### 11th Standard Maths Study material & Free Online Practice Tests - View Model Question Papers with Solutions for Class 11 Session 2019 - 2020 TN Stateboard [ Chapter , Marks , Book Back, Creative & Term Based Questions Papers - Syllabus, Study Materials, MCQ's Practice Tests etc..]

#### 11th Maths - Binomial Theorem, Sequences and Series Model Question Paper - by Anu - Ramanathapuram - View & Read

• 1)

The sequence$\frac { 1 }{ \sqrt { 3 } } ,\frac { 1 }{ \sqrt { 3 } +\sqrt { 2 } } \frac { 1 }{ \sqrt { 3 } +2\sqrt { 2 } }$...from an

• 2)

The sum up to n terms of the series $\frac { 1 }{ \sqrt { 1 } +\sqrt { 3 } } +\frac { 1 }{ \sqrt { 1 } +\sqrt { 5 } } +\frac { 1 }{ \sqrt { 5 } +\sqrt { 7 } } +$....is

• 3)

The coefficient of x5 in the series e-2x is

• 4)

The term without x in ${ \left( 2x-\frac { 1 }{ 2{ x }^{ 2 } } \right) }^{ 12 }$ is

• 5)

The value of ${ 9 }^{ \frac { 1 }{ 3 } }$ ,${ 9 }^{ \frac { 1 }{ 9 } }$${ 9 }^{ \frac { 1 }{ 27 } }$ ,$\infty$is

#### 11th Maths - Combinations and Mathematical Induction Model Question Paper - by Anu - Ramanathapuram - View & Read

• 1)

In an examination there are three multiple choice questions and each question has 5 choices. Number of ways in which a student can fail to get all answer correct is

• 2)

The number of five digit telephone numbers having at least one of their digits repeated is

• 3)

There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two points is

• 4)

Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is

• 5)

The product of r consecutive positive integers is divisible by

#### 11th Maths - Trigonometry Model Question Paper - by Anu - Ramanathapuram - View & Read

• 1)

$\frac { 1 }{ cos{ 80 }^{ 0 } } -\frac { \sqrt { 3 } }{ sin{ 80 }^{ 0 } }$=

• 2)

cos10+cos20+cos30+: : :+cos1790=

• 3)

$\frac { sin(A-B) }{ cosAcosB } +\frac { sin(B-C) }{ cosBcosC } +\frac { sin(C-A) }{ cosCcosA }$ is

• 4)

If tanA=$\frac { a }{ a+1 }$ and B=$\frac { 1 }{ 2a+1 }$ then the value of A+B is

• 5)

cosp=$\frac { 1 }{ 7 }$ and cosQ=$\frac { 13 }{ 14 }$ where P,Q are angles, then P-Q is

#### 11th Maths - Basic Algebra Important Questions - by Anu - Ramanathapuram - View & Read

• 1)

If ${ log }_{ \sqrt { x } }$ 0.25 =4 ,then the value of x is

• 2)

The value of loga b logb c logc a is

• 3)

If 8 and 2 are the roots of x2+ax+c=0 and 3,3 are the roots of x2+dx+b=0;then the roots of the equation x2+ax+b = 0 are

• 4)

If |x+3| ≥10 then

• 5)

The logarithmic form of 52=25 is

#### 11th Maths - Sets, Relations and Functions Important Questions - by Anu - Ramanathapuram - View & Read

• 1)

The number of constant functions from a set containing m elements to a set containing n elements is

• 2)

The function f:[0,2π]➝[-1,1] defined by f(x)=sin x is

• 3)

Let A and B be subsets of the universal set N, the set of natural numbers. Then A'∪[(A⋂B)∪B'] is

• 4)

If n(A) = 2 and n(B ∪ C) = 3, then n[(A x B) ∪ (A x C)] is

• 5)

If two sets A and B have 17 elements in common, then the number of elements common to the set A x B and B x A is

#### 12th Maths Half Yearly Model Question Paper 2019 - by Anu - Ramanathapuram - View & Read

• 1)

The relation R defined on a set A= {0,-1, 1, 2} by xRy if |x2+y2| ≤ 2, then which one of the following is true?

• 2)

Domain of the function $y={x-1\over x+1}$ is:

• 3)

If ${ log }_{ \sqrt { x } }$ 0.25 =4 ,then the value of x is

• 4)

$\sqrt [ 4 ]{ { \left( -2 \right) }^{ 4 } } \times { \left( -1000 \right) }^{ \frac { 1 }{ 3 } }$is

• 5)

Which of the following is not true?

#### 11th Standard Maths - Term II Model Question Paper - by Shankar - Pudukkottai - View & Read

• 1)

If the function f:[-3,3]➝S defined by f(x)=x2 is onto, then S is

• 2)

Let A and B be subsets of the universal set N, the set of natural numbers. Then A'∪[(A⋂B)∪B'] is

• 3)

If 3 is the logarithm of 343 then the base is

• 4)

$\frac { 1 }{ cos{ 80 }^{ 0 } } -\frac { \sqrt { 3 } }{ sin{ 80 }^{ 0 } }$=

• 5)

In $\triangle$ABC, $\hat{C}$ = 90° then a cosA + b cosB is:

#### 11th Standard Maths - Introduction To Probability Theory Three Marks Questions - by Anu - Ramanathapuram - View & Read

• 1)

An integer is chosen at random from the first ten positive integers. Find the probability that it is
(i) an even number (ii) multiple of three

• 2)

A die is rolled. If it shows an odd number, then find the probability of getting 5.

• 3)

Suppose a fair die is rolled. Find the probability of getting
(i) an even number (ii) multiple of three

• 4)

If A and B are two events associated with a random experiment for which
P(A) = 0.35, P(A or B) = 0.85, and P(A and B) = 0.15.
Find (i) P(only B)
(ii) P(B)
(iii) P(only A)

• 5)

A die is thrown twice. Let A be the event, ‘First die shows 5’ and B be the event 'second die shows 5’. Find $P(A\cup B)$ .

#### 11th Standard Maths - Integral Calculus Three Marks Questions - by Anu - Ramanathapuram - View & Read

• 1)

Evaluate $\int { \frac { { x }^{ 4 }+{ x }^{ 2 }+1 }{ { x }^{ 2 }+x-1 } }$dx

• 2)

Evaluate $\int { \frac { { sin }^{ 6 }x+cos^{ 6 }x }{ sin^{ 2 }xcos^{ 2 }x } }$

• 3)

Evaluate $\int { \frac { \left( { a }^{ x }+{ b }^{ x } \right) ^{ 2 } }{ { a }^{ x }{ b }^{ x } } }$dx

• 4)

Evaluate if f'(x) = 3x2 - $\frac { 2 }{ { x }^{ 3 } }$ and f (1) = 0, find f (x)

• 5)

Evaluate $\int { \sqrt { 1+sinx } }$ dx, 0< x < $\frac { \pi }{ 2 }$

#### 11th Standard Maths - Differential Calculus - Differentiability and Methods of Differentiation Three Marks Questions - by Anu - Ramanathapuram - View & Read

• 1)

Show that the function $f\left( x \right) =\begin{cases} x-1,\quad x<2 \\ 2x-3,\quad x\ge 2 \end{cases}$is not differentiable at x = 2.

• 2)

Show  that$f\left( x \right) ={ x }^{ 2 }$ is differentiable at x = 1 and find $f^{ ' }\left( 1 \right)$

• 3)

Differentiate $f\left( x \right) ={ e }^{ 2x }$from first principles.

• 4)

If $y=\sqrt { x+1 } +\sqrt { x-1 }$ prove that$\sqrt { { x }^{ 2 }+1 } \frac { dy }{ dx } =\frac { 1 }{ 2 } y.$

• 5)

If xy = 4, Prove that $x\left( \frac { dy }{ dx } +{ y }^{ 2 } \right) =3y.$

#### 11th Maths - Differential Calculus - Limits and Continuity Three Marks Questions - by Anu - Ramanathapuram - View & Read

• 1)

Calculate $\lim _{ x\rightarrow0}{|x| }$.

• 2)

Use the graph to find the limits (if it exists). If the limit does not exist, explain why?
$lim_{x\rightarrow{1}}sin \pi x$

• 3)

The velocity in ft/sec of a falling object is modeled by $r(t)=-\sqrt{32\over k}{1-e^{2t\sqrt{32k}}\over1+e^{-2r\sqrt{32k}}}$ ,where k is a constant that depends upon the size and shape of the object and the density of the air. Find the  limiting velocity of the object, that is, find $lim_{t\rightarrow \infty}r(t).$

• 4)

Find the left and right limits of $f(x)={x^2-4\over (x^2+4x+4)(x+3)}at \ x=-2$ .

• 5)

Evaluate the following limits $lim_{x\rightarrow\infty}{x^4-5x\over x^2-3x+1 }$

#### 11th Maths - Vector Algebra I Three Marks Questions - by Anu - Ramanathapuram - View & Read

• 1)

Find the value of $\lambda$ for which the vectors $\overrightarrow{a}=3\hat{i}+2\hat{j}+9\hat{k}$ and $\overrightarrow{b}=\overrightarrow{i}+\lambda \overrightarrow{j}+3\overrightarrow{k}$ are parallel.

• 2)

Show that the following vectors are coplanar $\hat{i}$ −2$\hat{j}$ +3$\hat{k}$,-2 $\hat{i}$ +3$\hat{j}$ - 4 $\hat{k}$ ,-$\hat{j}$ +2 $\hat{k}$ .

• 3)

Show that the following vectors are coplanar 5$\hat{i}$ +6$\hat{j}$ +7$\hat{k}$ ,7 $\hat{i}$ -8$\hat{j}$ +9 $\hat{k}$,3$\hat{i}$+20$\hat{j}$ +5$\hat{k}$ .

• 4)

If $|\overrightarrow{a}+\overrightarrow{b}|=|\overrightarrow{a}-\overrightarrow{b}|$ prove that $\overrightarrow{a}$ and $\overrightarrow{b}$ are perpendicular.

• 5)

For any vector $\overrightarrow{r}$ prove that $\overrightarrow{r}$ = ($\overrightarrow{r}.\hat{i}$) $\hat{i}$+ ($\overrightarrow{r}.\hat{j}$) $\hat{j}$+ + ($\overrightarrow{r}.\hat{k}$) $\hat{k}$.

#### 11th Maths - Matrices and Determinants Three Marks Questions - by Anu - Ramanathapuram - View & Read

• 1)

Prove that $\begin{vmatrix} 1& a & a^2-bc \\1 &b &b^2-ca \\ 1 & c & c^2-ab \end{vmatrix}=0.$

• 2)

If a, b, c are pth, qth and rth terms of an A.P, find the value of$\begin{vmatrix} a & b & c \\ p & q & r \\ 1& 1 &1 \end{vmatrix}$

• 3)

Solve the following problems by using Factor Theorem :
Solve $\begin{vmatrix} x+a &b &c \\ a & x+b & c \\ a & b &x+c \end{vmatrix}=0$

• 4)

Identify the singular and non-singular matrices:$\begin{bmatrix} 1&2 &3 \\ 4 & 5 &6 \\ 7 & 8 & 9 \end{bmatrix}$

• 5)

Identify the singular and non-singular matrices:$\begin{bmatrix} 2&-3 &5 \\ 6 & 0 &4 \\ 1 & 5 & -7 \end{bmatrix}$

#### 11th Standard Maths - Introduction To Probability Theory Model Question Paper - by Shankar - Pudukkottai - View & Read

• 1)

Four persons are selected at random from a group of 3 men, 2 women, and 4 children. The probability that exactly two of them are children is

• 2)

A man has 3 fifty rupee notes, 4 hundred rupees notes, and 6 five hundred rupees notes in his pocket. If 2 notes are taken at random, what are the odds in favour of both notes being of hundred rupee denomination?

• 3)

A matrix is chosen at random from a set of all matrices of order 2, with elements 0 or 1 only. The probability that the determinant of the matrix chosen is non zero will be

• 4)

If A and B are two events such that A⊂B and P(B)$\neq o$ ,then which of the following is correct?

• 5)

A number x is chosen at random from the first 100 natural numbers. Let A be the event of numbers which satisfies${(x-10)(x-50)\over x-30}\ge0$, then P(A) is

#### 11th Standard Maths - Integral Calculus Model Question Paper - by Shankar - Pudukkottai - View & Read

• 1)

If$\int f(x)dx=g(x)+c$ ,then$\int f(x)g'(x)dx$

• 2)

$\int {e^{6logx}-e^{5logx}\over e^{4logx}-e^{3logx}}dx$ is

• 3)

$\int tan^{-1}\sqrt{1-cos \ 2x\over 1+cos \ 2x}dx$ is

• 4)

$\int {sin^8x-cos^8x\over 1-2sin^2 \ x \ cos^2 \ x}dx$ is

• 5)

$\int{x^2+cos^2x\over x^2+1}cosec^2xdx$ is

#### 11th Standard Maths - Two Dimensional Analytical Geometry Three Marks Questions - by Anu - Ramanathapuram - View & Read

• 1)

If the sum of the distance of a moving point in a plane from the axis is 1, then find the locus of the point.

• 2)

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).

• 3)

Find the equation of the straight line which passes through the intersection of the straight lines 2x + Y= 8 and 3x - 2y + 7 = 0 and is parallel to the straight line 4x+ y-11 =0.

• 4)

Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of 120o with the positive direction of x-axis.

• 5)

Find the equation of the line which passes through the point (- 4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5: 3 by this point.

#### 11th Standard Maths - Basic Algebra Three Marks Questions - by Anu - Ramanathapuram - View & Read

• 1)

• 2)

Solve $\sqrt [ 8 ]{{{x}\over{x+3}} } -\sqrt{{{x+3}\over{x}}}=2.$

• 3)

A factory kept increasing its out-put by the same percentage every year. Find the percentage, if it is known that the output has doubled in the last two years.

• 4)

Find the value of log2 $\left({{\sqrt [ 3 ]{4 } }\over{4^2\sqrt{8}}} \right).$

• 5)

Find x if ${{1}\over{2}}$ log10 $(11+4\sqrt{7})$ = log10 (2+x).

#### 11th Maths - Trigonometry Three Marks Questions - by Anu - Ramanathapuram - View & Read

• 1)

Expand cos (A + B + C). Hence prove that cos A cos B cos C = sin A sin B cos C + sin B sin C cos A + sin C sin A cos B, if A + B + C = $\frac{\pi}{2}$

• 2)

What must be the radius of a circular running path, around which an athelete must run 5 times in order to describe 1 km?

• 3)

In a circular of diameter 40 cm, a chord is of length 20 cm. FInd the length of the minor is of the chord?

• 4)

if in two Circles, arcs of the same length subtend angles 600 and 750 at the center, find the ratio of their radii?

• 5)

Prove that sin 75o - sin 15o = cos 105o + cos 15o

#### 11th Maths - Combinations and Mathematical Induction Three Marks Questions - by Anu - Ramanathapuram - View & Read

• 1)

Find the number of strings that can be made using all letters of the word THING. If these words are written as in a dictionary, what will be the 85th string?

• 2)

Find the sum of all 4-digit numbers that can be formed using digits 1,2,3,4, and 5 repetitions not allowed?

• 3)

Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?

• 4)

Eighteen guests have to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three on the other side. Determine the number of ways in which the seating arrangement can be made?

• 5)

If p(h) is the statement "n2 + n is even" and if p(r) is true, then p(r + 1) is true.

#### 11th Maths - Binomial Theorem, Sequences and Series Three Marks Questions - by Anu - Ramanathapuram - View & Read

• 1)

Find $\sqrt [ 3 ]{ 1001 }$ approximately. (two decimal places).

• 2)

Prove that $\sqrt [ 3 ]{ { x }^{ 3 }+6 } -\sqrt [ 3 ]{ { x }^{ 3 }+3 }$ is approximately equal to $\frac { 1 }{ { x }^{ 2 } }$ when x is sufficiently large.

• 3)

The first term of a G.P is 1 .The sum of third and fifth terms is 90.Find the common ration of the G.P

• 4)

Find all the sequence which are simultaneously arithmetic and geometric progression.

• 5)

If the mth term of a H.P. is n and nth term is m, then show that its pth  term is $\frac{mn}{p}$.

#### 11th Maths - Sets, Relations and Functions Three Marks Questions - by Anu - Ramanathapuram - View & Read

• 1)

Graph the function f(x)=x3 and $g(x)\sqrt[3]x$ on the same co-ordinate plane. Find fog and graph it on the plane as well. Explain your results.

• 2)

Write the steps to obtain the graph of the function y=3(x-1)2+5 from the graph y=x2

• 3)

By taking suitable sets A, B, C, verify the following results:
(A$\times$ B)$\cap$(B$\times$A) = (A$\cap$B) $\times$ (B$\cap$A)

• 4)

By taking suitable sets A, B, C, verify the following results:
C-(B-A) = (C$\cap$ A) $\cup$ (C$\cap$B')

• 5)

If A$\times$ A has 16 elements, S={(a,b)$\in$A$\times$A:a

#### 11th Standard Maths - Differential Calculus - Differentiability and Methods of Differentiation Model Question Paper - by Shankar - Pudukkottai - View & Read

• 1)

If $y={1\over a-z}$ ,then ${dz\over dy}$ is

• 2)

If y=mx+c and f(0)=$f'(0)=1$,then f(2) is

• 3)

${d\over dx}(e^{x+5log \ x})$is

• 4)

$x={1-t^2\over 1+t^2},y={2t\over 1+t^2}$ then ${dy\over dx}$is

• 5)

The differential coefficient of log10 x with respect to logx10 is

#### 11th Standard Maths - Differential Calculus - Limits and Continuity Model Question Paper - by Shankar - Pudukkottai - View & Read

• 1)

$lim_{x\rightarrow\infty}{sin \ x \over x}$

• 2)

If f(x)=x(-1)$\left\lfloor 1\over x \right\rfloor$,$x\le0$,then the value of $lim_{x\rightarrow 0}f(x)$ is equal to

• 3)

If $lim_{x \rightarrow 0}{sin \ px\over tan \ 3x}=4$ , then the value of p is

• 4)

$lim_{x \rightarrow 0}{e^{tan \ x}-e^x\over tan x-x}=$

• 5)

The function is not defined for x = −1. The value of ( 1) f − so that the function extended by this value is continuous is

#### 11th Standard Maths - Matrices and Determinants Model Question Paper - by Shankar - Pudukkottai - View & Read

• 1)

If A=$\begin{bmatrix}\lambda & 1 \\ -1 & -\lambda \end{bmatrix}$ ,then for what value of $\lambda$, A2 = O?

• 2)

If A is a square matrix, then which of the following is not symmetric?

• 3)

If A and B are symmetric matrices of order n, where (A $\neq$ B), then

• 4)

If the points (x,−2), (5, 2), (8,8) are collinear, then x is equal to

• 5)

If A is skew-symmetric of order n and C is a column matrix of order n × 1, then CT AC is

#### 11th Standard Maths - Vector Algebra - I Model Question Paper - by Shankar - Pudukkottai - View & Read

• 1)

The value of $\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{DA}+\overrightarrow{CD}$ is

• 2)

A vector $\overrightarrow{OP}$ makes 60° and 45° with the positive direction of the x and y axes respectively.  Then the angle between $\overrightarrow{OP}$and the z-axis is

• 3)

One of the diagonals of parallelogram ABCD with $\overrightarrow{a}$ and $\overrightarrow{b}$ as adjacent sides is $\overrightarrow{a}+\overrightarrow{b}$The other diagonal $\overrightarrow{BD}$ is

• 4)

The value of  $\theta \in (0,{\pi\over 2})$ for which the vectors $\overrightarrow{a}=(sin \theta)\hat{i}+(cos\theta)\hat{j}$ and $\overrightarrow{b}=\hat{i}-\sqrt{3}\hat{j}+2\hat{k}$ are perpendicular, is equal to

• 5)

If $|\overrightarrow { a } |=|\overrightarrow { b } |$ then

#### 11th Standard Maths - Introduction To Probability Theory Two Marks Questions Paper - by Anu - Ramanathapuram - View & Read

• 1)

If an experiment has exactly the three possible mutually exclusive outcomes A, B, and C, check in each case whether the assignment of probability is permissible
$P(A)=\frac { 2 }{ 5 } ,\quad P(B)=\frac { 1 }{ 5 } ,\quad P(C)=\frac { 3 }{ 5 }$

• 2)

If an experiment has exactly the three possible mutually exclusive outcomes A, B, and C, check in each case whether the assignment of probability is permissible
P(A)=0.421, P(B)=0.527  P(C)=0.042

• 3)

There are two identical urns containing respectively 6 black and 4 red balls, 2 black and 2 red balls. An urn is chosen at random and a ball is drawn from it.
(i) find the probability that the ball is black
(ii) if the ball is black, what is the probability that it is from the first urn?

• 4)

If two coins are tossed simultaneously, then find the probability of getting
(i) one head and one tail (ii) at most two tails

• 5)

Five mangoes and 4 apples are in a box. If two fruits are chosen at random, find the probability that (i) one is a mango and the other is an apple (ii) both are of the same variety

#### 11th Maths - Integral Calculus Two Marks Questions - by Anu - Ramanathapuram - View & Read

• 1)

Integrate the following with respect to x.${1\over x^{10}}$

• 2)

Integrate the following with respect to x.$\sqrt{x}$

• 3)

Integrate the following with respect to x.${cot \ x \over sin \ x}$

• 4)

Integrate the following with respect to x:${1\over x^3}$

• 5)

Evaluate the following with respect to x:$\int{\sqrt{(15-2x)}}dx$

#### 11th Maths - Differential Calculus - Differentiability and Methods of Differentiation Two Marks Questions - by Anu - Ramanathapuram - View & Read

• 1)

Differentiate the following with respect to x :$y=(x-{1\over x})^2$

• 2)

Differentiate the following with respect to x: y=xex log x

• 3)

Find the derivatives of the following functions with respect to corresponding independent variables:y = sin x + cos x

• 4)

Differentiate the following:y = cos (tanx)

• 5)

Differentiate the following: f(t)$=3\sqrt{1+tan \ t}$

#### 11th Maths - Differential Calculus - Limits and Continuity Two Marks Questions - by Anu - Ramanathapuram - View & Read

• 1)

Complete the table using calculator and use the result to estimate the limit.
$lim_{x\rightarrow{0}}{\sqrt{x+3}-\sqrt{3}\over x}$

 x -0.1 -0.01 -0.001 0.001 0.01 0.1 f(x)
• 2)

Complete the table using calculator and use the result to estimate the limit.
$lim_{x\rightarrow 0}{sin x\over x}$

 x -0.1 -0.01 -0.001 0.001 0.01 0.1 f(x)
• 3)

Compute $lim_{x\rightarrow8}(5x)$

• 4)

Compute$lim_{x\rightarrow-2}(-{3\over 2}x)$

• 5)

Find the positive integer n so that $lim_{x\rightarrow 3}{x^n-3^n\over x-3}=27$

#### 11th Maths Unit 8 Vector Algebra I Two Marks Questions - by Anu - Ramanathapuram - View & Read

• 1)

If D and E are the midpoints of the sides AB and AC of a triangle ABC, prove that $\overrightarrow{BE}+\overrightarrow{DC}={3\over2}\overrightarrow{BC}$ .

• 2)

Find a unit vector along the direction of the vector 5$\hat{i}$-3$\hat{j}$+4$\hat{k}$ .

• 3)

Find the direction cosines of the line joining (2, 3, 1) and (3, - 1, 2).

• 4)

Verify whether the following ratios are direction cosines of some vector or not${4\over 3}.0,{3\over 4}$

• 5)

Find the direction cosines and direction ratios for the following vectors.5$\hat{i}$-3$\hat{j}$-48$\hat{k}$

#### 11th Maths - Term 1 Model Question Paper - by Shankar - Pudukkottai - View & Read

• 1)

Let f:R➝R be defined by f(x)=1-|x|. Then the range of f is

• 2)

The number of roots of (x+3)4+(x+5)4=16 is

• 3)

If tan400=λ, then $\frac { tan{ 140 }^{ 0 }-tan{ 130 }^{ 0 } }{ 1+tan{ 140 }^{ 0 }.tan{ 130 }^{ 0 } }$=

• 4)

In a $\triangle$ ABC, C = 90° then the value of sin A + sin B-2$\sqrt{2} cos{A\over2}cos {B\over 2}is$

• 5)

If Pr stands for r Pr then the sum of the series 1+ P1 + 2P2 + 3P3 +...+ nPn is

#### 11th Standard Maths - Matrices and Determinants Two Marks Question - by Anu - Ramanathapuram - View & Read

• 1)

If A=$\begin{bmatrix} 0 &c &b \\ c & 0 &a \\ b & a & 0 \end{bmatrix}$,compute A2

• 2)

Construct an m × n matrix A= [aij], where a ij is given by
$a_{ij}={(i-2j)^2\over 2}with \ m=2,n=3$

• 3)

Determine the value of x + y if $\begin{bmatrix} 2x+y & 4x \\ 5x-7 & 4x \end{bmatrix}=\begin{bmatrix} 7 & 7y-13 \\ y & x+6 \end{bmatrix}$

• 4)

Determine the matrices A and B if they satisfy
$2A-B+\begin{bmatrix} 6 & -6 & 0\\ -4 & 2 & 1\end{bmatrix}=0 \ and \ A-2B=\begin{bmatrix} 3 & 2&8 \\ -2 & 1&-7 \end{bmatrix}$

• 5)

Evaluate :$\begin{vmatrix} 2 & 4 \\ -1 & 2 \end{vmatrix}$

#### 11th Maths - Two Dimensional Analytical Geometry Two Marks Question - by Anu - Ramanathapuram - View & Read

• 1)

The sum of the squares of the distances of a moving point from two fixed points (a, 0) and (-0, 0) is equal to 2c2. Find the equation to its locus.

• 2)

Determine x so that the line passing through (3, 4) and (x, 5) makes 135° with the positive direction of x-axis.

• 3)

Find the values of k for which the line (k-3)x-(4-k2)y+(k2-7k+6)=0 passes through the origin.

• 4)

Two sides of a square lie on the lines x + y =1 and x + y + 2 = 0.What is its area?

• 5)

If 9x2 + 12xy + 4y2 + 6x + 4y - 3 = 0 represents two parallel lines, find the distance between them.

#### 11th Maths - Binomial Theorem, Sequences and Series Two Marks Question - by Anu - Ramanathapuram - View & Read

• 1)

Expand $\left( { 2x }^{ 2 }-3\sqrt { 1-{ x }^{ 2 } } \right) ^{ 4 }+({ 2x }^{ 2 }+3\sqrt { 1-{ x }^{ 2 }) } ^{ 4 }$

• 2)

Show that the sum of (m + n)th and (m - n)th term of an A.P is equal to twice the mth term.

• 3)

Using binomial theorem, indicate which of the following two number is larger (1.01)1000000 (OR)10, 000

• 4)

Find the last two digits of the number 3600

• 5)

In the binomial expansion of (a+b)n the coefficients of the 4th and 13th terms are equal to each other, find n.

#### 11th Maths - Combinations and Mathematical Induction Two Marks Question - by Anu - Ramanathapuram - View & Read

• 1)

count the total number of ways of answering 6 objective type questions,each question having 4 choices

• 2)

Find the value of $\frac { 12! }{ 9!\times 3! }$

• 3)

Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?

• 4)

Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?

• 5)

Prove that 15C3+2 x 15C4+ 15C4+ 15C5= 17C5.

#### 11th Maths Trigonometry Two Marks Questions - by Anu - Ramanathapuram - View & Read

• 1)

Identify the Quadrant in which a given measure lies;  250

• 2)

Identify the Quadrant in which a given measure lies; -550

• 3)

Two vehicles leave the same place P at the same time moving along two different roads. One vehicle moves at an average speed of 60 km/hr and the other vehicle moves at an average speed of 80 km/hr. After half an hour the vehicle reach the destinations A and B. If AB subtends 60 at the initial point P, then find AB.

• 4)

Show that $\frac { (cos\theta -cos3\theta )(sin8\theta +sin2\theta ) }{ (sin5\theta -sin\theta )(cos4\theta -cos6\theta ) } =1$

• 5)

For given Angle, find a coterminal angle with a measure $\theta$ of such that $0\le \theta \le 360°$
-4500

#### 11th Maths - Basic Algebra Two Marks Questions - by Anu - Ramanathapuram - View & Read

• 1)

Solve for x $\left| x \right| -10<-3$

• 2)

Solve $-3\left| x \right| +5\le -2$ and graph the solution set in a number line.

• 3)

Compute ${ log }_{ 9 }^{ 27 }-{ log }_{ 27 }^{ 9 }$

• 4)

Prove $log\frac { { a }^{ 2 } }{ bc } +log\frac { b^{ 2 } }{ ca } +log\frac { c^{ 2 } }{ ab } =0$

• 5)

Discuss the nature of roots of 4x2 - x - 2 = 0

#### 11th Maths Chapter 1 Sets, Relations and Functions Two Marks Questions - by Anu - Ramanathapuram - View & Read

• 1)

State whether the following sets are finite or infinite.
{x $\in$ N:x is an odd prime number}

• 2)

State whether the following sets are finite or infinite.
{x $\in$ Z:x is even and less than 10}

• 3)

Let A and B be two sets such that n(A)=3 and n(B)=2. If (x, 1) (y, 2) (z, 1) are in A$\times$B, find A and B, where x, y, z are distinct elements.

• 4)

Let X = {a, b, c, d}, and R = {(a, a) (b, b) (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it
Reflexive

• 5)

If U={x:1≤x≤10, x∈N}, A={1,3,5,7,9} and B={2,3,5,9,10} then find A'UB'.

#### 11th Maths - Term 1 Five Mark Model Question Paper - by Anu - Ramanathapuram - View & Read

• 1)

Discuss the following relations for reflexivity, symmetricity and transitivity :
The relation R defined on the set of all positive integers by "mRn if m divided n".

• 2)

Check whether the following for one-to-oneness and ontoness.
$f:R-\{0\}\rightarrow R$ defined by f $f(x)={1\over x}.$

• 3)

Resolve the following rational expressions into partial fractions.
${{1}\over{x^2-a^2}}$

• 4)

Show that$\frac { sin8x\quad cosx-sin6x\quad cos3x }{ cos2x\quad cosx-sin3x\quad sin4x } =tan2x$

• 5)

find the value of sin $\left( -\frac { 11\pi }{ 3 } \right)$

#### 11th Maths Quarterly Model Question Paper - by Anu - Ramanathapuram - View & Read

• 1)

The number of constant functions from a set containing m elements to a set containing n elements is

• 2)

If A={1,2,3}, B={1,4,6,9} and R is a relation from A to B defined by "x is greater than y". The range of R is

• 3)

$n(A\cap B)=4$ and $(A\cup B)=11$ then $n(p(A\triangle B))$ is:

• 4)

If A and B are any two finite sets having m and n elements respectively then the cardinality of the power set of A x B is

• 5)

If 3 is the logarithm of 343 then the base is

#### 11th Maths - Introduction To Probability Theory Book Back Questions - by Anu - Ramanathapuram - View & Read

• 1)

Four persons are selected at random from a group of 3 men, 2 women, and 4 children. The probability that exactly two of them are children is

• 2)

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

• 3)

A matrix is chosen at random from a set of all matrices of order 2, with elements 0 or 1 only. The probability that the determinant of the matrix chosen is non zero will be

• 4)

If two events A and B are independent such that P(A)=0.35 and $P(A\cup B)=0.6$ ,then P(B) is

• 5)

There are three events A, B, and C of which one and only one can happen. If the odds are 7 to 4 against A and 5 to 3 against B, then odds against C is

#### 11th Maths - Integral Calculus Book Back Questions - by Anu - Ramanathapuram - View & Read

• 1)

If$\int f(x)dx=g(x)+c$ ,then$\int f(x)g'(x)dx$

• 2)

$\int {e^x(1+x)\over cos^2(xe^x)}dx$ is

• 3)

$\int {sec \ x\over \sqrt{cos 2x}}dx$ is

• 4)

$\int{ {e^x}(x^2 \ tan^{-1}x+tan^{-1}x+1)\over x^2+1}dx$ is

• 5)

$\int \sqrt{{1-x\over 1+x}}dx$ is

#### 11th Maths Unit 10 Differential Calculus - Differentiability and Methods of Differentiation Book Back Questions - by Anu - Ramanathapuram - View & Read

• 1)

If y= f(x2+2) and f'(3)=5,then ${dy\over dx}$ at x=1 is

• 2)

If y=mx+c and f(0)=$f'(0)=1$,then f(2) is

• 3)

$x={1-t^2\over 1+t^2},y={2t\over 1+t^2}$ then ${dy\over dx}$is

• 4)

If pv=81,then ${dp\over dv}$ at v=9 is

• 5)

If ,then f '(2) is

#### 11th Maths Unit 9 Differential Calculus - Limits and Continuity Book Back Questions - by Anu - Ramanathapuram - View & Read

• 1)

$lim_{x\rightarrow\infty}{sin \ x \over x}$

• 2)

$lim_{x\rightarrow {\pi/2}}{2x-\pi\over cosx}$

• 3)

$lim_{x \rightarrow \infty}{\sqrt{x^2-1}\over 2x+1}=$

• 4)

If f(x)=x(-1)$\left\lfloor 1\over x \right\rfloor$,$x\le0$,then the value of $lim_{x\rightarrow 0}f(x)$ is equal to

• 5)

If f : $R \rightarrow R$ is defined by f(x)=$\left\lfloor x-3 \right\rfloor +|x-4|$ for $x \in R$, then$lim_{x\rightarrow 3^-}f(x)$ is equal to

#### 11th Standard Chapter 8 Vector Algebra - I Book Back Questions - by Anu - Ramanathapuram - View & Read

• 1)

The value of $\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{DA}+\overrightarrow{CD}$ is

• 2)

A vector makes equal angle with the positive direction of the coordinate axes. Then each angle is equal to

• 3)

The vectors $\overrightarrow{a}-\overrightarrow{b},\overrightarrow{b}-\overrightarrow{c},\overrightarrow{c}-\overrightarrow{a}$ are

• 4)

If$\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$are the position vectors of three collinear points, then which of the following is true?

• 5)

If $\lambda \hat{i}+2\lambda \hat{j}+2\lambda \hat{k}$ is a unit vector, then the value of $\lambda$is

#### 11th Standard Maths Unit 7 Matrices and Determinants Book Back Questions - by Anu - Ramanathapuram - View & Read

• 1)

If aij =${1\over2}(3i-2j)$ and A=[aij]2x2 is

• 2)

What must be the matrix X, if 2x+$\begin{bmatrix} 1& 2 \\ 3 & 4 \end{bmatrix}=\begin{bmatrix} 3 & 8 \\ 7 & 2 \end{bmatrix}?$

• 3)

If A is a square matrix, then which of the following is not symmetric?

• 4)

If A=$\begin{bmatrix}a & x \\ y& a \end{bmatrix}$ and if xy =1, then det(A AT ) is equal to

• 5)

If the points (x,−2), (5, 2), (8,8) are collinear, then x is equal to

#### 11th Standard Maths Unit 6 Two Dimensional Analytical Geometry Book Back Questions - by Anu - Ramanathapuram - View & Read

• 1)

The equation of the locus of the point whose distance from y-axis is half the distance from origin is

• 2)

Which of the following point lie on the locus of 3x2+3y2-8x-12y+17 = 0

• 3)

Equation of the straight line that forms an isosceles triangle with coordinate axes in the I-quadrant with perimeter 4 + 2$\sqrt{2}$ is

• 4)

The intercepts of the perpendicular bisector of the line segment joining (1, 2) and (3,4) with coordinate axes are

• 5)

The equation of the line with slope 2 and the length of the perpendicular from the origin equal to $\sqrt5$ is

#### 11th Standard Maths - Binomial Theorem, Sequences and Series Book Back Questions - by Anu - Ramanathapuram - View & Read

• 1)

If a, 8, b are in AP, a, 4, b are in GP, and if a, x, b are in HP then x is

• 2)

The HM of two positive numbers whose AM and GM are 16,8 respectively is

• 3)

The nth term of the sequence $\frac { 1 }{ 2 } ,\frac { 3 }{ 4 } ,\frac { 7 }{ 8 } ,\frac { 15 }{ 6 }$.+.....is

• 4)

The coefficient of x5 in the series e-2x is

• 5)

The value of 2 + 4 + 6 + + 2n is

#### 11th Standard Maths - Combinations and Mathematical Induction Book Back Questions - by Anu - Ramanathapuram - View & Read

• 1)

The sum of the digits at the 10th place of all numbers formed with the help of 2, 4, 5, 7 taken all at a time is

• 2)

The number of ways in which the following prize be given to a class of 30 boys first and second in mathematics, first and second in physics, first in chemistry and first in English is

• 3)

The product of r consecutive positive integers is divisible by

• 4)

The number of five digit telephone numbers having at least one of their digits repeated is

• 5)

The number of ways in which a host lady invite 8 people for a party of 8 out of 12 people of whom two do not want to attend the party together is

#### 11th Standard Maths - Trigonometry Book Back Questions - by Anu - Ramanathapuram - View & Read

• 1)

If cos280+sin280=k3, then cos 170 is equal to

• 2)

If $\pi <2\theta <\frac { 3\pi }{ 2 }$, then $\sqrt { 2+\sqrt { 2+2\quad cos4\theta } }$ equals to

• 3)

If cospፀ+cosqፀ=0 and if p≠q, then ፀ is equal to (n is any integer)

• 4)

In a triangle ABC, sin2A+sin2B+sin2C=2, then the triangle is

• 5)

The triangle of maximum area with constant perimeter 12m

#### 11th Standard Maths Unit 2 Basic Algebra Book Back Questions - by Anu - Ramanathapuram - View & Read

• 1)

Give that x;y and b are real numbers x<y;b>0, then

• 2)

If ${ log }_{ \sqrt { x } }$ 0.25 =4 ,then the value of x is

• 3)

If a and b are the roots of the equation x2-kx+16=0 and a2+b2=32 then the value of k is

• 4)

If a and b are the roots of the equation x2-kx+c = 0 then the distance between the points (a, 0) and (b, 0)

• 5)

The value of log3 11.log11 13.log13 15log15 27.log27 81 is

#### 11th Standard Maths Sets, Relations and Functions Book Back Questions - by Anu - Ramanathapuram - View & Read

• 1)

Let R be the universal relation on a set X with more than one element. Then R is

• 2)

Let X = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 3), (2, 2), (3, 3), (2, 1), (3, 1), (1, 4),(4, 1)}. Then R is

• 3)

The range of the function ${1\over 1-2sinx}$ is

• 4)

The range of the function $f(x) = \left| \left\lfloor x \right\rfloor - x \right| ,x \in R$  is

• 5)

The rule f(x) =x2 is a bijection if the domain and the co-domain are given by

#### 11th Standard Maths Unit 9 Differential Calculus - Limits and Continuity One Mark Question with Answer Key - by Anu - Ramanathapuram - View & Read

• 1)

$lim_{x\rightarrow\infty}{sin \ x \over x}$

• 2)

$lim_{x\rightarrow {\pi/2}}{2x-\pi\over cosx}$

• 3)

$lim_{x \rightarrow \infty}{\sqrt{x^2-1}\over 2x+1}=$

• 4)

$lim_{x \rightarrow \infty}{a^x-b^x\over x}=$

• 5)

$\lim _{ x\rightarrow \infty }{ \left( \frac { 1 }{ x } +2 \right) }$is equal to

#### 11th Standard Maths Unit 8 Vector Algebra - I One Mark Question with Answer Key - by Anu - Ramanathapuram - View & Read

• 1)

The value of $\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{DA}+\overrightarrow{CD}$ is

• 2)

If $\overrightarrow{a}+2\overrightarrow{b}$ and $3\overrightarrow{a}+m\overrightarrow{b}$ are parallel, then the value of m is

• 3)

The unit vector parallel to the resultant of the vectors $\hat{i}+\hat{j}-\hat{k}$ and$\hat{i}-2\hat{j}+\hat{k}$ is

• 4)

A vector $\overrightarrow{OP}$ makes 60° and 45° with the positive direction of the x and y axes respectively.  Then the angle between $\overrightarrow{OP}$and the z-axis is

• 5)

If $\overrightarrow{BA}=3\hat{i}+2\hat{j}+\hat{k}$ and the position vector of is $\hat{i}+3\hat{j}-\hat{k}$ ,then the position vector A is

#### 11th Standard Maths - Matrices and Determinants One Mark Question and Answer - by Anu - Ramanathapuram - View & Read

• 1)

If aij =${1\over2}(3i-2j)$ and A=[aij]2x2 is

• 2)

Which one of the following is not true about the matrix $\begin{bmatrix} 1 &0 &0 \\ 0 & 0 &0 \\ 0 & 0 & 5 \end{bmatrix}?$

• 3)

If A=$\begin{bmatrix}\lambda & 1 \\ -1 & -\lambda \end{bmatrix}$ ,then for what value of $\lambda$, A2 = O?

• 4)

If A=$\begin{bmatrix} 1& 2 &2 \\ 2 & 1 & -2 \\ a & 2 & b \end{bmatrix}$ is a matrix satisfying the equation AAT = 9I, where I is 3 × 3 identity matrix, then the ordered pair (a, b) is equal to

• 5)

The product of any matrix by the scalar____________is the null matrix.

#### 11th Standard Maths Chapter 4 Combinations and Mathematical Induction One Mark Question and Answer - by Anu - Ramanathapuram - View & Read

• 1)

The sum of the digits at the 10th place of all numbers formed with the help of 2, 4, 5, 7 taken all at a time is

• 2)

The number of ways in which the following prize be given to a class of 30 boys first and second in mathematics, first and second in physics, first in chemistry and first in English is

• 3)

The product of r consecutive positive integers is divisible by

• 4)

If a2-a C2=a2-a C4 then the value of 'a' is

• 5)

There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two points is

#### 11th Maths Unit 5 Binomial Theorem, Sequences and Series One Mark Question with Answer Key - by Anu - Ramanathapuram - View & Read

• 1)

If a, 8, b are in AP, a, 4, b are in GP, and if a, x, b are in HP then x is

• 2)

The HM of two positive numbers whose AM and GM are 16,8 respectively is

• 3)

The nth term of the sequence 1, 2, 4, 7, 11,... is

• 4)

The sum of an infinite GP is 18. If the first term is 6, the common ratio is

• 5)

If the sum of n terms of an A. P. be 3n2 - n and its common difference is 6, then its first term is

#### 11th Maths - Two Dimensional Analytical Geometry One Mark Question and Answer - by Anu - Ramanathapuram - View & Read

• 1)

The equation of the locus of the point whose distance from y-axis is half the distance from origin is

• 2)

Which of the following equation is the locus of (at2; 2at)

• 3)

The slope of the line which makes an angle 45 with the line 3x- y = -5 are

• 4)

Equation of the straight line that forms an isosceles triangle with coordinate axes in the I-quadrant with perimeter 4 + 2$\sqrt{2}$ is

• 5)

The intercepts of the perpendicular bisector of the line segment joining (1, 2) and (3,4) with coordinate axes are

#### 11th Maths Unit 3 Trigonometry - One Mark Questions Paper - by Anu - Ramanathapuram - View & Read

• 1)

$\frac { 1 }{ cos{ 80 }^{ 0 } } -\frac { \sqrt { 3 } }{ sin{ 80 }^{ 0 } }$=

• 2)

The maximum value of 4sin2x+3cos2x+$sin\frac { x }{ 2 } +cos\frac { x }{ 2 }$ is

• 3)

cos10+cos20+cos30+: : :+cos1790=

• 4)

cos2ፀ cos2ф+sin2(ፀ-ф)-sin2(ፀ+ф) is equal to

• 5)

If tan α and tan β are the roots of tan x2+atanx+b=0; then $\frac { sin(\alpha +\beta ) }{ sin\alpha sin\beta }$ is equal to

#### 11th Maths Chapter 2 Basic Algebra One Mark Question Paper - by Anu - Ramanathapuram - View & Read

• 1)

If |x+2| $\le$ 9, then x belongs to

• 2)

If $\frac { |x-2| }{ x-2 } \ge 0$, then x belongs to

• 3)

If ${ log }_{ \sqrt { x } }$ 0.25 =4 ,then the value of x is

• 4)

The value of loga b logb c logc a is

• 5)

If 3 is the logarithm of 343 then the base is

#### 11th Standard Sets, Relations and Functions One Mark Questions - by Anu - Ramanathapuram - View & Read

• 1)

The number of constant functions from a set containing m elements to a set containing n elements is

• 2)

If the function f:[-3,3]➝S defined by f(x)=x2 is onto, then S is

• 3)

The function f:R➝R be defined by f(x)=sinx+cosx is

• 4)

If A⊆B, then A\B is

• 5)

Let R be a relation on the set N given by R={(a,b):a=b-2, b>6}. Then

#### 11th Maths Two Dimensional Analytical Geometry Model Question Paper - by Anu - Ramanathapuram - View & Read

• 1)

The slope of the line which makes an angle 45 with the line 3x- y = -5 are

• 2)

A line perpendicular to the line 5x - y = 0 forms a triangle with the coordinate axes. If the area of the triangle is 5 sq. units, then its equation is

• 3)

If a vertex of a square is at the origin and its one side lies along the line 4x + 3y - 20 = 0, then the area of the square is

• 4)

The equation of the bisectors of the angle between the co-ordinate axes are

• 5)

The equation of the straight line bisecting the line segment joining the points (2,4) and (4,2) and making an angle of 450 with positive direction of x-axis is

#### 11th Maths Unit 5 Binomial Theorem, Sequences and Series Model Question Paper - by Anu - Ramanathapuram - View & Read

• 1)

If a, 8, b are in AP, a, 4, b are in GP, and if a, x, b are in HP then x is

• 2)

The sum up to n terms of the series $\frac { 1 }{ \sqrt { 1 } +\sqrt { 3 } } +\frac { 1 }{ \sqrt { 1 } +\sqrt { 5 } } +\frac { 1 }{ \sqrt { 5 } +\sqrt { 7 } } +$....is

• 3)

The value of the series$\quad \frac { 1 }{ 2 } +\frac { 7 }{ 4 } +\frac { 13 }{ 8 } +\frac { 19 }{ 6 } +$.....is

• 4)

If $\frac { { T }_{ 2 } }{ { T }_{ 3 } }$is the expansion of (a+b)n and $\frac { { T }_{ 3 } }{ { T }_{ 4 } }$ is the expansion of (a+b)n+3 are equal, then n=

• 5)

If in an infinite G. P., first term is equal to 10 times the sum of all successive terms, then its common ratio is

#### 11th Standard Maths First Mid Term Model Question Paper - by Anu - Ramanathapuram - View & Read

• 1)

The number of constant functions from a set containing m elements to a set containing n elements is

• 2)

• 3)

Find a so that the sum and product of the roots of the equation 2x2+(a-3)x+3a-5 = 0 are equal is

• 4)

In a $\triangle$ ABC, C = 90° then the value of sin A + sin B-2$\sqrt{2} cos{A\over2}cos {B\over 2}is$

• 5)

If nPt = 720 nCr, then the value of r =

#### 11th Maths Chapter 4 Combinations and Mathematical Induction Sample Question Paper - by Anu - Ramanathapuram - View & Read

• 1)

The sum of the digits at the 10th place of all numbers formed with the help of 2, 4, 5, 7 taken all at a time is

• 2)

The number of five digit telephone numbers having at least one of their digits repeated is

• 3)

If a2-a C2=a2-a C4 then the value of 'a' is

• 4)

The number of ways to average the letters of the word CHEESE are

• 5)

Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is

#### 11th Standard Maths Chapter 3 Trigonometry Important Question Paper - by Anu - Ramanathapuram - View & Read

• 1)

$\frac { 1 }{ cos{ 80 }^{ 0 } } -\frac { \sqrt { 3 } }{ sin{ 80 }^{ 0 } }$=

• 2)

If tan400=λ, then $\frac { tan{ 140 }^{ 0 }-tan{ 130 }^{ 0 } }{ 1+tan{ 140 }^{ 0 }.tan{ 130 }^{ 0 } }$=

• 3)

$\frac { sin(A-B) }{ cosAcosB } +\frac { sin(B-C) }{ cosBcosC } +\frac { sin(C-A) }{ cosCcosA }$ is

• 4)

If tanx=$\frac { -1 }{ \sqrt { 5 } }$ and x lies in the IV quadrant, then the value of cosx is

• 5)

Which of the following is incorrect?

#### 11th Standard Maths Unit 2 Basic Algebra Important Question Paper - by Anu - Ramanathapuram - View & Read

• 1)

If |x+2| $\le$ 9, then x belongs to

• 2)

Give that x;y and b are real numbers x<y;b>0, then

• 3)

If $\frac { |x-2| }{ x-2 } \ge 0$, then x belongs to

• 4)

The solution 5x-1<24 and 5x+1 > -24 is

• 5)

The solution set of the following inequality |x-1| $\ge$ |x-3| is

#### 11th Maths - Unit 1 Slip Test Question Paper - by Anu - Ramanathapuram - View & Read

• 1)

The number of constant functions from a set containing m elements to a set containing n elements is

• 2)

The function f:[0,2π]➝[-1,1] defined by f(x)=sin x is

• 3)

If the function f:[-3,3]➝S defined by f(x)=x2 is onto, then S is

• 4)

Given A={5,6,7,8}. Which one of the following is incorrect?

• 5)

#### 11th Standard Maths Public Exam March 2019 Important One Mark Questions - by Prishvi - View & Read

• 1)

The number of constant functions from a set containing m elements to a set containing n elements is

• 2)

Let f:R➝R be defined by f(x)=1-|x|. Then the range of f is

• 3)

The function f:R➝R be defined by f(x)=sinx+cosx is

• 4)

Given A={5,6,7,8}. Which one of the following is incorrect?

• 5)

If A = {(x,y) : y = ex, x∈R} and B = {(x,y) : y=e-x, x ∈ R} then n(A∩B) is

#### 11th Standard Maths Public Exam March 2019 Important 5 Marks Questions and Solutions - by Prishvi - View & Read

• 1)

The function for exchanging American dollars for Singapore Dollar on a given day is f(x)=1.23x, where x represents the number of American dollars. On the same day function for exchanging Singapore dollar to Indian Rupee is g(y)=50.50y, Where y represents the number of Singapore dollars. Write a function which will give the exchange rate of American dollars in terms of Indian rupee

• 2)

A simple cipher takes a number and codes it, using the function f(x)=3x-4. Find the inverse of this function, determine whether the inverse is also a function and verify the symmetrical property about the line y=x(by drawing the lines)

• 3)

For the given curve, $y=x^{1\over 3}$given in  figure draw
(i) $y=-x^{ \left( \frac { 1 }{ 3 } \right) }$
(ii) $y=x^{ \left( \frac { 1 }{ 3 } \right) }+1$
(iii) $y=x^{ \left( \frac { 1 }{ 3 } \right) }-1$
(iii) $y=(x+1)^{1\over 3}$

• 4)

Discuss the following relations for reflexivity, symmetricity and transitivity:
Let P denote the set of all straight lines in a plane. The relation R defined by "lRm if l is perpendicular to m".

• 5)

Let A = {a, b, c, d}, B = {a, c, e}, C = {a, e}.
Show that A ∩ (B ∩ C) = (A ∩ B) ∩ C

#### 11th Standard Mathematics Sets, Relations and Functions Important Questions - by Prishvi - View & Read

• 1)

The function f:[0,2π]➝[-1,1] defined by f(x)=sin x is

• 2)

Let f:R➝R be defined by f(x)=1-|x|. Then the range of f is

• 3)

• 4)

Let R be the set of all real numbers. Consider the following subsets of the plane R x R: S = {(x, y) : y =x + 1 and 0 < x < 2} and T = {(x,y) : x - y is an integer} Then which of the following is true?

• 5)

If f:R➝R is given by f(x)=3x-5, then f-1(x) is

#### 11th Standard Maths Public Exam Official Model Question Paper 2019 - by Prishvi - View & Read

• 1)

• 2)

If n((A x B) ∩(A x C)) = 8 and n(B ∩ C) = 2, then n(A) is

• 3)

The value of log3 11.log11 13.log13 15log15 27.log27 81 is

• 4)

The maximum value of 4sin2x+3cos2x+$sin\frac { x }{ 2 } +cos\frac { x }{ 2 }$ is

• 5)

The maximum value of 3 sinθ+4 cosθ is

#### 11th Standard Maths Public Exam March 2019 Model Test Question Paper - by Prishvi - View & Read

• 1)

If two sets A and B have 17 elements in common, then the number of elements common to the set A x B and B x A is

• 2)

The domain of the function $f(x)=\sqrt{ x - 5 }+ \sqrt{6 - x}$is

• 3)

If a and b are the roots of the equation x2-kx+c = 0 then the distance between the points (a, 0) and (b, 0)

• 4)

$\left( 1+cos\frac { \pi }{ 8 } \right) \left( 1+cos\frac { 3\pi }{ 8 } \right) \left( 1+cos\frac { 5\pi }{ 8 } \right) \left( 1+cos\frac { 7\pi }{ 8 } \right)$=

• 5)

In any ΔABC, a(b cosC-c Cos B)=

#### 11th Standard Maths Third Revision Test Question Paper 2019 - by Prishvi - View & Read

• 1)

The function f:[0,2π]➝[-1,1] defined by f(x)=sin x is

• 2)

Which one of the following is false?

• 3)

If a and b are the roots of the equation x2-kx+c = 0 then the distance between the points (a, 0) and (b, 0)

• 4)

If tan400=λ, then $\frac { tan{ 140 }^{ 0 }-tan{ 130 }^{ 0 } }{ 1+tan{ 140 }^{ 0 }.tan{ 130 }^{ 0 } }$=

• 5)

If tanθ=$\frac{-4}{3}$, then sinθ is

#### 11th Standard Maths Public Exam Important Creative Questions and Answers 2019 - by Prishvi - View & Read

• 1)

For real numbers x and y, define xRy if x-y+√2 is an irrational number. Then the relation R is

• 2)

The number of students who take both the subjects Mathematics and Chemistry is 70. This represents 10% of the enrollment in Mathematics and 14% of the enrollment in Chemistry. The number of students take at least one of these two subjects, is

• 3)

If $\frac { |x-2| }{ x-2 } \ge 0$, then x belongs to

• 4)

If sin(45 ° + 10°) - sin(45° -10°) =$\sqrt{2}$sin x then x is

• 5)

If $\alpha$ and $\beta$ are two values of θ obtained from the equation a cosθ+b sinθ=c then the value of $tan(\frac{\alpha+\beta}{2})$ is

#### 11th Standard Maths Public Exam Model Question Paper March 2019 - by Prishvi - View & Read

• 1)

If n((A x B) ∩(A x C)) = 8 and n(B ∩ C) = 2, then n(A) is

• 2)

If A = {x / x is an integer, x2 $\le$ 4} then elements of A are

• 3)

If 8 and 2 are the roots of x2+ax+c=0 and 3,3 are the roots of x2+dx+b=0;then the roots of the equation x2+ax+b = 0 are

• 4)

If $\pi <2\theta <\frac { 3\pi }{ 2 }$, then $\sqrt { 2+\sqrt { 2+2\quad cos4\theta } }$ equals to

• 5)

2 sin 5x cos x

#### 11th Maths Revision test Introduction to Probability Important 2 Mark Questions - by Palanivel - View & Read

• 1)

If A and B are two independent events such that, P(A)=0.4 and P$(A\cup B)$=0.9. Find P(B).

• 2)

A factory has two Machines-I and II. Machine-I produces 60% of items and Machine-II produces 40% of the items of the total output. Further 2% of the items produced by Machine-I are defective whereas 4% produced by Machine-II are defective. If an item is drawn at random what is the probability that it is defective?

• 3)

There are two identical urns containing respectively 6 black and 4 red balls, 2 black and 2 red balls. An urn is chosen at random and a ball is drawn from it.
(i) find the probability that the ball is black
(ii) if the ball is black, what is the probability that it is from the first urn?

• 4)

An experiment has the four possible mutually exclusive and exhaustive outcomes A, B, C, and D. Check whether the following assignments of probability are permissible.
P(A) =$\frac { 2 }{ 3 }$,  P(B)=$\frac { 3 }{ 5 }$,  P(C)=-$\frac { 1 }{ 5 }$,  P(D) =$\frac { 1 }{ 5 }$

• 5)

Five mangoes and 4 apples are in a box. If two fruits are chosen at random, find the probability that (i) one is a mango and the other is an apple (ii) both are of the same variety

#### +1 Maths Half Yearly Model Question Paper - by Prishvi - View & Read

• 1)

Let R be a relation on the set N given by R={(a,b):a=b-2, b>6}. Then

• 2)

If n(A) = 2 and n(B ∪ C) = 3, then n[(A x B) ∪ (A x C)] is

• 3)

If a and b are the roots of the equation x2-kx+c = 0 then the distance between the points (a, 0) and (b, 0)

• 4)

$\left( 1+cos\frac { \pi }{ 8 } \right) \left( 1+cos\frac { 3\pi }{ 8 } \right) \left( 1+cos\frac { 5\pi }{ 8 } \right) \left( 1+cos\frac { 7\pi }{ 8 } \right)$=

• 5)

Which of the following is incorrect?

#### 11th Maths First Revision Test Questions and Answers - by Prishvi - View & Read

• 1)

If n((A x B) ∩(A x C)) = 8 and n(B ∩ C) = 2, then n(A) is

• 2)

$n(A\cap B)=4$ and $(A\cup B)=11$ then $n(p(A\triangle B))$ is:

• 3)

The value of ${ log }_{ 3 }\frac { 1 }{ 81 }$ is

• 4)

The quadratic equation whose roots are tan75° and cot75° is:

• 5)

The numerical value of tan-11+tan-12+tan-13=

#### Integral Calculus Important Questions from the 11th Stateboard Mathematics - by Prishvi - View & Read

• 1)

If $\int {3^{1\over x}\over x^2}dx=k(3^{1\over x})+c$ ,then the value of k is

• 2)

$\int sin^3 \ xdx$ is

• 3)

$\int {dx\over e^x-1}$is

• 4)

$\int {sec^2x\over tan^2 \ x-1}$ dx

• 5)

$\int {1\over x\sqrt{(log \ x)^2+5}}dx$is

#### Introduction To Probability Theory Important Questions from 11th Maths - by Prishvi - View & Read

• 1)

A, B, and C try to hit a target simultaneously but independently. Their respective probabilities of hitting the target are${3\over4},{1\over2},{5\over 8}$. The probability that the target is hit by A or B but not by C is

• 2)

A bag contains 5 white and 3 black balls. Five balls are drawn successively without replacement. The probability that they are alternately of different colours is

• 3)

If two events A and B are independent such that P(A)=0.35 and $P(A\cup B)=0.6$ ,then P(B) is

• 4)

If m is a number such that m $\le$ 5, then the probability that quadratic equation 2x2+2mx+m+1=0 has real roots is

• 5)

A speaks truth in 75% cases and B speaks truth in 80% cases. Probability that they contradict each other in a statement is

#### Plus One Maths One Marks Revision Test - by Prishvi - View & Read

• 1)

The inverse of f(x)=$\begin{cases} x\quad if\quad x<1 \\ { x }^{ 2 }\quad if\quad 1\le x\le 4 \\ 8\sqrt { x } \quad if\quad x>4 \end{cases}$ is

• 2)

• 3)

If $f:[-2,2]\rightarrow A$ is given by f(x)=33 then f is onto, if A is:

• 4)

Which one of the following statements is false? The graph of the function $f(x)={1\over x}$

• 5)

Which one of the following is false?

#### 11th Mathematics Half yearly Model Question Paper 1 - by Prishvi - View & Read

• 1)

• 2)

Let X = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 3), (2, 2), (3, 3), (2, 1), (3, 1), (1, 4),(4, 1)}. Then R is

• 3)

If A = {x / x is an integer, x2 $\le$ 4} then elements of A are

• 4)

Solve $\sqrt{7+6x-x^2}=x+1$

• 5)

For the below figure of ax2 + bx + c = 0

#### Differential Calculus Important Five Marks Question In 11th Maths - by Prishvi - View & Read

• 1)

Check if $lim_{x\rightarrow-58}f(x)$exists or not, where

• 2)

• 3)

Evaluate the following limits :
$lim_{x\rightarrow5}{\sqrt{x-1}-2\over x-5}$

• 4)

Evaluate the following limits :$lim_{x\rightarrow 0}{\sqrt{1+sin x}-\sqrt{1-sinx}\over tanx}$

• 5)

State how continuity is destroyed at x= xofor each of the following graphs.

#### 11th Maths Important Five Mark Question Paper 3 - by Prishvi - View & Read

• 1)

If $\lambda \hat{i}+2\lambda \hat{j}+2\lambda \hat{k}$ is a unit vector, then the value of $\lambda$is

• 2)

If $\overrightarrow{a}=\hat{i}+2\hat{j}+2\hat{k},|\overrightarrow{b}|=5$ and the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is ${\pi\over 6},$ then the area of the triangle formed by these two vectors as two sides, is

• 3)

$lim_{x\rightarrow o}{8^x-4^x-2^x+1^x\over x^2}=$

• 4)

$lim_{n \rightarrow \infty}({1\over n^2}+{2\over n^2}+{3\over n^2}+..+{n\over n^2})$ is

• 5)

The function is not defined for x = −1. The value of ( 1) f − so that the function extended by this value is continuous is

#### 11th standard Maths- Important question-Trigonometry,Combinations and Mathematical Induction - by Prishvi - View & Read

• 1)

$\frac { 1 }{ cos{ 80 }^{ 0 } } -\frac { \sqrt { 3 } }{ sin{ 80 }^{ 0 } }$=

• 2)

If cos280+sin280=k3, then cos 170 is equal to

• 3)

$\frac { cos6x+6cos4x+15cos2x+10 }{ cos5x+5cos3x+10cosx }$ equal to

• 4)

cos350+cos850+cos1550=

• 5)

sin$(22{1\over 2}^o)$is

#### 11th standard maths-Important question-Sets, Relations and Functions,Basic Algebra - by Prishvi - View & Read

• 1)

Let f:R➝R be defined by f(x)=1-|x|. Then the range of f is

• 2)

For real numbers x and y, define xRy if x-y+√2 is an irrational number. Then the relation R is

• 3)

Let R be the set of all real numbers. Consider the following subsets of the plane R x R: S = {(x, y) : y =x + 1 and 0 < x < 2} and T = {(x,y) : x - y is an integer} Then which of the following is true?

• 4)

If f:R➝R is given by f(x)=3x-5, then f-1(x) is

• 5)

Let R be the universal relation on a set X with more than one element. Then R is

#### 11th Standard Maths Combinatorics and Mathematical Induction and Binomial Theorem, Sequences And Series important 5 Mark Questions - by Prishvi - View & Read

• 1)

Prove that 2nCn =  $\frac { { 2 }^{ n }\times 1\times3\times ...(2n-1) }{ n! }$

• 2)

Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly three aces in each combination.

• 3)

Prove 1.3+2.32+3.33+...+n-3n=$\frac{(2n-1)3^{n+1}+3}{4}$ for all n ∈ N

• 4)

Prove that the sum of the first n non-zero even numbers is n2 + n,

• 5)

n2 - n is divisible by 6, for each natural number n $\ge$ 2.

#### 11th Maths Important Five Mark Question Paper 4 - by Prishvi - View & Read

• 1)

Let A={1,2,3,4} and B = {a,b,c,d}. Give a function from A$\rightarrow$B for each of the following:
neither one- to -one and nor onto.

• 2)

Let A={1,2,3,4} and B = {a,b,c,d}. Give a function from A$\rightarrow$B for each of the following:
not one-to-one but onto.

• 3)

Let A={1,2,3,4} and B = {a,b,c,d}. Give a function from A$\rightarrow$B for each of the following:
one-to-one but not onto.

• 4)

Find the largest possible domain of the real valued function f(x)=$\frac { \sqrt { 4-{ x }^{ 2 } } }{ \sqrt { { x }^{ 2 }-9 } }$

#### 11th Maths Pre Half Yearly Question Paper - by Prishvi - View & Read

• 1)

There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two points is

• 2)

In a plane there are 10 points are there out of which 4 points are collinear, then the number of triangles formed is

• 3)

If nC4,nC5,nC6 are in AP the value of n can be

• 4)

The number of different signals which can be give from 6 flags of different colours taking one or more at a time is

• 5)

The product of r consecutive positive integers is divisible by

#### 11th Maths Important One Mark Question Paper - 2 - by Prishvi - View & Read

• 1)

The sum of the digits at the 10th place of all numbers formed with the help of 2, 4, 5, 7 taken all at a time is

• 2)

In a plane there are 10 points are there out of which 4 points are collinear, then the number of triangles formed is

• 3)

In 2nC3 : nC3 = 11 : 1 then n is

• 4)

The product of r consecutive positive integers is divisible by

• 5)

There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is

#### 11th Maths Important One Mark Question Paper 3 - by Prishvi - View & Read

• 1)

$\frac { 1 }{ cos{ 80 }^{ 0 } } -\frac { \sqrt { 3 } }{ sin{ 80 }^{ 0 } }$=

• 2)

cos2ፀ cos2ф+sin2(ፀ-ф)-sin2(ፀ+ф) is equal to

• 3)

$\frac { cos6x+6cos4x+15cos2x+10 }{ cos5x+5cos3x+10cosx }$ equal to

• 4)

The angle between the minute and hour hands of a clock at 8.30 is

• 5)

If tanA=$\frac { a }{ a+1 }$ and B=$\frac { 1 }{ 2a+1 }$ then the value of A+B is

#### 11th Maths Important One Mark Question Paper 2 - by Prishvi - View & Read

• 1)

The number of constant functions from a set containing m elements to a set containing n elements is

• 2)

The function f:[0,2π]➝[-1,1] defined by f(x)=sin x is

• 3)

Let X={1,2,3,4}, Y={a,b,c,d} and f={f(1,a),(4,b),(2,c),(3,d),(2,d)}. Then f is

• 4)

For real numbers x and y, define xRy if x-y+√2 is an irrational number. Then the relation R is

• 5)

Let R be the relation over the set of all straight lines in a plane such that l1Rl2 ⇔ l1丄l2 . Then  R is

#### 11th Maths Important Three Mark Question Paper - 5 - by Prishvi - View & Read

• 1)

Find the principal value of $sin^{ -1 }\left( \frac { 1 }{ \sqrt { 2 } } \right)$.

• 2)

An airplane propeller rotates 1000 times per minute. Find the number of degree that a point on the edge of the propeller will rotate in 1 second

• 3)

Find the principal solution and general solutions of the following:sin$\theta$=$-\frac { 1 }{ \sqrt { 2 } }$

• 4)

Prove that $\sin { 4\alpha } =4\tan { \alpha } .\frac { 1-\tan ^{ 2 }{ \alpha } }{ { \left( 1+\tan ^{ 2 }{ \alpha } \right) }^{ 2 } }$

• 5)

Show that $\cot { \left( 7\frac { 1° }{ 2 } \right) } =\sqrt { 2 } +\sqrt { 3 } +\sqrt { 4 } +\sqrt { 6 }$

#### 11th Maths Important Three Mark Question Paper - 1 - by Prishvi - View & Read

• 1)

Prove that the relation "less than or equal to" (<) on the set R of real numbers is antisymmetric.

• 2)

On the set of natural number let R be the relation defined by aRb if 2a + 3b = 30. Write down the relation by listing all the pairs. Check whether it is symmetric

• 3)

Write a description of each shaded area. Use symbols U, A, B, C, U, ∩, ' and \ as necessary.

• 4)

Check the following functions for one-to-oneness and ontoness.
$f:R\rightarrow R$ defined by f(n) = n2.

• 5)

Find the range of the following functions given by  $f(x) = \frac { 1 }{ 2-sin\ 3x } .$

#### 11th Maths Important Three Mark Question Paper - by Prishvi - View & Read

• 1)

If (n-1)P3:nP4 =1 :10,find n

• 2)

Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?

• 3)

If (n+2)C7 : (n-1)P4 = 13 : 24 find n.

• 4)

Five boys and 5 girls form a line. Find the number of ways of making the seating arrangement under the following condition.

 C1 C2 (a) Boys and girls sit alternate (i) 5! x 6! (b) No two girls sit together (ii) 10! - 5! 6! (c) All the girls sit together (iii) (5 !)2 + (5!)2 (d) All the girls are never together (iv) 2! 5! 5!
• 5)

Write the nth term of the following sequences
2,2,4,4,6,6

#### 11th Maths Important Two Mark Question Paper - 2 - by Prishvi - View & Read

• 1)

Write the following in roster form.
{x$\in$N:x2<121 and x is a prime}.

• 2)

Write the following in roster form.
The set of all positive roots of the equation (x-1)(x+1)(x2-1)=0.

#### 11th Standard Maths Model Question Paper - by Prishvi - View & Read

• 1)

The value of $\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{DA}+\overrightarrow{CD}$ is

• 2)

If $\overrightarrow{a}+2\overrightarrow{b}$ and $3\overrightarrow{a}+m\overrightarrow{b}$ are parallel, then the value of m is

• 3)

If $\overrightarrow{r}={9\overrightarrow{a}+7\overrightarrow{b}\over16}$ ,then the point P whose position vector $\overrightarrow{r}$divides the line joining the points with position vectors $\overrightarrow{a}$and $\overrightarrow{b}$ in the ratio

• 4)

Two vertices of a triangle have position vectors $3\hat{i}+4\hat{j}-4\hat{k}$ and$2\hat{i}+3\hat{j}+4\hat{k}$If the position vector of the centroid is $\hat{i}+2\hat{j}+3\hat{k}$ ,then the position vector of the third vertex is

• 5)

If $|\overrightarrow{a}|=13,|\overrightarrow{b}|=5$  and $\overrightarrow{a}.\overrightarrow{b}=60^o$ then $|\overrightarrow{a}\times\overrightarrow{b}|$ is

### TN Stateboard Education Study Materials

#### 11th Maths Chapter 6 Two Dimensional Analytical Geometry One Mark - by Anu - Ramanathapuram Sep 24, 2019 Sep 24, 2019

Two Dimensional Analytical Geometry One Mark

#### 11th Maths Chapter 5 Binomial Theorem Sequences And Series One Mark - by Anu - Ramanathapuram Sep 24, 2019 Sep 24, 2019

Binomial Theorem Sequences And Series One Mark

#### 11th Maths Chapter 4 Combinations And Mathematical Induction One Mark - by Anu - Ramanathapuram Sep 24, 2019 Sep 24, 2019

Chapter 4 Combinations And Mathematical Induction One Mark

#### 11th Maths Chapter 3 Trigonometry One Mark - by Anu - Ramanathapuram Sep 24, 2019 Sep 24, 2019

Chapter 3 Trigonometry One Mark

#### 11th Maths Chapter 2 Basic Algebra One Mark - by Anu - Ramanathapuram Sep 24, 2019 Sep 24, 2019

Basic Algebra One Mark

#### 11th Maths Chapter 1 Sets Relations And Functions One Mark - by Anu - Ramanathapuram Sep 23, 2019 Sep 23, 2019

Sets Relations And Functions One Mark

### TN Stateboard Updated Class 11th Maths Syllabus

#### Sets, Relations and Functions

Introduction-Sets-Cartesian Product-Constants and Variables, Intervals and Neighborhoods-Relations-Functions-Graphing Functions Using Transformations

#### Basic Algebra

Introduction-Real Number System-Absolute Value-Linear Inequalities-Quadratic Functions-Polynomial Functions-Rational Functions-Exponents and Radicals-Logarithm-Application of Algebra in Real Life

#### Trigonometry

Introduction-A Recall of Basic Results-Radian Measure-Trigonometric Functions and Their Properties-Trigonometric Identities-Trigonometric Equations-Properties of Triangle-Application to Triangle-Inverse Trigonometric Functions

#### Combinations and Mathematical Induction

Introduction-Fundamental Principles of Counting-Factorials-Permutations-Combinations-Mathematical Induction

#### Binomial Theorem, Sequences and Series

Introduction-Binomial Theorem-Particular Cases of Binomial Theorem-Finite Sequences-Finite Series-Infinite Sequences and Series

#### Two Dimensional Analytical Geometry

Introduction-Locus of a Point-Straight Lines-Angle between Two Straight Lines-Pair of Straight Lines

#### TN StateboardStudy Material - Sample Question Papers with Solutions for Class 11 Session 2019 - 2020

Latest Sample Question Papers & Study Material for class 11 session 2019 - 2020 for Subjects Commerce, Economics, Biology, Business Maths, Accountancy, Computer Science, Physics, Chemistry, Computer Applications , History , Computer Technology in PDF form to free download [ available question papers ] for practice. Download QB365 Free Mobile app & get practice question papers.

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