whose equation are y = m₁x + c₁ , y =m₂x + c₂ and y = m₃x + c₃ at a point then prove that m₁(c₂-c₃)+m₂(c₃-c₁)+m₃(c₁-c₂)=0

• 5)

  If 4-digit numbers greater than 5,000 are randomly formed from the digits 0, 1, 3, 5, and 7, what is the probability of forming a number divisible by 5 when, (i) the digits are repeated? (ii) the repetition of digits is not allowed?

CBSE 11th Standard Maths Subject HOT Questions 4 Mark Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  Out of 100 students, 15 passed in English, 12 passed in Mathematics, 8 in Science, 4 in English and Science, 4 in all the three.Find how many students passed in Mathematics and Science but not in English?

• 2)

  If \(cos\left( \alpha +\beta \right) =\frac { 4 }{ 5 } ,\quad sin(\alpha -\beta )=\frac { 5 }{ 13 } \) and \(\alpha , \beta \) lie between 0 and \(\frac { \pi }{ 4 } \) then prove that \(tan 2\alpha =\frac { 56 }{ 33 } .\)

• 3)

  If \(cos \left( \theta +\phi \right) = m\quad cos\quad \left( \theta -\phi \right) \)then find the value of \(\frac { 1-m }{ 1+m } cot\quad \phi .\)

• 4)

  If z is a complex number such that \(|z-1|=|z+1|\)  then show that Re(z) = 0.

• 5)

  If (1+i)(1+2i)(1+3i)...(1+ni)=(x+iy), then show that 2.5.10....(1+n²)=x²+y²

CBSE 11th Standard Maths Subject HOT Questions 4 Mark Questions 2021 Part - II - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  Out of 100 students, 15 passed in English, 12 passed in Mathematics, 8 in Science, 4 in English and Science, 4 in all the three.Find how many students passed in  English and Mathematics but not in Science?

• 2)

  If tan(πcosθ)=cot(πsinθ)  then prove that  \(cos\left( \theta -\frac { \pi }{ 4 } \right) =\pm \frac { 1 }{ 2\sqrt { 2 } } .\)

• 3)

  If \(cos \left( \theta +\phi \right) = m\quad cos\quad \left( \theta -\phi \right) \)then find the value of \(\frac { 1-m }{ 1+m } cot\quad \phi .\)

• 4)

  Find the modulus and argument of \(z=\frac { (1+i)^{ 13 } }{ (1+i)^{ 7 } }\)

• 5)

  If (1+i)(1+2i)(1+3i)...(1+ni)=(x+iy), then show that 2.5.10....(1+n²)=x²+y²

CBSE 11th Standard Maths Subject HOT Questions 4 Mark Questions 2021 Part - I - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  Out of 100 students, 15 passed in English, 12 passed in Mathematics, 8 in Science, 4 in English and Science, 4 in all the three.Find how many students passed in  English and Mathematics but not in Science?

• 2)

  Two trees A and B are on the same side of a river. From a point C in the river the distance of trees A and B are 250m and 300m, respectively of the angle C is 45⁰, find the distance between the trees.[use \(\sqrt { 2 } =1.44\)]

• 3)

  Find the value of x and y, if \(\frac { \left( 1+i \right) x-2i }{ 3+i } +\frac { \left( 2-3i \right) y+i }{ 3-i } =i\)

• 4)

  The area of a triangle is 5 sq units and two of its vertices are (2,1) and (3,-2).If third vertex is (x,y), where  y=x+3, then find the coordinates of the third vertex.

• 5)

  A box contains 4 red, 5 white and 6 black balls.A person draws 4 balls from the box at random.Find the probability of selecting atleast one ball of each colour.

CBSE 11th Standard Maths Subject HOT Questions 2 Mark Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  Each students in a class of 40 students study atlest one of the subjects English,Mathematics and Economics. 16 students study English, 22 Economics and 26 Mathematics, 5 study English and Economics, 14 Mathematics and Economics and 2 English, Economics and Mathematics. Find the number of students who study English and Mathematics

• 2)

  If f: R \(\rightarrow\) R be defined as follows
  \(f(x)=\begin{cases} 1,\quad \quad x\quad \in \quad Q \\ -1,\quad x\quad \notin \quad Q \end{cases}\)
  Find  \(f\left( \frac { 1 }{ 2 } \right) ,f\left( \pi \right) \)

• 3)

  Let A = {1,2,3,4}, B= {1,2,3} and c= (2,4). Find all sets X satisfying each pair of conditions
  X \(\subset\) A, X \(\subset\) B  and X \(\subset\) C.

• 4)

  Prove that
  \(tan\quad \theta \quad tan\quad ({ 60 }^{ o }-\theta )tan\quad ({ 60 }^{ o }+\theta )\quad =\quad tan\quad 3\theta .\)

• 5)

  How many 4-digit numbers are there with no digit repeated?

CBSE 11th Standard Maths Subject HOT Questions 2 Mark Questions 2021 Part - II - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  Let F₁ be the set of parallelograms, F₂ be the set of rectangles, F₃ be the set of rhombus and F₄ be the set of squares. Then, show that F₁ is equal to the union of all sets.

• 2)

  In each of the following, determine whether the statement is true or false. If it is true, prove it and if it is false, given an example
  If x \(\in\) P and P\(\nsubseteq\) Q then x \(\in\) Q

• 3)

  Let A = {1,2,3,4}, B= {1,2,3} and c= (2,4). Find all sets X satisfying each pair of conditions
  X \(\subseteq\) B, X \(\neq\)B and X \(\nsubseteq\) C

• 4)

  In a ΔABC, \(\frac { { a }^{ 2 }-{ b }^{ 2 } }{ { a }^{ 2 }+{ b }^{ 2 } } =\frac { \sin { \left( A-B \right) } }{ \sin { A+B } } \) , prove that it is either a right angled or an isosceles triangle.

• 5)

  How many 4-digit numbers are there with no digit repeated?

CBSE 11th Standard Maths Subject HOT Questions 2 Mark Questions 2021 Part - I - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  Show that n {P [P (P ( \(\phi\) ))]}=4

• 2)

  Let T = { \({x:\frac { x+5 }{ x-7 } -5=\frac { 4x-40 }{ 13-x }}\) }. Is T a singleton set? Justify your answer.

• 3)

  In \(\triangle \)ABC, if a cos A=b cos B, show that the triangle is either isosceles or right angled.

• 4)

  If cos \(\alpha \) +cos \(\beta\) = 0 = sin \(\alpha \) +sin\(\beta\), then find the value of cos2\(\alpha \)+cos 2\(\beta\)

• 5)

  Find the sum of n terms of the series whose nth term is given by
  (2n - 1)^{2 .}

CBSE 11th Standard Maths Subject Hot Questions 1 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  In a class of 140 students, 60 play Football, 48 play Hockey and 75 play Cricket, 30 play Hockey and Cricket, 18 play Football and Cricket, 42 play Football and Hockey and 8 play all the three games.Use diagram to find, Students who do not play any of these three games.

• 2)

  In a class of 140 students, 60 play Football, 48 play Hockey and 75 play Cricket, 30 play Hockey and Cricket, 18 play Football and Cricket, 42 play Football and Hockey and 8 play all the three games.Use diagram to find, Students who play only Cricket.

• 3)

  In a group of children, 35 play football out of which 20 play football only, 22 play hockey, 25 play cricket out of which 11 play cricket only. Out of these, 7play cricket and football but not hockey, 3 play football and hockey but not cricket and 12 play football and cricket both?How many play all the three games?

• 4)

  In a group of children, 35 play football out of which 20 play football only, 22 play hockey, 25 play cricket out of which 11 play cricket only. Out of these, 7play cricket and football but not hockey, 3 play football and hockey but not cricket and 12 play football and cricket both?How many play cricket and hockey but not football?

• 5)

  If A = {9,10,11,12,13} and \(f:A\rightarrow N\) be defined by f(n) = the highest prime factor of n, then find the range of f.

CBSE 11th Standard Maths Subject Hot Questions 1 Mark Questions 2021 - by Rupa Das - Bhubaneswar - May 29, 2021 - View & Read

• 1)

  In a class of 140 students, 60 play Football, 48 play Hockey and 75 play Cricket, 30 play Hockey and Cricket, 18 play Football and Cricket, 42 play Football and Hockey and 8 play all the three games.Use diagram to find, Students who do not play any of these three games.

• 2)

  In a class of 140 students, 60 play Football, 48 play Hockey and 75 play Cricket, 30 play Hockey and Cricket, 18 play Football and Cricket, 42 play Football and Hockey and 8 play all the three games.Use diagram to find, Students who play Football and Hockey,but not Cricket.

• 3)

  In a group of children, 35 play football out of which 20 play football only, 22 play hockey, 25 play cricket out of which 11 play cricket only. Out of these, 7play cricket and football but not hockey, 3 play football and hockey but not cricket and 12 play football and cricket both?How many play cricket and hockey but not football?

• 4)

  In a group of children, 35 play football out of which 20 play football only, 22 play hockey, 25 play cricket out of which 11 play cricket only. Out of these, 7play cricket and football but not hockey, 3 play football and hockey but not cricket and 12 play football and cricket both?How many play hockey only?

• 5)

  If A = {9,10,11,12,13} and \(f:A\rightarrow N\) be defined by f(n) = the highest prime factor of n, then find the range of f.

CBSE 11th Standard Maths Subject Probability Ncert Exemplar 6 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  A team of medical students doing their internship have to assist during surgeries at a city hospital.The probabilities of surgeries rated as very complex,routine,simple rated as very complex,complex,complex, routine,simple or very simple respectively 0.15,0.20,0.31,0.26 and 0.08.Find the probabilities that a particular surgery will be rated
  routine or complex

• 2)

  A team of medical students doing their internship have to assist during surgeries at a city hospital.The probabilities of surgeries rated as very complex,routine,simple rated as very complex,complex,complex, routine,simple or very simple respectively 0.15,0.20,0.31,0.26 and 0.08.Find the probabilities that a particular surgery will be rated
  routine or simple

• 3)

  If A and B are mutually exclusive events, such that P(A)=0.35 and P(B)=0.45, then find P(B')

• 4)

  If A and B are mutually exclusive events, such that P(A)=0.35 and P(B)=0.45, then find P(A\(\cup \)B)

• 5)

  If A and B are mutually exclusive events, such that P(A)=0.35 and P(B)=0.45, then find P(A\(\cap \)B)

CBSE 11th Standard Maths Subject Probability Ncert Exemplar 6 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  A team of medical students doing their internship have to assist during surgeries at a city hospital.The probabilities of surgeries rated as very complex,routine,simple rated as very complex,complex,complex, routine,simple or very simple respectively 0.15,0.20,0.31,0.26 and 0.08.Find the probabilities that a particular surgery will be rated
  neither very complex nor very simple

• 2)

  A team of medical students doing their internship have to assist during surgeries at a city hospital.The probabilities of surgeries rated as very complex,routine,simple rated as very complex,complex,complex, routine,simple or very simple respectively 0.15,0.20,0.31,0.26 and 0.08.Find the probabilities that a particular surgery will be rated
  routine or complex

• 3)

  One of the four persons John, Rita, Aslam or Gurpreet will be promoted next month.Consequently, the sample space consists of four elementary outcomes S={Johnpromoted, Rita promoted, Gurpreet promoted} You are told that the chances of John's promotion is same as that of Gurpreet, Rita's Chances of promotion are twice as likely as Johns.Aslam's chances are four times that of John.
  Determine P(John promoted)  P(Rita promoted);  P(Aslam promoted)
  P(Gurpreet promoted)

• 4)

  One of the four persons John, Rita, Aslam or Gurpreet will be promoted next month.Consequently, the sample space consists of four elementary outcomes S={Johnpromoted, Rita promoted, Gurpreet promoted} You are told that the chances of John's promotion is same as that of Gurpreet, Rita's Chances of promotion are twice as likely as Johns.Aslam's chances are four times that of John.
  If A={John promoted or Gurpreet promoted}, then find P(A)

• 5)

  If A and B are mutually exclusive events, such that P(A)=0.35 and P(B)=0.45, then find P(A\(\cap \)B)

CBSE 11th Standard Maths Subject Probability Ncert Exemplar 4 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  One card is drawn from a well-shuffled deck of 52 cards.Calculate the probability that the card will be
  an ace

• 2)

  One card is drawn from a well-shuffled deck of 52 cards.Calculate the probability that the card will be
  a black card

• 3)

  One card is drawn from a well-shuffled deck of 52 cards.Calculate the probability that the card will be
  not a black card

• 4)

  Suppose an integer from 1 through 1000 is chosen at random.Find the probability that the integer is a multiple of 2 or a multiple of 9.

• 5)

  Three squaresof chess board are selected 2 squares of ane colour and other of a different colour.

CBSE 11th Standard Maths Subject Probability Ncert Exemplar 4 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  One card is drawn from a well-shuffled deck of 52 cards.Calculate the probability that the card will be
  an ace

• 2)

  One card is drawn from a well-shuffled deck of 52 cards.Calculate the probability that the card will be
  a black card

• 3)

  One card is drawn from a well-shuffled deck of 52 cards.Calculate the probability that the card will be
  not an ace

• 4)

  Suppose an integer from 1 through 1000 is chosen at random.Find the probability that the integer is a multiple of 2 or a multiple of 9.

• 5)

  A die is rolled in such a way that each odd number is twice as likely to occur as likely to occur as each even number.Find P(G), where G is the event that a number greater than 3 occurs on a single roll of the die.

CBSE 11th Standard Maths Subject Probability Ncert Exemplar 2 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  Suppose that each child born is equally likely to be a boy or a girl. Consider a family with exactly three children.
  List the eight elements in the sample space whose outcomes are all possible genders of the three children.

• 2)

  A and B are two events that P(A) = 0.54, P(B) = 0.69 and \(P(A\cap B)\) = 0.35. Find \(P(B\cap A')\)

• 3)

  The probability that at least one of the events A and B occurs is 0.6. If A and B occurs simultaneously with probability 0.2, then find \(P(\overline { A } )+P(\overline { B } ).\)

• 4)

  One urn contains two black balls (labelled B₁ and B₂) and one white (W) ball. A second urn contains one black (B) ball and two white balls (labelled W₁ and W₂ ). Suppose the following experiment is performed.
  One of the two urns is chosen at random. Next , a ball is randomly chosen from the urn. Then, a second ball is chosen at random from the same urn without replacing the first ball. What is the probability that two balls of opposite colour are chosen?

• 5)

  If A and B are two events having \(P(A\cup B)=\frac { 1 }{ 2 } \ and\ P(\overline { A } )=\frac { 2 }{ 3 } ,\ then\ find\ P(\overline { A } \cap B).\)

CBSE 11th Standard Maths Subject Probability Ncert Exemplar 2 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  Suppose that each child born is equally likely to be a boy or a girl. Consider a family with exactly three children.
  List the eight elements in the sample space whose outcomes are all possible genders of the three children.

• 2)

  Suppose that each child born is equally likely to be a boy or a girl. Consider a family with exactly three children.
  Write each of the following events as a set and find its probability.
  (a) The event that exactly one child is a girl.
  (b) The event that atleast two children are girls.
  (c) The event that no child is a girl.

• 3)

  The probability that at least one of the events A and B occurs is 0.6. If A and B occurs simultaneously with probability 0.2, then find \(P(\overline { A } )+P(\overline { B } ).\)

• 4)

  One urn contains two black balls (labelled B₁ and B₂) and one white (W) ball. A second urn contains one black (B) ball and two white balls (labelled W₁ and W₂ ). Suppose the following experiment is performed.
  One of the two urns is chosen at random. Next , a ball is randomly chosen from the urn. Then, a second ball is chosen at random from the same urn without replacing the first ball. What is the probability that two balls of opposite colour are chosen?

• 5)

  If A and B are two events having \(P(A\cup B)=\frac { 1 }{ 2 } \ and\ P(\overline { A } )=\frac { 2 }{ 3 } ,\ then\ find\ P(\overline { A } \cap B).\)

CBSE 11th Standard Maths Subject Mathematical Reasoning Ncert Exemplar 2 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  Rewrite the following statements in the form of conditional statements
  Mohan will be a good student if he studies hard.

• 2)

  Rewrite the following statements in the form of conditional statements.
  Ramesh will get dessert only if he eats his dinner.

• 3)

  Rewrite the following statements in the form of conditional statements
  When you sing, my ears hurt.

• 4)

  Rewrite the following statements in the form of conditional statements
  A necessary condition for Indian team to win a cricket match is that the selection committee selects an all-rounder.

• 5)

  Rewrite the following statements in the form of conditional statements
  A sufficient condition for Tara to visit New Delhi is that she goes to the Rashtrapati Bhawan.

CBSE 11th Standard Maths Subject Mathematical Reasoning Ncert Exemplar 2 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  Rewrite the following statements in the form of conditional statements
  Mohan will be a good student if he studies hard.

• 2)

  Rewrite the following statements in the form of conditional statements.
  Ramesh will get dessert only if he eats his dinner.

• 3)

  Rewrite the following statements in the form of conditional statements
  A sufficient condition for Tara to visit New Delhi is that she goes to the Rashtrapati Bhawan.

• 4)

  Write the converse of the following statements.
  If x < y, then x + 5 < y+ 5.

• 5)

  Write the converse of the following statements.
  If ABC is an equilateral triangle, then ABC is an isosceles triangle.

CBSE 11th Standard Maths Subject Mathematical Reasoning Ncert Exemplar 1 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  Rewrite the following statements in the form of conditional statement.
  The square of an odd number is odd.

• 2)

  Rewrite the following statements in the form of conditional statement.
  The unit digit of an integer is 0 or 5, if it is divisible by 5.

• 3)

  Rewrite the following statements in the form of conditional statement.
  The square of a prime number is not prime.

• 4)

  Write down the contrapositive of the following statements.
  If n is a natural number, then n is an integer.

• 5)

  Write down the contrapositive of the following statements.
  If x and y are negative integers, then xy is positive.

CBSE 11th Standard Maths Subject Mathematical Reasoning Ncert Exemplar 1 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  Rewrite the following statements in the form of conditional statement.
  The unit digit of an integer is 0 or 5, if it is divisible by 5.

• 2)

  Rewrite the following statements in the form of conditional statement.
  The square of a prime number is not prime.

• 3)

  Write down the contrapositive of the following statements.
  If n is a natural number, then n is an integer.

• 4)

  Write down the contrapositive of the following statements.
  If x and y are negative integers, then xy is positive.

• 5)

  Write down the contrapositive of the following statements.
  If natural number n is divisible by 6, then n is divisible by 2 and 3.

CBSE 11th Standard Maths Subject Limits and Derivatives Ncert Exemplar 2 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  If \(f(x)=\left\{\begin{array}{l} x+2, x \leq-1 \\ c x^{2}, x>-1 \end{array}\right.\) then find c when \(\lim _{ x\rightarrow -1 }{ f(x) } \) exists.

• 2)

  Show that \(\lim _{ x\rightarrow 4 }{ \frac { |x-4| }{ x-4 } } \)does not exist.

• 3)

  Evaluate \(\lim _{x \rightarrow \pi / 6} \frac{\sqrt{3} \sin x-\cos x}{x-\frac{\pi}{6}}\)

• 4)

  Evaluate \(\lim _{x \rightarrow \pi / 6} \frac{2 \sin ^{2} x+\sin x-1}{2 \sin ^{2} x-3 \sin x+1}\) by using factorization method

• 5)

  Find the derivative of the following functions,
  \(\frac { sinx+cosx }{ sinx-cosx } \)
  First, consider the given function as f(x). Then, use quotient rule to find the required derivative.

CBSE 11th Standard Maths Subject Limits and Derivatives Ncert Exemplar 2 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  Show that \(\lim _{ x\rightarrow 4 }{ \frac { |x-4| }{ x-4 } } \)does not exist.

• 2)

  If the function f(x) satisfies \(\lim _{ x\rightarrow 1 }{ \frac { f(x)-2 }{ { x }^{ 2 }-1 } } =\pi \), then evaluate \(\lim _{ x\rightarrow 1 }{ f(x) } .\) Use the theorem \(\lim _{ x\rightarrow a }{ \frac { f(x) }{ g(x) } } =\frac { \lim _{ x\rightarrow a }{ f(x) } }{ \lim _{ x\rightarrow a }{ g(x) } } \)and simplify it.
   

• 3)

  Evaluate \(\lim _{x \rightarrow \pi / 6} \frac{2 \sin ^{2} x+\sin x-1}{2 \sin ^{2} x-3 \sin x+1}\) by using factorization method

• 4)

  Evaluate \(\lim _{x \rightarrow \pi / 6} \frac{\cot ^{2} x-3}{\operatorname{cosec} x-2}\)

• 5)

  If \(y=\sqrt { x } +\frac { 1 }{ \sqrt { x } } \) then find \(\frac { dy }{ dx } at\quad x=1\)

CBSE 11th Standard Maths Subject Limits and Derivatives Ncert Exemplar 1 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  Find the derivative of 2x⁴ + x

• 2)

  Find the derivative of the following functions.
  \(\frac { 3x+4 }{ 5x^{ 2 }-7x+9 } \)

• 3)

  Find the derivative of the following functions.
  cosecx cotx

• 4)

  Find the derivative of the following functions.
  (secx-1)(secx+1)

• 5)

  Find the derivative of the following functions.
  (ax²+cotx)(p+qcosx)

CBSE 11th Standard Maths Subject Limits and Derivatives Ncert Exemplar 1 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  Find the derivative of 2x⁴ + x

• 2)

  Find the derivative of the following functions.
  \(\frac { 3x+4 }{ 5x^{ 2 }-7x+9 } \)

• 3)

  Find the derivative of the following functions.
  cosecx cotx

• 4)

  Find the derivative of the following functions.
  (secx-1)(secx+1)

• 5)

  Find the derivative of the following functions.
  (ax²+cotx)(p+qcosx)

CBSE 11th Standard Maths Subject Introduction to Three Dimensional Geometry Ncert Exemplar 2 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  Let L,M,N be the feet of the perpendiculars drawn from a point P(3,4,5) on the X,Y and Z-axes respectively.Find the coordinates of L, M and N.

• 2)

  Find the centroid of a triangle, the mid-point of whose sides are D(1, 2, -3), E (3, 0, 1) and F(-1, 1, -4).

• 3)

  Find the point on X-axis which is equidistant from the points A(3,2,2) and B(5,5,4)

• 4)

  Find the coordinates of a point equidistant from the four points O(0,0,0), A(l,0,0), B(0,m,0), and C(0,0,n)

• 5)

  Let L,M,N be the feet of the perpendicules drawn from the point P (3,4,5) on the XY,YZ and ZX-planes, respectively. Find the distance of these points L,M,N from the point P.

CBSE 11th Standard Maths Subject Introduction to Three Dimensional Geometry Ncert Exemplar 2 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  Let L,M,N be the feet of the perpendiculars drawn from a point P(3,4,5) on the X,Y and Z-axes respectively.Find the coordinates of L, M and N.

• 2)

  Find the centroid of a triangle, the mid-point of whose sides are D(1, 2, -3), E (3, 0, 1) and F(-1, 1, -4).

• 3)

  Find the point on X-axis which is equidistant from the points A(3,2,2) and B(5,5,4)

• 4)

  Find the coordinates of a point equidistant from the four points O(0,0,0), A(l,0,0), B(0,m,0), and C(0,0,n)

• 5)

  Let L,M,N be the feet of the perpendicules drawn from the point P (3,4,5) on the XY,YZ and ZX-planes, respectively. Find the distance of these points L,M,N from the point P.

CBSE 11th Standard Maths Subject Introduction to Three Dimensional Geometry Ncert Exemplar 1 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  Name the octant in which the point lies (4,-2,-5)

• 2)

  Name the octant in which the point lies (4,2,-5)

• 3)

  Name the octant in which the point lies (-3,-1,6)

• 4)

  L is the foot of the perpendicular drawn from a point P(6,7,8) on the XY-plane.What are the coordinates of point L?

• 5)

  Find the distance from the origin to (6,6,7).

CBSE 11th Standard Maths Subject Introduction to Three Dimensional Geometry Ncert Exemplar 1 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  Name the octant in which the point lies (4,-2,-5)

• 2)

  Name the octant in which the point lies (4,2,-5)

• 3)

  Name the octant in which the point lies (-3,-1,6)

• 4)

  L is the foot of the perpendicular drawn from a point P(6,7,8) on the XY-plane.What are the coordinates of point L?

• 5)

  Find the distance from the origin to (6,6,7).

CBSE 11th Standard Maths Subject Straight Lines Ncert Exemplar 2 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  A variable line passes through a fixed point P. The algebraic sum of the perpendiculars drawn from the points (2, 0), (0, 2) and (1, 1) on the line is zero. Find the coordinates of the point P.

• 2)

  If p is the length of perpendicular from the origin on the line \(\frac { x }{ a } +\frac { y }{ b } =1\) and a² , p² and b² are in AP, then show that a⁴ + b⁴ = 0. 

• 3)

  If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes is (3, 2), then find the equation of the line.

• 4)

  Find the equation of line passing through the point \((a\ { cos }^{ 3 }\theta ,\ a \ sin^{ 3 } \ \theta )\) and perpendicular to the line \(x \sec \theta+y \operatorname{cosec} \theta=a\) .

• 5)

  A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.

CBSE 11th Standard Maths Subject Straight Lines Ncert Exemplar 2 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  Find the locus of a point which moves in such a way that the square of its distance from the point (3, -2) is numerically equal to its distance from the line 5x - 12y = 13.

• 2)

  A variable line passes through a fixed point P. The algebraic sum of the perpendiculars drawn from the points (2, 0), (0, 2) and (1, 1) on the line is zero. Find the coordinates of the point P.

• 3)

  If p is the length of perpendicular from the origin on the line \(\frac { x }{ a } +\frac { y }{ b } =1\) and a² , p² and b² are in AP, then show that a⁴ + b⁴ = 0. 

• 4)

  Find the equation of line passing through the point \((a\ { cos }^{ 3 }\theta ,\ a \ sin^{ 3 } \ \theta )\) and perpendicular to the line \(x \sec \theta+y \operatorname{cosec} \theta=a\) .

• 5)

  A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.

CBSE 11th Standard Maths Subject Straight Lines Ncert Exemplar 1 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  For specifying a straight line, how many geometrical parameters should be known?

• 2)

  Find the equation of a line, which passes through the point (2, 3) and makes an angle of 30\(^{o}\) with the positive direction of X - axis.

• 3)

  A straight line moves so that the sum of the reciprocals of its intercepts made on axes is constant. Show that the line passes through a fixed point.

• 4)

  Find the equation of the line passing through the point (5, 2) and perpendicular to the line joining the points (2, 3) and (3, - 1).

• 5)

  Find the distance of the point P(1, -3) from the line 2y - 3x = 4.

CBSE 11th Standard Maths Subject Straight Lines Ncert Exemplar 1 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  Find the equation of a line, which passes through the point (2, 3) and makes an angle of 30\(^{o}\) with the positive direction of X - axis.

• 2)

  A straight line moves so that the sum of the reciprocals of its intercepts made on axes is constant. Show that the line passes through a fixed point.

• 3)

  Find the equation of the line passing through the point (5, 2) and perpendicular to the line joining the points (2, 3) and (3, - 1).

• 4)

  Find the distance of the point P(1, -3) from the line 2y - 3x = 4.

• 5)

  Find the distance between the following pair of lines.
  3x + 4y = 9 and 6x + 8y = 15

CBSE 11th Standard Maths Subject Sequences and Series Ncert Exemplar 2 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  If 9 times the  9th term of an AP is equal to 13 times the 13th term, then find the 22nd term of the AP.

• 2)

  The p th term of an AP is a and q th term is b. Prove that sum of its (p+q) th term is \(\frac { p+q }{ 2 } \left[ a+b+\frac { a-b }{ p-q } \right] .\)

• 3)

  (i) If a, b, c, d are four distinct positive quantities in AP, then show that bc > ad.

• 4)

  (ii) If a, b, c, d are four distinct positive quantities in GP then show that a + d > b + c.

• 5)

  At the end of each yearthe value of a certain machine has depreciated by 20% of its value at the begining of that year. If its initial value was Rs.1250, then find the value at the end of 5 yrs.

CBSE 11th Standard Maths Subject Sequences and Series Ncert Exemplar 2 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  If 9 times the  9th term of an AP is equal to 13 times the 13th term, then find the 22nd term of the AP.

• 2)

  The p th term of an AP is a and q th term is b. Prove that sum of its (p+q) th term is \(\frac { p+q }{ 2 } \left[ a+b+\frac { a-b }{ p-q } \right] .\)

• 3)

  (i) If a, b, c, d are four distinct positive quantities in AP, then show that bc > ad.

• 4)

  (ii) If a, b, c, d are four distinct positive quantities in GP then show that a + d > b + c.

• 5)

  At the end of each yearthe value of a certain machine has depreciated by 20% of its value at the begining of that year. If its initial value was Rs.1250, then find the value at the end of 5 yrs.

CBSE 11th Standard Maths Subject Binomial Theorem Ncert Exemplar 2 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  Find n in the binomial\({ \left( \sqrt [ 3 ]{ 2 } +\frac { 1 }{ \sqrt [ 3 ]{ 3 } } \right) }^{ n }\), if the ratio of 7th term from the beginning to the 7th term from the end is\(\frac { 1 }{ 6 } \).

• 2)

  Find the ratio of coefficient of xⁿ in the expansion of (1 + x)²ⁿ and (1+x)^2n-1.

• 3)

  Evaluate\(\left( { x }^{ 2 }-\sqrt { 1-{ x }^{ 2 } } \right) ^{ 4 }+\left( { x }^{ 2 }+\sqrt { 1-{ x }^{ 2 } } \right) ^{ 4 }\)

• 4)

  Find the coefficient of x⁴ in the expansion of (1+x+x²+x³)¹¹

• 5)

  If \({ 25 }^{ 15 }\) is divided by 13, then find the remainder.

CBSE 11th Standard Maths Subject Binomial Theorem Ncert Exemplar 2 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  Find n in the binomial\({ \left( \sqrt [ 3 ]{ 2 } +\frac { 1 }{ \sqrt [ 3 ]{ 3 } } \right) }^{ n }\), if the ratio of 7th term from the beginning to the 7th term from the end is\(\frac { 1 }{ 6 } \).

• 2)

  Find the ratio of coefficient of xⁿ in the expansion of (1 + x)²ⁿ and (1+x)^2n-1.

• 3)

  Evaluate\(\left( { x }^{ 2 }-\sqrt { 1-{ x }^{ 2 } } \right) ^{ 4 }+\left( { x }^{ 2 }+\sqrt { 1-{ x }^{ 2 } } \right) ^{ 4 }\)

• 4)

  Find the coefficient of x⁴ in the expansion of (1+x+x²+x³)¹¹

• 5)

  If \({ 25 }^{ 15 }\) is divided by 13, then find the remainder.

CBSE 11th Standard Maths Subject Permutation and Combination Ncert Exemplar 6 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  Find the number of combinations , whwn some or all of n objects are taken at a time.

• 2)

  How many automobile lincene plates can be made, if each plate contains two different letters followed by three different digits?

• 3)

  A student has to answer 10 questiion choosing atleast 4 from each part A and B . If there are 6 question in part A and 7 question from part B, in how many ways can the student choose 10 queations?

• 4)

  Find the number of arrangements of the letters of the word 'INDEPENDENCE' . In how many of these arrangements
  (i) do the words start with P?
  (ii) do all the vowels always occur together?
  (iii) do all the vowels never occur together ?
  (iv) do the words begin with I and end in P?

• 5)

  Using the digits 1,2,3,4,5,6,7,a number of different digit is formed . Find how many numbers are formed ? Further , Find how many of these are
  (i) exactly divisible by 2 ?
  (ii) exactly divisible by 25 ?
  (iii) exactly divisible by 4 ?

CBSE 11th Standard Maths Subject Permutation and Combination Ncert Exemplar 6 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  Three balls are drawn from a bag containing 5 red 4 White and 3 black balls , find the number of ways in which this can be done , if alteast 2 balls are red.

• 2)

  Find the number of combinations , whwn some or all of n objects are taken at a time.

• 3)

  How many automobile lincene plates can be made, if each plate contains two different letters followed by three different digits?

• 4)

  A student has to answer 10 questiion choosing atleast 4 from each part A and B . If there are 6 question in part A and 7 question from part B, in how many ways can the student choose 10 queations?

• 5)

  Using the digits 1,2,3,4,5,6,7,a number of different digit is formed . Find how many numbers are formed ? Further , Find how many of these are
  (i) exactly divisible by 2 ?
  (ii) exactly divisible by 25 ?
  (iii) exactly divisible by 4 ?

CBSE 11th Standard Maths Subject Permutation and Combination Ncert Exemplar 2 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  How many 2 digit even numbers can be formed from the digits 1, 2, 3, 4, 5 if the digits can be repeated?

• 2)

  In how many ways can 5 children be arranged in a line such that
  (i) two particular children of them are always together?
  (ii)  two particular children of them are never together?

• 3)

  In how many ways 3 Mathematics books, 4 History books, 3 Chemistry books and 2 Biology books can be arranged on a shelf so that all books of the same subjects are together?

• 4)

  Find the number of ways in which 5 boys and 5 girls be seated in a row, so that no two girls sit together.

• 5)

  Find the number of ways in which 5 boys and 5 girls be seated in a row, so that boys and girls sit alternatively.

CBSE 11th Standard Maths Subject Permutation and Combination Ncert Exemplar 2 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  How many 2 digit even numbers can be formed from the digits 1, 2, 3, 4, 5 if the digits can be repeated?

• 2)

  In how many ways can 5 children be arranged in a line such that
  (i) two particular children of them are always together?
  (ii)  two particular children of them are never together?

• 3)

  Find the number of ways in which 5 boys and 5 girls be seated in a row, so that boys and girls sit alternatively.

• 4)

  Find the number of different words that can be formed from the letters of the word 'INTERMEDIATE' such that two vowels never come together

• 5)

  Find the number of 5-digit telephone numbers having atleast one of their digits repeated.

CBSE 11th Standard Maths Subject Linear Inequalities Ncert Exemplar 4 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  Solve for  \(x,\frac { 4 }{ x+1 } \le 3\le \frac { 6 }{ x+1' } x>0\)

• 2)

  The water acidity in a pool is considered normal when the average pH reading of three daily measurements is between 8.2 and 8.5. If the two pH readings are 8.48 and 8.35, find the range of pH value for the third reading that will result in the acidity level being normal.

• 3)

  The cost and revenue functions of products given by C(X)=20+4000 and R(X)=60+2000 respectively, where x is the number of items produced and sold. How many items must be sold to realise some profit?

• 4)

  The longest side of a triangle is twice the shortest side and the third side is 2cm longer than the shortest side. If the perimeter of the triangle is more than 166cm then find the minimum length of the shortest side.

• 5)

  Find the linear inequalities for which the shaded region on the given figure is the solution set.
  

CBSE 11th Standard Maths Subject Linear Inequalities Ncert Exemplar 4 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  Solve for  \(x,\frac { 4 }{ x+1 } \le 3\le \frac { 6 }{ x+1' } x>0\)

• 2)

  The water acidity in a pool is considered normal when the average pH reading of three daily measurements is between 8.2 and 8.5. If the two pH readings are 8.48 and 8.35, find the range of pH value for the third reading that will result in the acidity level being normal.

• 3)

  The cost and revenue functions of products given by C(X)=20+4000 and R(X)=60+2000 respectively, where x is the number of items produced and sold. How many items must be sold to realise some profit?

• 4)

  The longest side of a triangle is twice the shortest side and the third side is 2cm longer than the shortest side. If the perimeter of the triangle is more than 166cm then find the minimum length of the shortest side.

• 5)

  Find the linear inequalities for which the shaded region on the given figure is the solution set.
  

CBSE 11th Standard Maths Subject Linear Inequalities Ncert Exemplar 2 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  Solve \(|x-1|\le 2\).

• 2)

  Solve \(|x+3|\ge 10\).

• 3)

  Solve \(|3x-7|>2\).

• 4)

  Solve \(|3-4x|\ge 9\).

• 5)

  A solution of 9% acid is to be diluted by adding 3%acid solution to it. The resulting mixture is to be more than 5%but less than 7% acid. If there is 460 litres of the 9% solution, how many litres of 3%solution will have to be added?

CBSE 11th Standard Maths Subject Linear Inequalities Ncert Exemplar 2 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  Solve \(|x-1|\le 2\).

• 2)

  Solve \(|x+3|\ge 10\).

• 3)

  Solve \(|3x-7|>2\).

• 4)

  Solve \(|3-4x|\ge 9\).

• 5)

  A solution of 9% acid is to be diluted by adding 3%acid solution to it. The resulting mixture is to be more than 5%but less than 7% acid. If there is 460 litres of the 9% solution, how many litres of 3%solution will have to be added?

CBSE 11th Standard Maths Subject Complex Numbers and Quadratic Equations Ncert Exemplar 4 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  What is the value of \(\frac { { i }^{ 4x+1 }-{ i }^{ 4x-1 } }{ 2 } ?\)

• 2)

  Find the real value of 'a' for which 3i³- 2ai²+(1-a)i + 5 is real.

• 3)

  If f(z) = \(\frac { 7-z }{ 1-{ z }^{ 2 } } \) where z= 1 + 2i , then find \(|f(z)|\)

• 4)

  If \(\frac { z-1 }{ z+1 } \)  is a purely imaginary number \((z\neq -1)\) then find the value of \(|z|\)

• 5)

  Find \(​​\left| (1+i)\frac { (2+i) }{ (3+i) } \right| \)

CBSE 11th Standard Maths Subject Complex Numbers and Quadratic Equations Ncert Exemplar 4 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  Find the real value of 'a' for which 3i³- 2ai²+(1-a)i + 5 is real.

• 2)

  If f(z) = \(\frac { 7-z }{ 1-{ z }^{ 2 } } \) where z= 1 + 2i , then find \(|f(z)|\)

• 3)

  If \(\frac { z-1 }{ z+1 } \)  is a purely imaginary number \((z\neq -1)\) then find the value of \(|z|\)

• 4)

  Find \(​​\left| (1+i)\frac { (2+i) }{ (3+i) } \right| \)

• 5)

  Find the value of \({ 2x }^{ 4 }+{ 5x }^{ 3 }+{ 7x }^{ 2 }-x+41,when\ x=-2-\sqrt { 3i } \)

CBSE 11th Standard Maths Subject Complex Numbers and Quadratic Equations Ncert Exemplar 2 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  If (1 + i)z = (1 - i)\(\overline { z }\) , then show that z = \(-i\overline { z } \).

• 2)

  Find the conjugate of the complex number \(\frac { 1-i }{ 1+i }\)

• 3)

  Evaluate \({ \left( 1+i \right) }^{ 6 }+{ \left( 1-i \right) }^{ 3 }\) . 

• 4)

  If \({ \left( x+iy \right) }^{ 1/3 }\) = a + ib, where x, y, a, b \(\epsilon \) R, then show that\(\frac { x }{ a } -\frac { y }{ b } =-2\left( { a }^{ 2 }+{ b }^{ 2 } \right) \).Firstly, use identity \({ \left( a+b \right) }^{ 3 }={ a }^{ 3 }+{ 3a }^{ 2 }b+{ 3ab }^{ 2 }+{ b }^{ 3 }\)and then equate the coefficients of real and imaginary parts.

• 5)

  Find the real value of \(\theta \) for which the expression \(\frac { 1+icos\theta }{ 1-2icos\theta } \) is a real number.

CBSE 11th Standard Maths Subject Complex Numbers and Quadratic Equations Ncert Exemplar 2 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 27, 2021 - View & Read

• 1)

  If (1 + i)z = (1 - i)\(\overline { z }\) , then show that z = \(-i\overline { z } \).

• 2)

  Find the conjugate of the complex number \(\frac { 1-i }{ 1+i }\)

• 3)

  Evaluate \({ \left( 1+i \right) }^{ 6 }+{ \left( 1-i \right) }^{ 3 }\) . 

• 4)

  If \({ \left( x+iy \right) }^{ 1/3 }\) = a + ib, where x, y, a, b \(\epsilon \) R, then show that\(\frac { x }{ a } -\frac { y }{ b } =-2\left( { a }^{ 2 }+{ b }^{ 2 } \right) \).Firstly, use identity \({ \left( a+b \right) }^{ 3 }={ a }^{ 3 }+{ 3a }^{ 2 }b+{ 3ab }^{ 2 }+{ b }^{ 3 }\)and then equate the coefficients of real and imaginary parts.

• 5)

  Find the real value of \(\theta \) for which the expression \(\frac { 1+icos\theta }{ 1-2icos\theta } \) is a real number.

CBSE 11th Standard Maths Subject Principle of Mathematical Induction Ncert Exemplar 2 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 26, 2021 - View & Read

• 1)

  If p(n): "49ⁿ +16ⁿ +k is divisible by 64 for n\(\epsilon \)N" is true, then find the least negative integral value of K.

• 2)

  If P(n): "3.5²ⁿ⁺¹ +2³ⁿ⁺¹ is divisible by  for all n \(\in\) N" is true, then find the value of \(\lambda \).

• 3)

  Prove that \(2n+1 <{ 2 }^{ n }\),for all natural numbers \(n(n\ge 3)\) by using principle of mathematical induction.

• 4)

  Prove that 1+2+2²+...+2ⁿ = 2ⁿ⁺¹ 1 for all natural numbers n.

• 5)

  Prove that \(\sum _{ t=1 }^{ n-1 }{ t(t+1) } =\frac { n(n-1)(n+1) }{ 3 } \) , for all natural numbers \(n\ge 2\)

CBSE 11th Standard Maths Subject Principle of Mathematical Induction Ncert Exemplar 2 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 26, 2021 - View & Read

• 1)

  If p(n): "49ⁿ +16ⁿ +k is divisible by 64 for n\(\epsilon \)N" is true, then find the least negative integral value of K.

• 2)

  If P(n): "3.5²ⁿ⁺¹ +2³ⁿ⁺¹ is divisible by  for all n \(\in\) N" is true, then find the value of \(\lambda \).

• 3)

  Prove that \(2n+1 <{ 2 }^{ n }\),for all natural numbers \(n(n\ge 3)\) by using principle of mathematical induction.

• 4)

  Prove that 1+2+2²+...+2ⁿ = 2ⁿ⁺¹ 1 for all natural numbers n.

• 5)

  Prove that \(\sum _{ t=1 }^{ n-1 }{ t(t+1) } =\frac { n(n-1)(n+1) }{ 3 } \) , for all natural numbers \(n\ge 2\)

CBSE 11th Standard Maths Subject Trigonometric Functions Ncert Exemplar 2 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 26, 2021 - View & Read

• 1)

  Prove that \(sin2x+2sin4x+sin6x=4cos^{ 2 }x.sin4x.\)

• 2)

  If \(\frac { sin(x+y) }{ sin(x-y) } =\frac { a+b }{ a-b } \) then show that \(\frac { sin(x+y) }{ sin(x-y) } =\frac { a+b }{ a-b } \)

• 3)

  Prove that \({ sec }^{ 2 }\theta +{ cosec }^{ 2 }\theta \ge 4\).

• 4)

  Prove that \(cos\frac { 2\pi }{ 15 } cos\frac { 4\pi }{ 15 } cos\frac { 8\pi }{ 15 } cos\frac { 16\pi }{ 15 } =\frac { 1 }{ 16 } \)

• 5)

  Find the value of \(cos12^{ \circ }+cos84^{ \circ }+cos156^{ \circ }+cos132^{ \circ }.\)

CBSE 11th Standard Maths Subject Trigonometric Functions Ncert Exemplar 2 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 26, 2021 - View & Read

• 1)

  Which of the following is not correct?
  \(sin\theta =-\frac { 1 }{ 5 } \) 
  Verify through the range of trigonometric function.

• 2)

  Prove that \(sin2x+2sin4x+sin6x=4cos^{ 2 }x.sin4x.\)

• 3)

  Prove that \({ sec }^{ 2 }\theta +{ cosec }^{ 2 }\theta \ge 4\).

• 4)

  Prove that \(cos\frac { 2\pi }{ 15 } cos\frac { 4\pi }{ 15 } cos\frac { 8\pi }{ 15 } cos\frac { 16\pi }{ 15 } =\frac { 1 }{ 16 } \)

• 5)

  Find the value of \(cos12^{ \circ }+cos84^{ \circ }+cos156^{ \circ }+cos132^{ \circ }.\)

CBSE 11th Standard Maths Subject Trigonometric Functions Ncert Exemplar 1 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 26, 2021 - View & Read

• 1)

  Find the value of  \(sin \left( { 45 }^{ o }+\theta \right) -cos\left( { 45 }^{ o }-\theta \right) .\)

• 2)

  If \(tan \alpha =\frac { m }{ m+1 } \) and \(tan \beta =\frac { 1 }{ 2m+1 } ,\) then find the value of  \(\alpha +\beta \)

• 3)

  Find the value of tan 3A - tan 2A - tan A.

• 4)

  If \(sin\theta +cosec\theta =2\), then find the value of \({ sin }^{ 2 }\theta +{ cosec }^{ 2 }\theta .\)

• 5)

  Which of the following are correct?
  (i) sin1⁰>sin1
  (ii) sin1⁰
  (iii) sin1⁰=sin1
  (iv) \(sin{ 1 }^{ 0 }=\frac { \pi }{ 180 } sin1\)

CBSE 11th Standard Maths Subject Trigonometric Functions Ncert Exemplar 1 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 26, 2021 - View & Read

• 1)

  Find the value of  \(sin \left( { 45 }^{ o }+\theta \right) -cos\left( { 45 }^{ o }-\theta \right) .\)

• 2)

  If \(tan \alpha =\frac { m }{ m+1 } \) and \(tan \beta =\frac { 1 }{ 2m+1 } ,\) then find the value of  \(\alpha +\beta \)

• 3)

  Find the value of tan 3A - tan 2A - tan A.

• 4)

  If \(sin\theta +cosec\theta =2\), then find the value of \({ sin }^{ 2 }\theta +{ cosec }^{ 2 }\theta .\)

• 5)

  Which of the following are correct?
  (i) sin1⁰>sin1
  (ii) sin1⁰
  (iii) sin1⁰=sin1
  (iv) \(sin{ 1 }^{ 0 }=\frac { \pi }{ 180 } sin1\)

CBSE 11th Standard Maths Subject Sets Ncert Exemplar 2 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 26, 2021 - View & Read

• 1)

  Let F₁ be the set of parallelograms, F₂ be the set of rectangles, F₃ be the set of rhombus and F₄ be the set of squares. Then, show that F₁ is equal to the union of all sets.

• 2)

  Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set.Find the values of m and n.

• 3)

  Prove that \(\cos\theta\cos2\theta\cos2^{ 2 }\theta ...{ \cos2 }^{ n-1 }\theta =\frac { { \sin2 }^{ n }\theta }{ { 2 }^{ n }\sin\theta } for\ all\ n\in N.\)

• 4)

  For every positive integer n, prove that 7ⁿ-2ⁿ is divisible by 5.

• 5)

  Let \(T=[x:\frac{x+5}{x-7}-5=\frac{4x-40}{13x-x}]\) Is T an empty set? Justify your answer.

CBSE 11th Standard Maths Subject Sets Ncert Exemplar 2 Marks Questions 2021 - by Rupa Das - Bhubaneswar - May 26, 2021 - View & Read

• 1)

  Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set.Find the values of m and n.

• 2)

  Prove that \((A\cap B')\cup (B\cap C)=A'\cup B\)

• 3)

  Is g = {(1,1), (2, 3), (3, 5), (4, 7),} a function justify?
  If this is described by the relation, g(x)=\(\alpha x+\beta ,\) then what values should be assigned to \(\alpha x+\beta ?\)

• 4)

  Suppose A₁,A₂ ,....,A₃₀ are thirty sets each having 5 elements and B₁ , B₂ ,....,B_n are n sets each with 3 elements, let \(\bigcup _{ i=1 }^{ 30 }{ { A }_{ i } } =\bigcup _{ i=1 }^{ n }{ { B }_{ j } } =S\) and each element of 's' belongs to exactly 10 of the A_i 's and exactly 9 of the B_j .Find 'n'.

• 5)

  Prove that \(\cos\theta\cos2\theta\cos2^{ 2 }\theta ...{ \cos2 }^{ n-1 }\theta =\frac { { \sin2 }^{ n }\theta }{ { 2 }^{ n }\sin\theta } for\ all\ n\in N.\)

CBSE 11th Standard Maths Subject Ncert Exemplar 6 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 26, 2021 - View & Read

• 1)

  Find the simplified form of \(f(x)=|x-2|+|2+x|,\quad if-3\le x\le 3.\)

• 2)

  Find the value of the expression
  \({ cos }^{ 4 }\frac { \pi }{ 8 } +{ cos }^{ 4 }\frac { 3\pi }{ 8 } +{ cos }^{ 4 }\frac { 5\pi }{ 8 } +{ cos }^{ 4 }\frac { 7\pi }{ 8 } .\)

• 3)

  If \({ \left( \frac { 1+i }{ 1-i } \right) }^{ 3 }-{ \left( \frac { 1-i }{ 1+i } \right) }^{ 3 }=x+iy\), then find (x,y).

• 4)

  Find the complex number satisfying the equation \(z+\sqrt { 2 } \left| (z+1) \right| +i=0\)

• 5)

  Solve \(1\le |x-2|\le 3\).

CBSE 11th Standard Maths Subject Ncert Exemplar 6 Marks Questions 2021 Part - II - by Rupa Das - Bhubaneswar - May 26, 2021 - View & Read

• 1)

  Find the simplified form of \(f(x)=|x-2|+|2+x|,\quad if-3\le x\le 3.\)

• 2)

  Find the value of the expression
  \({ cos }^{ 4 }\frac { \pi }{ 8 } +{ cos }^{ 4 }\frac { 3\pi }{ 8 } +{ cos }^{ 4 }\frac { 5\pi }{ 8 } +{ cos }^{ 4 }\frac { 7\pi }{ 8 } .\)

• 3)

  If \({ \left( \frac { 1+i }{ 1-i } \right) }^{ 3 }-{ \left( \frac { 1-i }{ 1+i } \right) }^{ 3 }=x+iy\), then find (x,y).

• 4)

  If z₁ =\(\sqrt { 3 } +i\sqrt { 3 } \) and \({ z }_{ 2 }=\sqrt { 3 } +i\)  then find the quadrant in which \((\frac { { z }_{ 1 } }{ { z }_{ 2 } } )\)  lies.

• 5)

  Find the complex number satisfying the equation \(z+\sqrt { 2 } \left| (z+1) \right| +i=0\)

CBSE 11th Standard Maths Subject Ncert Exemplar 6 Marks Questions 2021 Part - I - by Rupa Das - Bhubaneswar - May 26, 2021 - View & Read

• 1)

  Find the simplified form of \(f(x)=|x-2|+|2+x|,\quad if-3\le x\le 3.\)

• 2)

  Find the value of the expression
  \({ cos }^{ 4 }\frac { \pi }{ 8 } +{ cos }^{ 4 }\frac { 3\pi }{ 8 } +{ cos }^{ 4 }\frac { 5\pi }{ 8 } +{ cos }^{ 4 }\frac { 7\pi }{ 8 } .\)

• 3)

  If \({ \left( \frac { 1+i }{ 1-i } \right) }^{ 3 }-{ \left( \frac { 1-i }{ 1+i } \right) }^{ 3 }=x+iy\), then find (x,y).

• 4)

  If z₁ =\(\sqrt { 3 } +i\sqrt { 3 } \) and \({ z }_{ 2 }=\sqrt { 3 } +i\)  then find the quadrant in which \((\frac { { z }_{ 1 } }{ { z }_{ 2 } } )\)  lies.

• 5)

  Solve \(1\le |x-2|\le 3\).

CBSE 11th Standard Maths Subject Ncert Exemplar 4 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 26, 2021 - View & Read

• 1)

  Let f and g be real functions defined by
  f(x)=2x+1 and g(x)=4x-7.
  For what real numbers x, f(x)=g(x)?

• 2)

  Draw the Venn diagrams to illustrate the following relationship among sets E, M and U, where E is the set of students studying  English in a school, M is the set of students studying Mathematics in the same school and U is the set of all students in that school.
  (i) All the students who study Mathematics also study English, but some students who study English do not study Mathematics.
  Firstly , make a relation between sets under given condition. Then, it is easy to draw a Venn diagram.

• 3)

  Let S= Set of points inside the square, T=Set of points inside the triangle and C=Set of points inside the circle. If the triangle and circle intersect each other and are contained in a square. Then, prove that 
  \(S\cup T\cup C=S\) , by Venn diagram

• 4)

  Find the domain of the function f defined by \(f(x)=\sqrt { 4-x } +\frac { 1 }{ \sqrt { { x }^{ 2 }-1 } } \)

CBSE 11th Standard Maths Subject Ncert Exemplar 4 Marks Questions 2021 Part - II - by Rupa Das - Bhubaneswar - May 26, 2021 - View & Read

• 1)

  Draw the Venn diagrams to illustrate the following relationship among sets E, M and U, where E is the set of students studying  English in a school, M is the set of students studying Mathematics in the same school and U is the set of all students in that school.
  (i) All the students who study Mathematics also study English, but some students who study English do not study Mathematics.
  Firstly , make a relation between sets under given condition. Then, it is easy to draw a Venn diagram.

• 2)

  Find the domain of the function f defined by \(f(x)=\sqrt { 4-x } +\frac { 1 }{ \sqrt { { x }^{ 2 }-1 } } \)

• 3)

  Prove by the principle of mathematical induction that \(1\times 1!+2\times 2!+3\times 3!+....+n\times n!=(n+1)!-1\)for all natural numbers n.

• 4)

  Prove that 2n<(n+2)! for all natural numbers n.

CBSE 11th Standard Maths Subject Ncert Exemplar 4 Marks Questions 2021 Part - I - by Rupa Das - Bhubaneswar - May 26, 2021 - View & Read

• 1)

  Draw the Venn diagrams to illustrate the following relationship among sets E, M and U, where E is the set of students studying  English in a school, M is the set of students studying Mathematics in the same school and U is the set of all students in that school.
  (i) All the students who study Mathematics also study English, but some students who study English do not study Mathematics.
  Firstly , make a relation between sets under given condition. Then, it is easy to draw a Venn diagram.

• 2)

  Let S= Set of points inside the square, T=Set of points inside the triangle and C=Set of points inside the circle. If the triangle and circle intersect each other and are contained in a square. Then, prove that 
  \(S\cup T\cup C=S\) , by Venn diagram

• 3)

  Find the domain of the function f defined by \(f(x)=\sqrt { 4-x } +\frac { 1 }{ \sqrt { { x }^{ 2 }-1 } } \)

• 4)

  Prove by the principle of mathematical induction that \(1\times 1!+2\times 2!+3\times 3!+....+n\times n!=(n+1)!-1\)for all natural numbers n.

• 5)

  Prove that 2n<(n+2)! for all natural numbers n.

CBSE 11th Standard Maths Subject Ncert Exemplar 2 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 26, 2021 - View & Read

• 1)

  Prove that \((A\cap B')\cup (B\cap C)=A'\cup B\)

• 2)

  Is g = {(1,1), (2, 3), (3, 5), (4, 7),} a function justify?
  If this is described by the relation, g(x)=\(\alpha x+\beta ,\) then what values should be assigned to \(\alpha x+\beta ?\)

• 3)

  Suppose A₁,A₂ ,....,A₃₀ are thirty sets each having 5 elements and B₁ , B₂ ,....,B_n are n sets each with 3 elements, let \(\bigcup _{ i=1 }^{ 30 }{ { A }_{ i } } =\bigcup _{ i=1 }^{ n }{ { B }_{ j } } =S\) and each element of 's' belongs to exactly 10 of the A_i 's and exactly 9 of the B_j .Find 'n'.

• 4)

  Prove that \(\cos\theta\cos2\theta\cos2^{ 2 }\theta ...{ \cos2 }^{ n-1 }\theta =\frac { { \sin2 }^{ n }\theta }{ { 2 }^{ n }\sin\theta } for\ all\ n\in N.\)

• 5)

  If the function 't'  which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by \(t(c)=\frac { 9C }{ 5 } +32,\) then find t (28)

CBSE 11th Standard Maths Subject Ncert Exemplar 2 Marks Questions 2021 Part - II - by Rupa Das - Bhubaneswar - May 26, 2021 - View & Read

• 1)

  Let F₁ be the set of parallelograms, F₂ be the set of rectangles, F₃ be the set of rhombus and F₄ be the set of squares. Then, show that F₁ is equal to the union of all sets.

• 2)

  Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set.Find the values of m and n.

• 3)

  Find the domain for which the functions \(f\left( x \right) =2{ x }^{ 2 }-1\) and \(g\left( x \right) =1-3x\) are equal

• 4)

  Find the real value of \(\theta \) for which the expression \(\frac { 1+icos\theta }{ 1-2icos\theta } \) is a real number.

• 5)

  Evaluate \(\frac { { \left( 1-i \right) }^{ 3 } }{ 1-{ i }^{ 3 } } \)

CBSE 11th Standard Maths Subject Ncert Exemplar 2 Marks Questions 2021 Part - I - by Rupa Das - Bhubaneswar - May 26, 2021 - View & Read

• 1)

  Prove that \((A\cap B')\cup (B\cap C)=A'\cup B\)

• 2)

  Is g = {(1,1), (2, 3), (3, 5), (4, 7),} a function justify?
  If this is described by the relation, g(x)=\(\alpha x+\beta ,\) then what values should be assigned to \(\alpha x+\beta ?\)

• 3)

  Suppose A₁,A₂ ,....,A₃₀ are thirty sets each having 5 elements and B₁ , B₂ ,....,B_n are n sets each with 3 elements, let \(\bigcup _{ i=1 }^{ 30 }{ { A }_{ i } } =\bigcup _{ i=1 }^{ n }{ { B }_{ j } } =S\) and each element of 's' belongs to exactly 10 of the A_i 's and exactly 9 of the B_j .Find 'n'.

• 4)

  Prove that \(\cos\theta\cos2\theta\cos2^{ 2 }\theta ...{ \cos2 }^{ n-1 }\theta =\frac { { \sin2 }^{ n }\theta }{ { 2 }^{ n }\sin\theta } for\ all\ n\in N.\)

• 5)

  For every positive integer n, prove that 7ⁿ-2ⁿ is divisible by 5.

CBSE 11th Standard Maths Subject Ncert Exemplar 1 Marks Questions With Solution 2021 - by Rupa Das - Bhubaneswar - May 26, 2021 - View & Read

• 1)

  Let U={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A={1, 2, 3}, B={2, 4, 6, 7} and C={2, 3, 4, 8}, then find (B \(\cup\) C)', (A \(\cup\) B)'

• 2)

  If n(A) = m and n(B) = n, then find the total number of non-empty relations that can be defined from A to B.

• 3)

  Find the value of  \(sin \left( { 45 }^{ o }+\theta \right) -cos\left( { 45 }^{ o }-\theta \right) .\)

• 4)

  Find the value of tan 3A - tan 2A - tan A.

• 5)

  If \(sin\theta +cosec\theta =2\), then find the value of \({ sin }^{ 2 }\theta +{ cosec }^{ 2 }\theta .\)

CBSE 11th Standard Maths Subject Ncert Exemplar 1 Marks Questions 2021 Part - II - by Rupa Das - Bhubaneswar - May 26, 2021 - View & Read

• 1)

  Let U={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A={1, 2, 3}, B={2, 4, 6, 7} and C={2, 3, 4, 8}, then find (B \(\cup\) C)', (A \(\cup\) B)'

• 2)

  If n(A) = m and n(B) = n, then find the total number of non-empty relations that can be defined from A to B.

• 3)

  Find the value of  \(sin \left( { 45 }^{ o }+\theta \right) -cos\left( { 45 }^{ o }-\theta \right) .\)

• 4)

  If \(tan \alpha =\frac { m }{ m+1 } \) and \(tan \beta =\frac { 1 }{ 2m+1 } ,\) then find the value of  \(\alpha +\beta \)

• 5)

  Find the value of tan 3A - tan 2A - tan A.

CBSE 11th Standard Maths Subject Ncert Exemplar 1 Marks Questions 2021 Part - I - by Rupa Das - Bhubaneswar - May 26, 2021 - View & Read

• 1)

  Let U={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A={1, 2, 3}, B={2, 4, 6, 7} and C={2, 3, 4, 8}, then find (B \(\cup\) C)', (A \(\cup\) B)'

• 2)

  If n(A) = m and n(B) = n, then find the total number of non-empty relations that can be defined from A to B.

• 3)

  If \(tan \alpha =\frac { m }{ m+1 } \) and \(tan \beta =\frac { 1 }{ 2m+1 } ,\) then find the value of  \(\alpha +\beta \)

• 4)

  Find the value of tan 3A - tan 2A - tan A.

• 5)

  If \(sin\theta +cosec\theta =2\), then find the value of \({ sin }^{ 2 }\theta +{ cosec }^{ 2 }\theta .\)

CBSE 11th Standard Mathematics Trignometric Functions (Textbook) - 2021 - by users_admin - May 19, 2021 - View & Read

CBSE 11th Standard Mathematics Straight Lines (Textbook) - 2021 - by users_admin - May 19, 2021 - View & Read

CBSE 11th Standard Mathematics Statistics (Textbook) - 2021 - by users_admin - May 19, 2021 - View & Read

CBSE 11th Standard Mathematics Sets (Textbook) - 2021 - by users_admin - May 19, 2021 - View & Read

CBSE 11th Standard Mathematics Sequences And Series (Textbook) - 2021 - by users_admin - May 19, 2021 - View & Read

CBSE 11th Standard Mathematics Relations And Functions (Textbook) - 2021 - by users_admin - May 19, 2021 - View & Read

CBSE 11th Standard Mathematics Probability (Textbook) - 2021 - by users_admin - May 19, 2021 - View & Read

CBSE 11th Standard Mathematics Principle Of Mathematical Induction (Textbook) - 2021 - by users_admin - May 19, 2021 - View & Read

CBSE 11th Standard Mathematics Permutations And Combinations (Textbook) - 2021 - by users_admin - May 19, 2021 - View & Read

CBSE 11th Standard Mathematics Mathematical Reasoning (Textbook) - 2021 - by users_admin - May 19, 2021 - View & Read

CBSE 11th Standard Mathematics Mathematical Modelling (Textbook) - 2021 - by users_admin - May 19, 2021 - View & Read

CBSE 11th Standard Mathematics Linear Inequalities (Textbook) - 2021 - by users_admin - May 19, 2021 - View & Read

CBSE 11th Standard Mathematics Limits And Derivatives (Textbook) - 2021 - by users_admin - May 19, 2021 - View & Read

CBSE 11th Standard Mathematics Introduction To Three Dimensional Geometry (Textbook) - 2021 - by users_admin - May 19, 2021 - View & Read

CBSE 11th Standard Mathematics Infinite Series (Textbook) - 2021 - by users_admin - May 19, 2021 - View & Read

CBSE 11th Standard Mathematics Conic Sections (Textbook) - 2021 - by users_admin - May 19, 2021 - View & Read

CBSE 11th Standard Mathematics Complex Numbers And Quadratic Equations (Textbook) - 2021 - by users_admin - May 19, 2021 - View & Read

CBSE 11th Standard Mathematics Binomial Theorem (Textbook) - 2021 - by users_admin - May 19, 2021 - View & Read

CBSE 11th Standard Mathematics Contents (Textbook) - 2021 - by users_admin - May 19, 2021 - View & Read

CBSE 11th Standard Mathematics Textbook - 2021 - by users_admin - May 19, 2021 - View & Read

CBSE 11th Standard Mathematics Syllabus 2019-20 - by users_admin - May 17, 2021 - View & Read

CBSE 11th Standard Mathematics Conic Sections Key Points - by users_admin - Apr 28, 2021 - View & Read

CBSE 11th Standard Mathematics Trigonometric Functions Key Points - by users_admin - Apr 28, 2021 - View & Read

CBSE 11th Standard Mathematics Straight Lines Key Points - by users_admin - Apr 28, 2021 - View & Read

CBSE 11th Standard Mathematics Statistics Key Points - by users_admin - Apr 28, 2021 - View & Read

CBSE 11th Standard Mathematics Sets Key Points - by users_admin - Apr 28, 2021 - View & Read

CBSE 11th Standard Mathematics Sequences and Series Key Points - by users_admin - Apr 28, 2021 - View & Read

CBSE 11th Standard Mathematics Relations and Functions Key Points - by users_admin - Apr 28, 2021 - View & Read

CBSE 11th Standard Mathematics Probability Key Points - by users_admin - Apr 28, 2021 - View & Read

CBSE 11th Standard Mathematics Principle of Mathematical Induction Key Points - by users_admin - Apr 28, 2021 - View & Read

CBSE 11th Standard Mathematics Permutations and Combinations Key Points - by users_admin - Apr 28, 2021 - View & Read

CBSE 11th Standard Mathematics Mathematical Reasoning Key Points - by users_admin - Apr 28, 2021 - View & Read

CBSE 11th Standard Mathematics Linear Inequalities Key Points - by users_admin - Apr 28, 2021 - View & Read

CBSE 11th Standard Mathematics Limits and Derivatives Key Points - by users_admin - Apr 28, 2021 - View & Read

CBSE 11th Standard Mathematics Introduction to Three Dimensional Geometry Key Points - by users_admin - Apr 28, 2021 - View & Read

CBSE 11th Standard Mathematics Syllabus - by users_admin - Apr 26, 2021 - View & Read