100 MCQ of Maths of Class 11

Section A (Multiple Choice Questions – 1 mark each)

Mark the Correct alternative in the following: The value of $\left(\cot \frac{\pi}{2}-\tan \frac{\pi}{2}\right)^{2}(1-2 \tan x \cot 2 x)$ is

a) 4

b) 1

c) 5

d) 3

Ans: (c) 4

Explanation:

Given to find the value of $\displaystyle {{\left( {\cot \frac{x}{2}-\tan \frac{x}{2}} \right)}^{2}}\left( {1-2\tan x\cot 2x} \right)$

We will solve the expression in two parts,

Now Solving 1^st term = $\displaystyle {{\left( {\frac{1}{{\tan \frac{x}{2}}}-\tan \frac{x}{2}} \right)}^{2}}$

= $\displaystyle {{\left( {\frac{{1-{{{\tan }}^{2}}\frac{x}{2}}}{{\tan \frac{x}{2}}}} \right)}^{2}}$

If multiply and divide the term by 2, we get,

= $\displaystyle {{\left( {\frac{{2\left( {1-{{{\tan }}^{2}}\frac{x}{2}} \right)}}{{2\tan \frac{x}{2}}}} \right)}^{2}}$

Using the formula for $\displaystyle \cot 2x=\frac{{1-{{{\tan }}^{2}}x}}{{2\tan x}}$ and $\displaystyle \cot x=\frac{1}{{\tan x}}$

Solve the 2^nd term

$\displaystyle \left( {1-2\tan x\cos x} \right)$

= $\displaystyle 1-2\tan x\left( {\frac{{1-{{{\tan }}^{2}}x}}{{2\tan x}}} \right)$

Using the formula $\displaystyle \cot 2x=\left( {\frac{{1-{{{\tan }}^{2}}x}}{{2\tan x}}} \right)$

$\displaystyle 1-2\tan x\cot 2x$

= $\displaystyle 1-\left( {1-{{{\tan }}^{2}}x} \right)$

= $\displaystyle 1-1+{{\tan }^{2}}x$

= $\displaystyle {{\tan }^{2}}x$

Now combining

$\displaystyle {{\left( {\cot \frac{x}{2}-\tan \frac{x}{2}} \right)}^{2}}\left( {1-2\tan x\cot x} \right)$ = $\displaystyle \frac{4}{{{{{\tan }}^{2}}x}}\left( {{{{\tan }}^{2}}x} \right)$

= 4

If R is a relation on the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9} given by $x R y \Leftrightarrow y=3 x$ , then R =

a) {(3, 1), (2, 6), (3, 9)}

b) {(3, 1), (6, 2), (9, 3)}

c) {(3, 1), (6, 2), (8, 2), (9, 3)}

d) none of these

Ans (d) none of these

Explanation:

For A = {1, 2, 3, 4, 5, 6, 7, 8, 9} the satisfying complete relation is: R={(1,3),(2,6),(3,9)}

A digit is selected at random from either of the two sets {1, 2, 3, 4, 5, 6, 7, 8, 9} and {1, 2, 3, 4, 5, 6, 7, 8, 9}. What is the chance that the sum of the digits selected is 10?

a) $\frac{1}{9}$

b) $\frac{9}{81}$

c) $\frac{10}{18}$

d) $\frac{10}{81}$

Ans. (a) $\displaystyle \frac{1}{9}$

Explanation:

Let A—{1, 2, 3,4,5,6,7, 8, 9} then, n (A A) = g²

Let B be the event that sum of the digits is 10. Then,

B ={(1,9), (9, 1), (4,6), (6, 4), (8, 2), (2, 8), (7, 3), (3, 7), (5, 5))

Required probability = $\displaystyle \frac{{n\left( B \right)}}{{n\left( {A\times A} \right)}}=\frac{9}{{{{9}^{2}}}}=\frac{1}{9}$

If $y=\frac{1+\frac{1}{x}}{1-\frac{1}{x}}$ , then $\frac{d y}{d x}$ is equal to

a) $\frac{4 x}{\left(x^{2}-1\right)^{2}}$

b) $\frac{2 x}{\left(x^{2}-1\right)^{2}}$

c) $\frac{-4 x}{\left(x^{2}-1\right)^{2}}$

d) $\frac{-2 x}{\left(x^{2}-1\right)^{2}}$

Ans (c) $\displaystyle \frac{{-4x}}{{{{{\left( {{{x}^{2}}-1} \right)}}^{2}}}}$

Explanation:

Given

$\displaystyle y=\frac{{1+\frac{1}{{{{x}^{2}}}}}}{{1-\frac{1}{{{{x}^{2}}}}}}$

$\displaystyle \Rightarrow$ $\displaystyle y=\frac{{{{x}^{2}}+1}}{{{{x}^{2}}-1}}$

$\displaystyle \therefore \frac{{dy}}{{dx}}=\frac{{\left( {{{x}^{2}}-1} \right).2x-\left( {{{x}^{2}}+1} \right).2x}}{{{{{\left( {{{x}^{2}}-1} \right)}}^{2}}}}$

= $\displaystyle \frac{{2x\left( {{{x}^{2}}-1-{{x}^{2}}-1} \right)}}{{{{{\left( {{{x}^{2}}-1} \right)}}^{2}}}}$ = $\displaystyle \frac{{2x\left( {-2} \right)}}{{{{{\left( {{{x}^{2}}-1} \right)}}^{2}}}}$ = $\displaystyle \frac{{-4x}}{{{{{\left( {{{x}^{2}}-1} \right)}}^{2}}}}$

Given the three straight lines with equations $5 x+4 y=0, x+2 y-10=0$ and $2 x+y+5=0$ , then these lines are

a) the sides of an equilateral triangle

b) the sides of an isosceles triangle

c) the sides of a right angled triangle

d) concurrent

Ans (d) concurrent Explanation:

The lines are said to be concurrent $\displaystyle \left| {\begin{array}{*{20}{c}} 5 & 4 & 0 \\ 1 & 2 & {-10} \\ 2 & 1 & 5 \end{array}} \right|=0$

On expanding we get

5(10 + 10) – 4(5 + 20) + 0 = 0

Hence the lines are concurrent.

Let A and B be two non-empty subsets of a set X such that A is not a subset of B, then

a) A and the complement of B are always non-disjoint

b) A is always a subset of B

c) A and B are always disjoint

d) B is always a subset of A

Ans (a) A and the complement of B are always non-disjoint

Explanation:

Let x∈ A, then x ∉B as A is not a subset of B

x ∈ A and x ∉B

x ∈ A and x ∈ B’

x ∈ A ⋂ B’

A and B’ are non – disjoint.

Mark the correct answer for $3 i^{34}+5 i^{27}-2 i^{38}+5 i^{41}=$ ?

a) $1$

b) $i$

c) $-i$

d) $10 i$

The domain of the function $f(x)=\log _{3+x}\left(x^{2}-1\right)$ is

a) $(-3,-2) \cup(-2,1) \cup(1, \infty)$

b) $[-3,-1] \cup[1, \infty)$

c) $(-3,-1) \cup(1, \infty)$

d) $[-3,-2) \cup(-2,-1] \cup[1, \infty)$

If $x<7$ , then

a) $-\infty>x>-7$

b) $-\infty \geq x \geq-7$

c) $x<-7$

d) $-x \leq-7$

$\frac{\cos x}{1-\sin x}=$ ?

a) $\tan \left(\frac{\pi}{4}+x\right)$

b) $\tan \frac{x}{2}$

c) $\tan \left(\frac{\pi}{4}-\frac{x}{2}\right)$

d) $\tan \frac{\pi}{2}$

If A ⊂ B, then

a) $A^{c} \subset B^{c}$

b) $B^{c} \not\subset A^{c}$

c) $A^{c}=B^{c}$

d) $B^{c} \subset A^{c}$

If $a, x, b$ are in GP then

a) $x= \frac{a+b}{2}$

b) $x=ab$

c) $x^2 = ab$

d) $x = \frac{1}{2}(a+b)$

$(\sqrt{5}+1)^{4}+(\sqrt{5}-1)^{4}$ is

a) an irrational number

b) a negative real number

c) a rational number

d) a negative integer

If $a, b, c$ are real numbers such that $a>b, c<0$

a) $ac>bc$

b) $ac<bc$

c) $ac \geq bc$

d) $ac \not\ge bc$

If A = { $x : x \ne x$ } represents

a) {1}

b) { }

c) {x}

d) {0}

The value of $\cos 12^{\circ}+\cos 84^{\circ}+\cos 156^{\circ}+\cos 132^{\circ}$ is

a) $-\frac{1}{2}$

b) $\frac{1}{2}$

c) $1$

d) $\frac{1}{2}$

The complex number $z$ such that $\left|\frac{z-5 i}{z+5 i}\right|=1$ lies on

a) the y-axis

b) Negative axis

c) A circle

d) The x-axis

How many different committees of 5 can be formed from 6 men and 4 women on which exact 3 men and 2 women serve?

a) 20

b) 6

c) 60

d) 120

Assertion-Reason Based Questions (1 mark each)

In question numbers 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option.

Assertion (A): The expansion of $(1+x)^{n}=n C_{0}+n C_{1} x+n C_{2} x^{2}+\ldots+n C_{n} x^{n}$ . Reason (R): If $x=-1$ , then the above expansion is zero.

a) Both A and R are true and R is the correct explanation of A.

b) Both A and R are true but R is not the correct explanation of A.

c) A is true but R is false.

d) A is false but R is true.

Consider the following data:

$x_i$	4	8	11	17	20	24	32
$f_i$	3	5	9	5	4	3	1

Assertion (A): The variance of the data is 45.8.

Reason (R): The standard deviation of the data is 6.77.

a) Both A and R are true and R is the correct explanation of A.

b) Both A and R are true but R is not the correct explanation of A.

c) A is true but R is false.

d) A is false but R is true.

If $\tan x = x-\frac{1}{4 x}$ , then $\sec x - \tan x$ is equal to

a) $2x$

b) $\frac{1}{2x}$

c) $\frac{-1}{2x}$

d) $\frac{1}{2x}, \frac{-1}{2x}$

If $2 f(x)-3 f\left(\frac{1}{x}\right)=x^{2}(x \ne 0)$ Then $f(2)$ is equal to

a) $-1$

b) $\frac{5}{2}$

c) $-\frac{7}{4}$

d) $2$

Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.

a) $\frac{25}{102}$

b) $\frac{27}{102}$

c) $\frac{1}{102}$

d) $\frac{26}{51}$

If $y=\log \left(x+\sqrt{1+x^{2}}\right)$ then $\frac{d y}{d x}$ is equal to

a) $\frac{x}{\sqrt{(x^{2}+1)^{2}}}$

b) $\frac{x^{2}}{\sqrt{x^{2}+1}}$

c) $\frac{1}{\sqrt{x^{2}+1}}$

d) $\frac{x^{2}}{(x^{2}+1)^{3/2}}$

The area of a triangle formed by the lines $y=x, y=2x$ and $y=3x+4$ is

a) $8$

b) $7$

c) $9$

d) $4$

Let $F_1$ be the set of parallelograms, $F_2$ the set of rectangles, $F_3$ the set of rhombuses, $F_4$ the set of squares and $F_5$ the set of trapeziums in a plane. Then $F_1$ may be equal to

a) $F_2 \cap F_3$

b) $F_3 \cup F_4$

c) $F_2 \cup F_5$

d) $F_2 \cup F_3 \cup F_4 \cup F_1$

If $z=x+iy; x, y \in R$ then:

a) $z\bar{z} < |z|^2$

b) $z\bar{z} = |z|^2$

c) $z\bar{z} > |z|^2$

d) $z\bar{z} \ne |z|^2$

If A = { $x : x^2-5x+6=0$ }, B = {2, 4}, C = {4, 5} then A x ( $B \cap C$ ) is

a) (4, 2), (4, 3)

b) (2, 2), (3, 3), (4, 4), (5, 5)

c) (2, 4), (3, 4), (4, 4)

d) {(2, 4), (3, 4)}

The solution set of $6x-1 > 5$ is:

a) { $x: x>1, x \in N$ }

b) { $x: x>1, x \in R$ }

c) { $x: x<1, x \in N$ }

d) { $x: x<1, x \in W$ }

The extremum values of $\sin \theta$ are

a) $0$ and $1$

b) $-1$ and $0$

c) $-1$ and $1$

d) $-\frac{1}{\sqrt{2}}$ and $\frac{1}{\sqrt{2}}$

If A = {1, 3, 5, 7, 9, 11, 13, 15, 17}, B = {2, 4, …, 18} and N the set of natural numbers is the universal set, then A’ $\cup$ (A $\cup$ B)’ is

a) A

b) B

c) $\phi$

d) N

Sum of an infinitely many terms of a G.P. is 3 times the sum of even terms. The common ratio of the G.P. is

a) $\frac{1}{3}$

b) $\frac{2}{3}$

c) $\frac{1}{4}$

d) $\frac{1}{2}$

If A and B are the sums of odd and even terms respectively in the expansion of $(x+a)^n$ , then $(x+a)^{2n} + (x-a)^{2n}$ is equal to

a) AB

b) $4AB$

c) $4 (A-B)$

d) $4 (A+B)$

If $X < 5$ , then

a) $-x > -5$

b) none of these.

c) $-x < 5$

d) $x > -5$

If A, B, C be any three sets such that $A \cup B = A \cup C$ and $A \cap B = A \cap C$ , then

a) $B = C$

b) $A = B = C$

c) $A = C$

d) $A = B$

If $3 \sin x + 4 \cos x = 5$ , then $4 \sin x - 3 \cos x =$

a) $1$

b) $5$

c) $3$

d) $0$

If $z = x+yi; x, y \in R$ , then locus of the equation $b\bar{z} + bz = c$ , where $c \in R$ and $b \in C, b \ne 0$ are fixed, is

a) a parabola

b) a straight line

c) a circle

d) a hyperbola

The number of all 4 digit numbers which are all different that can be formed by using the digits 0, 2, 3, 5, 8, 9 is

a) 660

b) 360

c) 1080

d) 300

Assertion-Reason Based Questions (1 mark each)

A statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option.

Assertion (A): The expansion of $(1+x)^{n}=n C_{0}+n C_{1} x+n C_{2} x^{2}+\ldots+n C_{n} x^{n}$ . Reason (R): If $x = -1$ , then the above expansion is zero.

a) Both A and R are true and R is the correct explanation of A.

b) Both A and R are true but R is not the correct explanation of A.

c) A is true but R is false.

d) A is false but R is true.

Assertion (A): If each of the observations $x_1, x_2, ..., x_n$ is increased by a, where a is a negative or positive number, then the variance remains unchanged. Reason (R): Adding or subtracting a positive or negative number to (or from) each observation of a group does not affect the variance.

a) Both A and R are true and R is the correct explanation of A.

b) Both A and R are true but R is not the correct explanation of A.

c) A is true but R is false.

d) A is false but R is true.

41. If a tan θ = b, then $\displaystyle \left( {\frac{{b\sin \theta -a\cos \theta }}{{b\sin \theta +a\cos \theta }}} \right)$ = ?
a) $\displaystyle \frac{{\left( {{{b}^{2}}-{{a}^{2}}} \right)}}{{\left( {{{b}^{2}}+{{a}^{2}}} \right)}}$
b) $\displaystyle \frac{{\left( {{{a}^{2}}-{{b}^{2}}} \right)}}{{\left( {{{a}^{2}}+{{b}^{2}}} \right)}}$
c) $\displaystyle \frac{{\left( {{{b}^{2}}+{{a}^{2}}} \right)}}{{\left( {{{b}^{2}}-{{a}^{2}}} \right)}}$
d) $\displaystyle \frac{{\left( {{{a}^{2}}+{{b}^{2}}} \right)}}{{\left( {{{a}^{2}}-{{b}^{2}}} \right)}}$

42. The domain of the function f defined by $\displaystyle f\left( x \right)=\sqrt{{4-x}}+\frac{1}{{\sqrt{{{{x}^{2}}-1}}}}$ is equal to
a) $\displaystyle \left( {-\infty ,-1} \right)\bigcup \left[ {1,4} \right)$
b) $\displaystyle \left( {-\infty ,-1} \right]\bigcup \left( {1,4} \right)$
c) $\displaystyle \left( {-\infty ,-1} \right]\bigcup \left( {1,4} \right]$
d) $\displaystyle \left( {-\infty ,-1} \right)\bigcup \left[ {1,4} \right]$
43. Consider the following statements:
If A and B are exhaustive events, then their union is the sample space.
If A and B are exhaustive events, then their intersection must be an empty space. Which of the above statement(s) is/are correct?
a) Neither i nor ii
b) Both i and ii
c) Only i
d) Only ii
44. $\displaystyle \underset{{x\to 2}}{\mathop{{\lim }}}\,\frac{{\sqrt{{1+\sqrt{{2+x}}}}-\sqrt{3}}}{{x-2}}$ is equal to
a) $\displaystyle \frac{1}{{8\sqrt{3}}}$
b) $\displaystyle 8\sqrt{3}$
c) $\displaystyle \sqrt{3}$
d) $\displaystyle \frac{1}{{\sqrt{3}}}$
45. The point on the axis of y which is equidistant from (−1, 2) and (3, 4) is
a) (0, 4)
b) (4, 0)
c) (5, 0)
d) (0, 5)
46. If the point P(a, b, 0) lies on the line $\displaystyle \frac{{x+1}}{2}=\frac{{y+2}}{3}=\frac{{z+3}}{4}$ , then (a, b) is:
a) (1, 2)
b) (0, 0)
c) $\displaystyle \left( {\frac{1}{2},\frac{2}{3}} \right)$
d) $\displaystyle \left( {\frac{1}{2},\frac{1}{4}} \right)$
47. The angle between the two straight lines $\displaystyle 6{{y}^{2}}-xy-{{x}^{2}}+30y+36=0$ is
a) 30°
b) 50°
c) 45°
d) 60°
48. If A = {1, 2, 3}, B = {x, y} Then the number of functions that can be defined from A into B is.
a) 12
b) 8
c) 8
d) 3
49. The solution set for |x| > 7 is
a) (−∞, 7) U (7, ∞)
b) (−7, ∞)
c) (7, ∞)
d) (−∞, −7) U (7, ∞)
50. If θ lies in quadrant II, then $\displaystyle \sqrt{{\frac{{1-\sin \theta }}{{1+\sin \theta }}}}-\sqrt{{\frac{{1+\sin \theta }}{{1-\sin \theta }}}}$ is equal to
a) cot θ
b) tan θ
c) 2cot θ
d) 2tan θ
51. Let S = set of points inside the square, T = the set of points inside the triangle and C = the set of points inside the circle. If the triangle and circle intersect each other and are contained in a square. Then
a) S ∩ T = S ∩ C
b) S ∩ T ∩ C = φ
c) S ∪ T ∪ C = C
d) S ∪ T ∪ C = S
52. Two positive numbers are in the ratio $\displaystyle \left( {2+\sqrt{3}} \right)$ : $\displaystyle \left( {2-\sqrt{3}} \right)$ . The ratio of their A.M. to G.M. is:
a) 1 : 2
b) 2 : 1
c) $\displaystyle \sqrt{3}:2$
d) $\displaystyle \sqrt{3}:1$
53. The number 111111………….1 (91 times)
a) is not an odd number
b) is an even number
c) is not a prime
d) has a factor as 6
54. Solve the system of inequalities: $\displaystyle \frac{{x+7}}{{x-8}}>2,\frac{{2x+1}}{{7x-1}}>5$
a) (4, 8)
b) (3, 6)
c) no solution
d) (2, 5)
55. If aN = {ax : x ∈ N}, then the set 3N ∩ 7N is
a) 10N
b) 7N
c) 21N
d) 4N
56. cos 405° = ?
a) $\displaystyle \frac{{-1}}{{\sqrt{2}}}$
b) $\displaystyle -\sqrt{2}$
c) $\displaystyle \sqrt{2}$
d) $\displaystyle \frac{1}{{\sqrt{2}}}$
57. The complex number $\displaystyle \frac{{{{{\left( {1+i} \right)}}^{n}}}}{{{{{\left( {1-i} \right)}}^{{n-2}}}}}$ is equal to
a) $\displaystyle 4{{i}^{{n-2}}}$
b) $\displaystyle 2{{i}^{{n-2}}}$
c) $\displaystyle 2{{i}^{{n-4}}}$
d) $\displaystyle 2{{i}^{{n-1}}}$
58. The number of diagonals that can be drawn by joining the vertices of an octagon is :
a) 12
b) 20
c) 28
d) 48
59. Assertion (A): The expansion of $\displaystyle {{\left( {1+x} \right)}^{n}}={}^{n}{{C}_{0}}+{}^{n}{{C}_{1}}x+{}^{n}{{C}_{2}}{{x}^{2}}....++{}^{n}{{C}_{n}}{{x}^{n}}$ .
Reason (R): If x = -1, then the above expansion is zero.
a) Both A and R are true and R is the correct explanation of A.
b) Both A and R are true but R is not the correct explanation of A.
c) A is true but R is false.
d) A is false but R is true.
60. Assertion (A): The difference between maximum and minimum values of variate is called Range.
Reason (R): Coeff. of Range = $\displaystyle \frac{{L-S}}{{L+S}}$ , where L is the largest value S is the smallest value
a) Both A and R are true and R is the correct explanation of A.
b) Both A and R are true but R is not the correct explanation of A.
c) A is true but R is false.
d) A is false but R is true.

At 3: 40, the hour and minute hands of a clock are inclined at

a) $\frac{13\pi}{18}$

b) $\frac{2\pi}{3}$

c) $\frac{3\pi}{18}$

d) $\frac{13\pi}{15}$

If f(x) = $\frac{x-1}{x^2-1}$ , then f(y) =

a) 1 + x

b) 1 – x

c) x – 1

d) x

If two squares are chosen at random on a chess board, the probability that they have a side common is

a) $\frac{2}{7}$

b) $\frac{1}{18}$

c) $\frac{1}{4}$

d) $\frac{9}{4}$

Lim $_{x \to 0}$ $\frac{\tan x - \sin x}{x^3}$ is equal to

a) 1

b) a real number other than 0 and 1

c) -1

d) 0

The locus of a point, whose abscissa and ordinate are always equal is

a) x – y = 0

b) x + y + 1 = 0

c) x + y = 1

d) x + y – 1 = 0

For two sets A U B = A if

a) A = B

b) A $\neq$ B

c) B $\subset$ A

d) A $\subset$ B

The solution of the equation |z| = z + 1 + 2i is

a) 3 – 2i

b) $\frac{3}{2}$ + 2i

c) 3 + 2i

d) $\frac{3}{2}$ – 2i

Number of relations that can be defined on the set A = {a, b, c, d} is

a) 24

b) 4 $^4$

c) 16

d) 2 $^{16}$

Solve the system of inequalities 2x + 5 $\le$ 0, x – 3 < 0.

a) x $\le$ – $\frac{5}{2}$

b) x $\ge$ – $\frac{5}{2}$

c) x $\ge$ – $\frac{5}{2}$

d) x $\le$ – $\frac{5}{2}$

If tan x = $-\frac{4}{3}$ and x lies in the IV quadrant, then the value of cos x is

a) $\frac{3}{\sqrt{5}}$

b) $\frac{1}{\sqrt{5}}$

c) $\frac{3}{5}$

d) $\frac{4}{5}$

The set A = {x: x is a positive prime number less than 10} in the tabular form is

a) {2, 3, 5, 7}

b) {1, 2, 3, 5, 7}

c) {3, 5, 7}

d) {1, 3, 5, 7, 9}

Sum of an infinite G.P. is $\frac{3}{2}$ times the sum of all the odd terms. The common ratio of the G.P. is

a) $\frac{1}{2}$

b) $\frac{4}{3}$

c) $\frac{1}{4}$

d) $\frac{2}{3}$

(C $_1$ + 2C $_2$ + 3C $_3$ + … + nC $_n$ ) = ?

a) (n – 1) $\cdot$ 2 $^n$

b) n $\cdot$ 2 $^n$

c) (n + 1) $\cdot$ 2 $^n$

d) n $\cdot$ 2 $^{n-1}$

The solution set for (x + 3) + 4 > -2x + 5:

a) (- $\infty$ , -2)

b) (- $\frac{2}{3}$ , $\infty$ )

c) (- $\infty$ , $\infty$ )

d) (2, $\infty$ )

For any two sets A and B, A U B = A if

a) A = B

b) B $\in$ A

c) A $\not\subset$ B

d) B $\subseteq$ A

cos 405° = ?

a) $\frac{1}{\sqrt{2}}$

b) – $\frac{1}{\sqrt{2}}$

c) $\sqrt{2}$

d) – $\sqrt{2}$

The complex number $\frac{(1+i)^n}{(1-i)^n}$ is equal to

a) 4i $^{n-2}$

b) 2i $^{n-2}$

c) 2i $^{n-4}$

d) 2i $^{n-1}$

The number of diagonals that can be drawn by joining the vertices of an octagon is :

a) 12

b) 20

c) 28

d) 48

Assertion (A): The expansion of $(1+x)^n = nC_0 + nC_1x + nC_2x^2 + \dots + nC_nx^n$ .

Reason (R): If x = -1, then the above expansion is zero.

a) Both A and R are true and R is the correct explanation of A.

b) Both A and R are true but R is not the correct explanation of A.

c) A is true but R is false.

d) A is false but R is true.

Assertion (A): The difference between maximum and minimum values of variate is called Range.

Reason (R): Coeff. of Range = $\frac{L-S}{L+S}$ where L is the largest value S is the smallest value

a) Both A and R are true and R is the correct explanation of A.

b) Both A and R are true but R is not the correct explanation of A.

c) A is true but R is false.

d) A is false but R is true.

tan $\frac{\pi}{4}$ = ?

a) -1

b) $\frac{1}{\sqrt{3}}$

c) 1

d) $\sqrt{3}$

If f: R $\to$ R be given by f(x) = $\frac{x^2-1}{x^2+1}$ for all x $\in$ R Then,

a) f(x) = f(-x)

b) f(x) + f(1-x) = 0

c) f(x) + f (1 – x) = 1

d) f(x) + f (x – 1) = 0

One of the two events must occur. If the chance of one is $\frac{2}{3}$ of the other, then odds in favour of the other are

a) 2:3

b) 3:1

c) 1:3

d) 3:2

Lim $_{x \to 3}$ $\frac{\sqrt{x^2+7}-10}{x-3}$ is equal to

a) 1

b) $\frac{6}{\sqrt{10}}$

c) $\frac{3}{\sqrt{10}}$

d) 0

Given the 4 lines with equations x + 2y – 3 = 0, 2x + 3y – 4 = 0, 3x + 4y – 5 = 0, 4x + 5y – 6 = 0, then these lines are

a) concurrent

b) the sides of a quadrilateral

c) sides of a parallelogram

d) sides of a Rhombus

For any two sets A and B, A $\cap$ (A U B) = …

a) A

b) $\phi$

c) $\ne \phi$

d) B

If $3+2i\sin\theta$ is a real number and $0 < \theta < 2\pi$ , then $\theta =$

a) $\frac{\pi}{2}$

b) $\frac{3\pi}{2}$

c) $\pi$

d) $\frac{2\pi}{2}$

Which one of the following is not a function?

a) {(x, y): x, y $\in$ R, y = x $^2$ }

b) {(x, y): x, y $\in$ R, y $^2$ = x}

c) {(x, y): x, y $\in$ R, y = x}

d) {(x, y): x, y $\in$ R, y $^3$ = x}

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

a) $x \in (-\infty, 2)$

b) $x \in (-\infty, 2]$

c) $x \in [2, \infty)$

d) $x \in (2, \infty)$

The value of sin $^2$ 5° + sin $^2$ 10° + sin $^2$ 15° + … + sin $^2$ 85° + sin $^2$ 90° is

a) 10

b) 9.5

c) 7

d) 8

If sets A and B are defined as A = {(x, y)| y = $\frac{1}{x}$ , x $\ne$ 0, x $\in$ R}, B = {(x, y)| y = -x, x $\in$ R}, then

a) A $\cap$ B = A

b) A U B = A

c) A $\cap$ B = $\phi$

d) A $\cap$ B = B

If (k-1), (2k+1), (6k+3) are in GP then k = ?

a) -2

b) 7

c) 0

d) 4

$(\sqrt{3}+1)^{2n} + (\sqrt{3}-1)^{2n}$ is

a) a negative real number

b) an even positive integer

c) an odd positive integer

d) irrational number

The solution of the inequalities comprising a system in variable x are represented on number lines as given below, then

a) x $\in$ [-3, 1]

b) $x \in (-\infty, -4] \cup [3, \infty)$

c) x $\in$ [-4, 3]

d) $x \in (-\infty, \infty)$

The number of proper subsets of the set {1, 2, 3} is:

a) 6

b) 7

c) 8

d) 5

sin(40° + $\theta$ ) cos(10° + $\theta$ ) – cos(40° + $\theta$ ) sin(10° + $\theta$ ) is equal to

a) $\frac{1}{2}$

b) $\frac{\sqrt{3}}{2}$

c) $\frac{1}{\sqrt{2}}$

d) 2

If $i^2 = -1$ , then sum $i+i^2+i^3+...$ upto 1000 terms is equal to

a) 0

b) 1

c) -1

d) i

The number of three digit numbers having atleast one digit as 5 is

a) 648

b) 225

c) 252

d) 246

Assertion (A): The expansion of $(1+x)^n = nC_0 + nC_1x + nC_2x^2 + \dots + nC_nx^n$ .

Reason (R): If x = -1, then the above expansion is zero.

a) Both A and R are true and R is the correct explanation of A.

b) Both A and R are true but R is not the correct explanation of A.

c) A is true but R is false.

d) A is false but R is true.

Assertion (A): The proper measure of dispersion about the mean of a set of observations i.e. standard deviation is expressed as positive square root of the variance.

Reason (R): The units of individual observations x $_i$ and the unit of their mean are different that of variance.

a) Both A and R are true and R is the correct explanation of A.

b) Both A and R are true but R is not the correct explanation of A.

c) A is true but R is false.

d) A is false but R is true.

100 MCQ of Maths of Class 11

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