MCQ of Class 11 Maths

Section A

If cosec x = $\displaystyle \frac{{-2}}{{\sqrt{3}}}$ and x lies in quadrant IV, then tan x = ?

a) $\displaystyle -\sqrt{3}$

b) √3

c) $\displaystyle \frac{1}{{\sqrt{3}}}$

d) $\displaystyle \frac{{-1}}{{\sqrt{3}}}$

The domain of definition of the function $\displaystyle f\left( x \right)=\sqrt{{x-1}}+\sqrt{{3-x}}$ is

a) (1, 3]

b) (-∞, 3)

c) [1, 3)

d) (1, ∞)

If the sum of numbers obtained on throwing a pair of dice is 9, then the probability that number obtained on one of the dice is 4, is:

a) 1/18

b) 1/2

c) 4/9

d) 1/9

lim $\displaystyle \underset{{x\to 3}}{\mathop{{\lim }}}\,\frac{{\sum\limits_{{r=1}}^{n}{{{{x}^{r}}}}-\sum\limits_{{r=1}}^{n}{{{{3}^{r}}}}}}{{x-3}}$ is equal to

a) $\displaystyle \frac{{\left( {2n-1} \right)\times {{3}^{n}}}}{4}$

b) $\displaystyle \frac{{\left( {2n-1} \right)\times {{3}^{n}}-1}}{4}$

c) $\displaystyle {\left( {2n-1} \right)\times {{3}^{n}}+1}$

d) $\displaystyle \frac{{\left( {2n-1} \right)\times {{3}^{n}}+1}}{4}$

The distance between the orthocentre and circumcentre of the triangle with vertices (1, 2), (2, 1) and $\displaystyle \left( {\frac{{3+\sqrt{3}}}{3},\frac{{3+\sqrt{3}}}{3}} \right)$ is

a) 2+√3

b) 0

c) 3+√3

d) √2

If A = {(x,y): x² + y² = 25} and B = {(x,y): x² + 9y² = 144} then A ∩ B contains

a) three points

b) two points

c) one point

d) four points

If a + ib = c + id, then

a) b² + c² = 0

b) b² + d² = 0

c) c² + d² = 0

d) a² + b² = c² + d²

If $\displaystyle \frac{{{{2}^{x}}+{{2}^{{-x}}}}}{2}$ Then f(x+y) f(x-y)) is equals to

a) ½ {f(2x) – f(2y)}

b) 1/2 {f(2x) + f(2y)}

c) 1/4 {f(2x) – f(2y)}

d) 1/4 {f(2x) + f(2y)}

A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm longer than the shortest and third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least 5 cm longer than the second?

a) 3 ≤ x ≤ 91

b) 3 ≤ x ≤ 5

c) 5 ≤ x ≤ 91

d) 8 ≤ x ≤ 22

The extremum values of cos θ are

a) -1 and 1

b) 0 and 1

c) $\displaystyle \frac{{-\sqrt{3}}}{2}$ and √2

d) -1 and 0

If A = {x : x is a multiple of 3, x natural no., x < 30} and B = {x : x is a multiple of 5, x is natural no., x < 30} then A – B is

a) {3, 6, 9, 12, 15, 18, 21, 24, 27, 30}

b) {3, 6, 9, 12, 18, 21, 24, 27}

c) {3, 6, 9, 10, 12, 15, 18, 20, 21, 25, 27, 30}

d) {3, 6, 9, 12, 18, 21, 24, 27, 30}

If a, b, c are in A.P. and x, y, z are in G.P., then the value of $\displaystyle {{x}^{{b-c}}}{{y}^{{c-a}}}{{z}^{{a-b}}}$ is

a) $\displaystyle {{x}^{a}}{{y}^{b}}{{z}^{c}}$

b) 1

c) 0

d) xyz

If n is a positive integer, then $\displaystyle {{\left( {\sqrt{3}+i} \right)}^{n}}+{{\left( {\sqrt{3}-i} \right)}^{n}}$ is

a) a negative integer

b) a real number

c) a positive integer

d) a non real number

If x belongs to set of integers, A is the solution set of 2(x – 1) < 3x – 1 and B is the solution set of 4x – 3 ≤ 8 + x, find A ∩ B

a) {0, 2, 4}

b) {1, 2, 3}

c) {0, 1, 2}

d) {0, 1, 2, 3}

If Q = {x : x = 1/y, where y ∈ N}, then

a) 1 ∈ Q

b) ½ ∉ Q

c) 2 ∈ Q

d) 0 ∈ Q

sin 47° + sin 61° – sin 11° – sin 25° is equal to

a) cos 36°

b) cos 7°

c) sin 36°

d) sin 7°

The multiplicative inverse of (3 + 2i)² is

a) $\displaystyle \left( {\frac{{-4}}{{169}}+\frac{{12}}{{169}}i} \right)$

b) $\displaystyle \left( {\frac{5}{{169}}-\frac{{12}}{{169}}i} \right)$

c) $\displaystyle \left( {\frac{5}{{169}}+\frac{{12}}{{169}}i} \right)$

d) $\displaystyle \left( {\frac{{-5}}{{169}}+\frac{{12}}{{169}}i} \right)$

Different calendars for the month of February are made so as to serve for all the coming years. The number of such calendars is

a) 2

b) 14

c) 7

d) 8

Assertion (A): The expansion of (1 + x)ⁿ = nC₀ + nC₁x + nC₂x² + … + nCnxⁿ.

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 $\displaystyle \tan \left( {\frac{\pi }{4}+X} \right)+\tan \left( {\frac{\pi }{4}-X} \right)$ = λ sec 2x, then the value of λ will be

a) 4

b) 1

c) 3

d) 2

If f(x) = |cos x|, then $\displaystyle f\left( {\frac{{3\pi }}{4}} \right)$ is

a) 1

b) -1

c) 1/√2

d) -1/√2

For the following distribution

Marks below	Number of Students
10	1
20	5
30	13
40	15
50	16

the modal class is:

a) 20 – 30

b) 40 – 50

c) 10 – 20

d) 30 – 40

$\displaystyle \underset{{\delta x\to \frac{x}{4}}}{\mathop{{\lim }}}\,\frac{{{{{\sec }}^{2}}x-2}}{{\tan x-1}}$ is equal to

a) 1

b) 0

c) 1/2

d) 3

The angle between the two straight lines 6x² – xy – x² + 30y + 36 = 0 is

a) 30°

b) 50°

c) 45°

d) 60°

If A and B are two given sets, then A ∩ (A ∩ B)ᶜ is equal to

a) A

b) B

c) A ∩ Bᶜ

d) ∅

The region of Argand’s plane represented by the inequality |1 – z| ≤ |1 + z| is

a) Re(z) ≤ 0

b) Im(z) < 0

c) Im(z) > 0

d) Re(z) ≥ 0

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

a) mⁿ

b) mⁿ – 1

c) nᵐ – 1

d) 2ᵐⁿ-1

If x is a real number and |x| < 5, then

a) -5 < x < 5

b) -5 ≤ x ≤ 5

c) x ≥ 5

d) x ≤ -5

If 3π/4 < α < π, then $\displaystyle \sqrt{{2\cot \alpha +\frac{1}{{{{{\sin }}^{2}}\alpha }}}}$ is equal to

a) -1 + cot α

b) -1 – cot α

c) 1 + cot α

d) 1 + cot α

If A ∪ B = B then

a) B ⊂ A

b) A ⊆ B

c) B = ∅

d) A ≠ ∅

If a, b, c are in GP and $\displaystyle {{a}^{{\frac{1}{x}}}}={{b}^{{\frac{1}{y}}}}={{c}^{{\frac{1}{z}}}}$ then x, y, z are in

a) GP

b) AP

c) H.M.

d) HP

$\displaystyle \left\{ {\frac{{{{c}_{1}}}}{{{{c}_{0}}}}+2\frac{{{{c}_{2}}}}{{{{c}_{1}}}}+3\frac{{{{c}_{3}}}}{{{{c}_{2}}}}+.......n\frac{{{{c}_{n}}}}{{{{c}_{{n-1}}}}}} \right\}$ = ?

a) ½ n(n+1)

b) 2n

c) 2^(n-1)

d) n(n+1)

The solution set for |3x – 2| ≤ ½ is

a) [2/3, 5/6]

b) [1/2, 5/6]

c) [1/2, 3/4]

d) [1/2, 2/3]

If A = {1, 3, 5, B} and B = {2, 4}, then

a) {4} ⊂ A

b) None of these

c) B ⊂ A

d) {4} ⊂ A

If $\displaystyle \tan \left( {\frac{\pi }{4}+x} \right)+\tan \left( {\frac{\pi }{4}-x} \right)$ = a, then $\displaystyle {{\tan }^{2}}\left( {\frac{\pi }{4}+x} \right)+{{\tan }^{2}}\left( {\frac{\pi }{4}-x} \right)$ =

a) a² + 1

b) a² – 2

c) a² + 2

d) a² + 2

Mark the correct answer for $\displaystyle \left( {{{i}^{{109}}}+{{i}^{{144}}}+{{i}^{{119}}}+{{i}^{{124}}}} \right)$ = ?

a) 0

b) i

c) 2

d) -2i

Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?

a) 60

b) 125

c) 20

d) 15

Assertion (A): The expansion of (1 + x)ⁿ = nC₀ + nC₁x + nC₂x² + … + nCnxⁿ.

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 x₁, x₂,…, 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.

$\displaystyle \frac{{1-\cos 2x+\sin x}}{{\sin 2x+\cos x}}$ = ?

a) cosec x

b) sec x

c) cot x

d) tan x

Domain of definition of the function f(x) = $\displaystyle \frac{3}{{4-{{x}^{2}}}}$ + log₁₀(x³ – x) is

a) (-1, 0) U (1, 2) U (2, ∞)

b) (1, 2) U (2, ∞)

c) (-1, 0) U (1, 2)

d) (1, 2)

The probability that a card drawn at random from a pack of 52 cards is either a king or a heart is
- a) 1/13
- b) 1/26
- c) 4/13
- d) 16/52
is equal to
- a) 2/3
- b) 4/3
- c) -2√3
- d) -4/3
The area of a triangle with vertices at (-4, -1), (1, 2) and (4, -3) is

a) 17

b) 16

c) 15

d) 14

Let A = {a, b, c}, B = {a, b, d}, C = {d, e} and D = {e, d}. Then which of the following statement is not correct?

a) D ⊇ E

b) C – B = E

c) B U E = C

d) C – D = E

Mark the correct answer for $\displaystyle {{\left( {1+i} \right)}^{{-1}}}$ = ?

a) $\displaystyle \left( {\frac{{-1}}{2}+\frac{1}{2}i} \right)$

b) (2 – 3i)

c) $\displaystyle \left( {\frac{{-1}}{2}-\frac{1}{2}i} \right)$

d) (2 – i)

Let A = {x ∈ R : x ≠ 0, -4 ≤ x ≤ 4} and f : A → R be defined by f(x) = $\displaystyle \frac{{\left| x \right|}}{x}$ for x ∈ A Then A is

a) |x| : -4 ≤ x ≤ 0

b) {1}

c) |x| : x ≤ 4

d) {1, -1}

If x and a are real numbers such that a > 0 and |x| > a, then

a) x ∈ (-∞, -a)

b) x ∈ (-∞, a) U (a, ∞)

c) x ∈ (-a, a)

d) x ∈ [-a, a]

If 5 cot θ = 4, then $\displaystyle \left( {\frac{{5\sin \theta -3\cos \theta }}{{\sin \theta +2\cos \theta }}} \right)$ = ?

a) 1

b) 3/14

c) 1/14

d) 4

Let R be set of points inside a rectangle of sides a and b (a, b > 1) with two sides along the positive direction of x-axis and y-axis. Then

a) R = {(x, y): 0 ≤ x ≤ a, 0 ≤ y ≤ b}

b) R = {(x, y): 0 ≤ x < a, 0 ≤ y < b}

c) R = {(x, y): 0 < x < a, 0 < y < b}

d) R = {(x, y): x < a, y < b}

In a G.P. (m + n)ᵗʰ and (m – n)ᵗʰ terms are respectively p and q. Its mᵗʰ term is

a) pq

b) √(p/q)

c) √(pq)

d) p – q

If $\displaystyle {{\left( {1-x+{{x}^{2}}} \right)}^{n}}={{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+......+{{a}_{2}}{{x}^{{2n}}}$ , then a₀ + a₄ + a₈ + … + a₂n equals.

a) $\displaystyle {{3}^{n}}+\frac{1}{2}$

b) $\displaystyle \frac{{{{3}^{n}}+1}}{2}$

c) $\displaystyle \frac{{{{3}^{n}}-1}}{2}$

d) $\displaystyle \frac{{1-{{3}^{n}}}}{2}$

If |x + 2| ≤ 9, then

a) x ∈ (-7, 11)

b) x ∈ (-∞, 7) U (11, ∞)

c) x ∈ [-11, 7]

d) x ∈ (-7, -∞) U [11, ∞)

For any two sets A and B, A ∩ (A ∪ B)’ is equal to

a) A ∩ B

b) ∅

c) B

d) A

(sin 36° cos 9° + cos 36° sin 9°) = ?

a) 1/2

b) √(3)/2

c) 1/4

d) 1

For any positive integer n, $\displaystyle {{\left( {-\sqrt{{-1}}} \right)}^{{4n+3}}}$ = ?

a) 1

b) i

c) -i

d) -1

If $\displaystyle ^{{20}}{{C}_{r}}{{=}^{{20}}}{{C}_{{r-10}}}$ , then $\displaystyle ^{{18}}{{C}_{r}}$ is equal to

a) 4896

b) 816

c) 1632

d) 1342

Assertion (A): The expansion of (1 + x)ⁿ = nC₀ + nC₁x + nC₂x² + … + nCnxⁿ.

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 x₁, x₂,…, 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.

If the angles of a triangle are in A.P. then the measure of one of the angles in radians is

a) π/3

b) π/2

c) π/5

d) π/4

Let f(x) = x² then, dom (f) and range (f) are respectively

a) R⁺ and R⁺

b) R and R – {0}

c) R and R

d) R and R⁺

If the S.D. of the 1, 2, 3, 4, 5,…, ………………10 is σ, then the S.D. of the 11, 12, 13, 14, ………………… 20 is

a) σ/10

b) 10σ

c) σ + 10

d) σ

If $\displaystyle f\left( x \right)=\left\{ {\begin{array}{*{20}{c}} {{{x}^{2}}-1,} & {0<x<2} \\ {2x+3,} & {2\le x<3} \end{array}} \right.$ , then the quadratic equation whose roots are $\displaystyle \underset{{x\to {{2}^{-}}}}{\mathop{{\lim }}}\,f\left( x \right)$ and $\displaystyle \underset{{x\to {{2}^{+}}}}{\mathop{{\lim }}}\,f\left( x \right)$ is

a) x² – 10x + 21 = 0

b) x² – 14x + 49 = 0

c) x² – 6x + 9 = 0

d) x² – 7x + 8 = 0

The equation of the line passing through (1, 2) and perpendicular to x + y + 7 = 0 is

a) y – x – 1 = 0

b) y – x + 1 = 0

c) y + x – 2 = 0

d) y – x – 2 = 0

The equation of the plane parallel to y – axis

a) x = d

b) y = d

c) cx + az = 0, a² + c² ≠ 0

d) ax + cz + d = 0, a² + c² ≠ 0

The equation |z – i| = |z – 1 + i| represents a

a) hyperbola

b) circle

c) straight line

d) parabola

If C(n, 12) = C(n, 8), then C (22, n) is equal to

a) 231

b) 303

c) 252

d) 210

If y = $\displaystyle \sqrt{{x+\sqrt{{x+\sqrt{{x+...+to\infty \infty }}}}}}$ then $\displaystyle \frac{{dy}}{{dx}}$ =

a) $\displaystyle \frac{1}{{2y+1}}$

b) $\displaystyle \frac{1}{{2y-1}}$

c) $\displaystyle \frac{x}{{y+1}}$

d) $\displaystyle \sqrt{{\frac{x}{{y+1}}}}$

$\displaystyle 2\sin \frac{{5\pi }}{{12}}\cos \frac{\pi }{{12}}$ = ?

a) $\displaystyle \frac{{\left( {2+\sqrt{3}} \right)}}{2}$

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

c) $\displaystyle \frac{{\sqrt{3}+1}}{2}$

d) ½

Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and n are

a) 7, 4

b) 6, 4

c) 3, 3

d) 6, 3

$\displaystyle {{\left( {\sqrt{5}+1} \right)}^{{2n+1}}}-{{\left( {\sqrt{5}-1} \right)}^{{2n+1}}}$ is

a) 0

b) an even positive integer

c) an odd positive integer

d) not an integer

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

a) an even positive integer

b) an irrational number

c) an odd positive integer

d) a rational number

Solve the system of inequalities $\displaystyle -15<\frac{{3\left( {x-2} \right)}}{5}\le 0$

a) -13 < x < 13

b) -23 < x ≤ 2

c) -23 < x < 23

d) -13 < x < 2

The set of all prime numbers is

a) an infinite set

b) a singleton set

c) a finite set

d) a multi set

$\displaystyle \frac{{\sin 3x}}{{1+2\cos 2x}}$ is equal to

a) $\displaystyle -\frac{1}{2}\cos 2x$

b) sin x

c) 0

d) 1/2

If $\displaystyle \begin{array}{*{20}{c}} {\frac{{\sin \left| x \right|}}{{\left[ x \right]}},} & {\left[ x \right]\ne 0} \\ {0,} & {\left[ x \right]=0} \end{array}$ , where [.] denotes the greatest integer function, then $\displaystyle \underset{{x\to 0}}{\mathop{{\lim }}}\,f\left( x \right)$ is equal to

a) -1

b) does not exist

c) is equal to 0

d) is equal to 1

If ⁿP₃ : ⁿP₄ = 1 : 9, find n

a) 8

b) 4

c) 9

d) 7

Assertion (A): The set A = {a, b, c, d, e, g} is finite set.

Reason (R): The set B = {men living presently in different parts of the world} is finite set.

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 the numbers $\displaystyle \frac{{-2}}{7}$ , K, $\displaystyle \frac{{-7}}{2}$ are in GP, then K = ±1.

Reason (R): If a₁, a₂, a₃ are in GP, then $\displaystyle \frac{{{{a}_{2}}}}{{{{a}_{1}}}}=\frac{{{{a}_{3}}}}{{{{a}_{2}}}}$ .

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.

Section A

Mark the correct alternative in the following: If $\displaystyle \tan \alpha =\frac{{1-\cos \beta }}{{\sin \beta }}$ , then

a) tan2β = tan2α

b) tanβ = tanα

c) tan3α = tan2β

d) tanβ = tan2α

A function f from the natural numbers to the set of integers defined by $\displaystyle f\left( x \right)=\left\{ {\begin{array}{*{20}{c}} {\frac{{n-1}}{2},} & {\text{when n is odd}} \\ {-\frac{n}{2}} & {\text{when n is even}} \end{array}} \right.$ . Which of the following is correct?

a) neither one-one nor onto

b) onto but not one-one

c) both one-one and onto

d) one-one but not onto

Which of the following is not a measure of dispersion?

a) mode

b) mean deviation

c) standard deviation

d) variance

$\displaystyle \underset{{x\to 0}}{\mathop{{\lim }}}\,\frac{{{{x}^{2}}\cos x}}{{1-\cos x}}$ is equal to

a) 2

b) -3/2

c) 3/2

d) 1

In a △ABC, if A is the point (1, 2) and equations of the median through B and C are respectively x + y = 5 and x = 4, then B is

a) (-2, 7)

b) (1, 4)

c) (7, -2)

d) (4, 1)

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) $\displaystyle \left( {\frac{1}{2},\frac{1}{4}} \right)$

If z is a complex number, then

a) |z| = |z|²

b) |z| < |z|²

c) |z| ≥ |z|²

d) |z| > |z|²

There are 10 points in a plane, out of which 4 points are collinear. The number of line segments obtained from the pairs of these points is

a) 41

b) 39

c) 45

d) 40

$\displaystyle \frac{d}{{dx}}\left( {{{{\tan }}^{{-1}}}\left( {\frac{2}{{{{x}^{{-1}}}-x}}} \right)} \right)$ is equal to

a) $\displaystyle \sqrt{{1-{{x}^{2}}}}$

b) $\displaystyle \frac{2}{{1+{{x}^{2}}}},x\ne 0,\pm 1$

c) $\displaystyle \frac{1}{{1+{{x}^{2}}}},x\ne 0,\pm 1$

d) $\displaystyle \frac{{-2}}{{\sqrt{{1-{{x}^{2}}}}}}$

cot 120° = ?

a) -√(3)

b) -1/√3

c) √3

d) 1/√3

If A ∩ B = B then

a) A = ∅

b) B = ∅

c) B ≠ ∅

d) B ⊆ A

In the expansion of (x + a)ⁿ, if the sum of odd terms be P and the sum of even terms be Q, then 4PQ = ?

a) (x + a)ⁿ – (x – a)ⁿ

b) (x + a)²ⁿ – (x – a)²ⁿ

c) (x + a)ⁿ + (x – a)ⁿ

d) (x + a)²ⁿ + (x – a)²ⁿ

If x = 99⁵⁰+100⁵⁰ and y = (101)⁵⁰ then

a) x < y

b) x > y

c) x = y

d) x ≥ y

The solution set for: $\displaystyle \left| {\frac{{2\left( {3-x} \right)}}{5}} \right|<\frac{3}{5}$ is

a) $\displaystyle \left( {\frac{1}{2},\frac{3}{2}} \right)$

b) $\displaystyle \left( {\frac{3}{4},\frac{9}{4}} \right)$

c) $\displaystyle \left( {\frac{3}{2},\frac{9}{2}} \right)$

d) $\displaystyle \left( {\frac{1}{4},\frac{3}{4}} \right)$

Given the sets A = {1, 2, 3}, B = {3, 4}, C = {4, 5, 6}, then A ∪ (B ∩ C) is

a) {1, 2, 3, 4, 5, 6}

b) {3}

c) {1, 2, 3, 4, 5, 6}

d) {1, 2, 3, 4, 5}

cot x – 2cot 2x = ?

a) tan x

b) cos 2x

c) sin x

d) cos x

If $\displaystyle y=\frac{{\sin \left( {x+9} \right)}}{{\cos x}}$ , then $\displaystyle \frac{{dy}}{{dx}}$ at x = 0 is equal to

a) cos 9

b) 1

c) 0

d) sin 9

The greatest possible number of points of intersection of 8 straight lines and 4 circles is

a) 32

b) 104

c) 128

d) 64

Assertion (A): Let A = {a, b} and B = {a, b, c}. Then, A ⊄ B.

Reason (R): If every element of X is also an element of Y, then X is a subset of Y.

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 sum of infinite terms of a geometric progression is given by $\displaystyle {{S}_{\infty }}=\frac{a}{{1-r}}$ , provided |r| < 1.

Reason (R): The sum of n terms of Geometric progression is $\displaystyle {{S}_{n}}=\frac{{a\left( {{{r}^{n}}-1} \right)}}{{r-1}}$ .

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.

MCQ of Class 11 Maths

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