11th Standard Syllabus & Materials
11th Standard
TN 11th Tamil இயற்கை வேளாண்மை,சுற்றுச்சூழல் -செய்யுள் - மனோன்மணீயம் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil என்னுயிர் என்பேன் -துணைப்பாடம் - இசைத்தமிழர் இருவர் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil மொழி கலை -செய்யுள் - ஒவ்வொரு புல்லையும் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil பீடு பெற நில் - இலக்கணம் - பகுபத உறுப்புகள் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil பீடு பெற நில் - துணைப்பாடம் - வாடிவாசல் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil பீடு பெற நில் - செய்யுள் - குறுந்தொகை Important Questions And Answers Study Material - QB365 Set A
Published on: 10/11/2020
11th Standard Maths English Medium Free Online Test Volume 2 One Mark Questions with Answer Key 2020
Download Tamil Nadu 11th Standard Maths question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.
Questions + Answers key
Take MCQ Maths Test1.
Choose the correct statement
Permutation and Combination are equal
Permutation is greater than combination
Permutation is lesser than combination
Permutation and combination are unrelated
2.
Choose the incorrect pair :
P(A) + P (B) -2P(A∩B) - Exactly one of them occur
P(A∩B) - Simultaneous occurrence of A and B
peA) + P (B) - P(A∩B) - Occurrence of either A or B or both
1 - P(A∪B) - Occurrence of only A
3.
Match List - I with List II.
| List - I | List - II | ||
| i | \(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ log(tan\quad x)dx } \) | a | \(\frac { 16 }{ 35 } \) |
| ii | \(\int _{ 0 }^{ 1 }{ x{ (1-x) }^{ 10 }dx } \) | b | \(\frac { 120 }{ 46 } \) |
| iii | \(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ si{ n }^{ 7 }xdx } \) | c | \(\frac { 1 }{ 132 } \) |
| iv | \(\int _{ 0 }^{ \infty }{ { x }^{ 5 }{ e }^{ -4x }dx } \) | d | 0 |
The Correct match is
| i | ii | iii | iv |
| d | c | a | b |
| i | ii | iii | iv |
| d | c | b | a |
| i | ii | iii | iv |
| b | d | c | a |
| i | ii | iii | iv |
| b | c | a | d |
4.
Assertion (A) : f (x) =\(\begin{cases} \begin{matrix} x+1, & x<2 \end{matrix} \\ \begin{matrix} 2x-1, & x\ge 2 \end{matrix} \end{cases}\) then f'(2) does not exist.
Reason (R) : f(x) is not continuous at 2.
Both A and it are true and R is the correct explanation of A
Both A and R are true but R is not the correct explantion of A
A is true R is false
A is false R is true
5.
\(\int { \frac { 1 }{ 9x^{ 2 }-4 } } \) dx = ________+c.
log\(\left| \frac { 3x-2 }{ 3x+2 } \right| \)
\(\frac { 1 }{ 12 } \)log\(\left| \frac { 3x-2 }{ 3x+2 } \right| \)
12log\(\left| \frac { 3x-2 }{ 3x+2 } \right| \)
\(\frac { 1 }{ 12 } log\left| \frac { 3x+2 }{ 3x-2 } \right| \)
6.
A flash light has 8 batteries out of which 3 are dead. If 2 batteries are selected without replacement and tested, the probability that both are dead is
\(\frac { 3 }{ 28 } \)
\(\frac { 1 }{ 14 } \)
\(\frac { 9 }{ 64 } \)
\(\frac { 33 }{ 56 } \)
7.
If P(B)=\(\frac { 3 }{ 5 } \), P(A/B)=\(\frac { 1 }{ 2 } \) and P(AUB)=\(\frac { 4 }{ 5 } \), then P(B/\(\bar { A } \)) =
\(\frac { 1 }{ 5 } \)
\(\frac { 3 }{ 10 } \)
\(\frac { 1 }{ 2 } \)
\(\frac { 3 }{ 5 } \)
8.
If A and B are two events such that P(A) = \(\frac { 4 }{ 5 } \) and \(P(A\cap B)=\frac { 7 }{ 10 } \) then P(B/A) =
\(\frac { 1 }{ 10 } \)
\(\frac { 1 }{ 8 } \)
\(\frac { 7 }{ 8 } \)
\(\frac { 17 }{ 20 } \)
9.
If P(A\(\cup \)B) = 0.8 and P(A\(\cap \)B) = 0.3 then \(P(\bar { A } )+P(\bar { B } )\) =
0.3
0.5
0.7
0.9
10.
Three integers are chosen at random from the first 20 integers. The probability that their product is even is
\(\frac { 2 }{ 19 } \)
\(\frac { 3 }{ 19 } \)
\(\frac { 17 }{ 19 } \)
\(\frac { 4 }{ 19 } \)
11.
A function f(x) is said to be continuous at x=a if \(\lim _{ x\rightarrow a }{ f\left( x \right) } \)is equal to
\(f\left( a \right) \)
\(f\left( -a \right) \)
\(2f\left( a \right) \)
\(f\left( \frac { 1 }{ a } \right) \)
12.
The function \(f\left( x \right) =\tan { x } \) is discontinuous on the set
\(\left\{ n\pi :\quad n\in z \right\} \)
\(\left\{ 2n\pi :\quad n\in z \right\} \)
\(\left\{ (2n+1)\frac { \pi }{ 2 } ,\quad n\in z \right\} \)
\(\left\{ n\frac { \pi }{ 2 } ,\quad n\in z \right\} \)
13.
\(\lim _{ x\rightarrow 1 }{ \frac { { x }^{ m }-1 }{ { x }^{ n }-1 } } is\)
mn
m+n
m-n
\(\frac { m }{ n } \)
14.
Choose the correct or the most suitable answer from the given four alternatives.
If, \(y=a+b{ x }^{ 2 }\) where a, b are arbitrary constants, then ____
\(\frac { d^{ 2 }y }{ d{ x }^{ 2 } } =2xy\)
\(x\frac { d^{ 2 }y }{ d{ x }^{ 2 } } ={ y }_{ 1 }\)
\(x\frac { d^{ 2 }y }{ d{ x }^{ 2 } } -\frac { dy }{ dx } +y=0\)
\(x\frac { d^{ 2 }y }{ d{ x }^{ 2 } } =2xy\)
15.
Choose the correct or the most suitable answer from the given four alternatives.
\(If\sin { (x+y)= } \log { (x+y) } \) then \(\frac { dy }{ dx } \) is _____
2
-2
1
-1
16.
Two items are chosen from a lot containing twelve items of which four are defective, then the probability that at least one of the item is defective
\({19\over 33}\)
\({17\over 33}\)
\({23\over 33}\)
\({13\over 33}\)
17.
\(\int \frac{x^2+\cos ^2 x}{x^2+1} \operatorname{cosec}^2 x d x\) is
cot x + sin -1x + c
-cot x + tan-1x + c
-tan x + cot-1x + c
-cot x - tan-1x + c
18.
\(\int \sin ^3 x d x\) is
\({-3\over 4}cos \ x-{cos \ 3x\over 12}+c\)
\({3\over 4}cos \ x+{cos \ 3x\over 12}+c\)
\({-3\over 4}cos \ x+{cos \ 3x\over 12}+c\)
\({-3\over 4}sin \ x-{sin \ 3x\over 12}+c\)
19.
20.
0
2
3
4
21.
If the derivative of (ax - 5)e3x at x = 0 is -13, then the value of a is
8
-2
5
2
22.
Let f :\(R \rightarrow R\) be defined by \(f(x)= \begin{cases}x & x \text { is irrational } \\ 1-x & x \text { is rational }\end{cases}\) then f is
discontinuous at x = \({1\over 2}\)
continuous at x = \({1\over 2}\)
continuous everywhere
discontinuous everywhere
23.
24.
The value of the determinant of A = \(\begin{bmatrix} 0&a &-b \\ -a & 0 & c \\ b & -c & 0 \end{bmatrix}is\)
-2abc
abc
0
a2 + b2 + c2
25.
If \(\begin{vmatrix}2a & x_1 &y_1 \\ 2b & x_2 & y_2 \\ 2c & x_3 &y_3 \end{vmatrix}={abc\over 2}\neq 0,\) then the area of the triangle whose vertices are \(\begin{pmatrix} {x_1\over a}, {y_1\over a} \end{pmatrix}\), \(\begin{pmatrix} {x_2\over b}, {y_2\over b} \end{pmatrix}\), \(\begin{pmatrix} {x_3\over c}, {y_3\over c} \end{pmatrix}\) is
\({1\over 4}\)
\({1\over 4} abc\)
\({1\over 8}\)
\({1\over 8}abc\)
1.
(b)
Permutation is greater than combination
2.
(d)
1 - P(A∪B) - Occurrence of only A
3.
(c)
| i | ii | iii | iv |
| b | d | c | a |
4.
(c)
A is true R is false
5.
(b)
\(\frac { 1 }{ 12 } \)log\(\left| \frac { 3x-2 }{ 3x+2 } \right| \)
6.
(a)
\(\frac { 3 }{ 28 } \)
7.
(d)
\(\frac { 3 }{ 5 } \)
8.
(c)
\(\frac { 7 }{ 8 } \)
9.
(d)
0.9
10.
(c)
\(\frac { 17 }{ 19 } \)
11.
(a)
\(f\left( a \right) \)
12.
(c)
\(\left\{ (2n+1)\frac { \pi }{ 2 } ,\quad n\in z \right\} \)
13.
(d)
\(\frac { m }{ n } \)
14.
(b)
\(x\frac { d^{ 2 }y }{ d{ x }^{ 2 } } ={ y }_{ 1 }\)
15.
(d)
-1
16.
Defective = 4
Not Defective = 8
\(\mathrm{n}(\mathrm{S})=12 \mathrm{C}_{2}=\frac{12 \times 11}{1 \times 2}=66\)
\(\mathrm{P} \text { (one defective) }=\frac{4 \mathrm{C}_{1} \times 8 \mathrm{C}_{1}}{12 \mathrm{C}_{2}}=\frac{32}{66}\)
\(\mathrm{P} \text { (two defective) }=\frac{4 \mathrm{C}_{2}}{12 \mathrm{C}_{2}}=\frac{6}{66}\)
\(P \text { (atleast one defective) }=\frac{32}{66}+\frac{6}{66}=\frac{19}{33}\)
17.
\(\int \frac{x^{2}+\cos ^{2} x}{x^{2}+1} \operatorname{cosec}^{2} x d x \)
\(=\int \frac{x^{2}+\left(1-\sin ^{2} x\right)}{x^{2}+1} \times \frac{1}{\sin ^{2} x} d x \)
\(=\int \frac{\left(x^{2}+1\right)-\sin ^{2} x}{\left(x^{2}+1\right) \sin ^{2} x} d x \)
\(=\int\left(\frac{1}{\sin ^{2} x}-\frac{1}{x^{2}+1}\right) d x \)
\(=\int\left(\operatorname{cosec}^{2} x-\frac{1}{x^{2}+1}\right) d x \)
\(=-\cot x-\tan ^{-1} x+c \)
18.
\(\sin 3 x =3 \sin x-4 \sin ^{3} x \)
\(\therefore 4 \sin ^{3} x =3 \sin x-\sin 3 x \)
\(\therefore \sin ^{3} x =\frac{1}{4}[3 \sin x-\sin 3 x] \)
\(\therefore \int \sin ^{3} x d x =\frac{1}{4}\left[-3 \cos x+\frac{\cos 3 x}{3}\right]+c \)
\(=\frac{-3}{4} \cos x+\frac{\cos 3 x}{12}+c \)
19.
(c)
20.
\(\text { The right hand derivative of } f(x) \text { at } x=2 \text { is }\)
\(f^{\prime}\left(2^{+}\right) =\lim _{x \rightarrow 2^{+}} \frac{f(x)-f(2)}{x-2} \)
\(=\lim _{x \rightarrow 2^{+}} \frac{(3 x+4)-(3(2)+4)}{x-2} \)
\(=\lim _{x \rightarrow 2^{+}} \frac{3 x+4-6-4}{x-2} \)
\(=\lim _{x \rightarrow 2^{+}} \frac{3(x-2)}{(x-2)}=3 \)
21.
\(y =(a x-5) e^{3 x} \)
\(\frac{d y}{d x} =(a x-5) e^{3 x}(3)+e^{3 x}(a) \)
\(-13 =(-5)(3)+a \quad(\text { At } x=0) \)
\(-13 =-15+a \)
\(a =-13+15=2 \)
\(\therefore a =2 \)
22.
\(f(x)=\left\{\begin{array}{cc}
x, & x \text { is irrational } \\
1-x, & x \text { is rational }
\end{array}\right.\)
\(\text { Let } C \in R \text { be any element. }\)
\(\text { As } x \text { is getting close to } C, f(x) \text { oscillates between }C \text { and } 1 \text { - } C \text {. }\)
\(\therefore f(x) \text { is discontinuous everywhere }\)
23.
(c)
24.
\(|A|=\left|\begin{array}{ccc} 0 & a & -b \\ -a & 0 & c \\ b & -c & 0 \end{array}\right|\)
\(=0-a(-b c)-b(a c)=a b c-a b c=0\)
25.
\(\text { Area of triangle }=\frac{1}{2}\left|\begin{array}{lll} \frac{x_{1}}{a} & \frac{y_{1}}{a} & 1 \\ \frac{x_{2}}{b} & \frac{y_{2}}{b} & 1 \\ \frac{x^{3}}{c} & \frac{y_{3}}{c} & 1 \end{array}\right|\)
\(=\frac{1}{2 a b c}\left|\begin{array}{lll} x_{1} & y_{1} & a \\ x_{2} & y_{2} & b \\ x_{3} & y_{3} & c \end{array}\right| \text { Multiply }R_{1}, R_{2} \& R_{3} \text { by } a, b, c\text { respectively }\)
\(=\frac{1}{2 a b c} \frac{1}{(2)}\left|\begin{array}{ccc} 2 a & x_{1} & y_{1} \\ 2 b & x_{2} & y_{2} \\ 2 c & x_{3} & y_{3} \end{array}\right|=\frac{1}{4 a b c}\left(\frac{a b c}{2}\right)\)
\(=\frac{1}{8}\)
11th Standard Syllabus & Materials
11th Standard
TN 11th Tamil பீடு பெற நில் - செய்யுள் - காவடிச்சிந்து Important Questions And Answers Study Material - QB365 Set A
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TN 11th Tamil மாமழை போற்றுதும் - துணைப்பாடம் - யானை டாக்டர் Important Questions And Answers Study Material - QB365 Set A
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Tamilnadu Stateboard 11th Standard Subjects
Maths
Commerce
Economics
Biology
Business Maths and Statistics
Accountancy
Computer Science
Physics
Chemistry
Maths
Biology
Economics
Physics
Chemistry
History
Business Maths and Statistics
Computer Science
Accountancy
Computer Applications
History
Computer Technology
Commerce
Computer Applications
Computer Technology
Tamil
English
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Tamilnadu Stateboard Standards
