Maths MCQ's of Class 11

Section A:

The radius of a circle is 30 cm. The length of the arc of this circle whose chord is 30 cm long, is.

a) 9π cm

b) 2π cm

c) 13.6π cm

d) 10π cm

Let A = {1, 2, 3, B = {1, 3, 5}. If relation R from A to B is given by R = {(1, 1), (2, 3), (3, 3), (1,3)}. Then R is.

a) neither symmetric, nor transitive

b) symmetric and transitive

c) reflexive but not symmetric

d) reflexive but not transitive

Which of the following, in case of a discrete data, is not equal to the median?.

a) 2nd quartile

b) 50th percentile

c) 5th decile

d) lower quartile

$\displaystyle \underset{{x\to 4}}{\mathop{{\lim }}}\,\frac{{3-\sqrt{{5+x}}}}{{1-\sqrt{{5-x}}}}$ is equal to.

a) does not exist

b) 0

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

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

The equation of the straight line which passes through the point (-4, 3) such that the portion of the line between the axes is divided internally by the point in the ratio 5:3.

a) 9x + 20y – 96 = 0

b) 9x + 20y = 24

c) 9x – 20y + 96 = 0

d) 20x + 9y + 53 = 0

The locus of the equation xy + yz = 0 is.

a) a pair of straight lines

b) a pair of parallel planes

c) a pair of curvy lines

d) a pair of perpendicular planes

Mark the correct answer for $\displaystyle \frac{{\left( {3-5i} \right)}}{{\left( {-2+3i} \right)}}$ = ?.

a) $\displaystyle \left( {\frac{{21}}{{13}}-\frac{3}{{13}}i} \right)$

b) $\displaystyle \left( {\frac{{-21}}{{13}}+\frac{1}{{13}}i} \right)$

c) $\displaystyle \left( {\frac{{21}}{{13}}-\frac{1}{{13}}i} \right)$

d) $\displaystyle \left( {\frac{{21}}{{13}}+\frac{1}{{13}}i} \right)$

In how many ways can a cricket team be chosen out of a batch of 15 players, if a particular player is always chosen?.

a) 965

b) 1364

c) 1001

d) 364

If $\displaystyle f\left( x \right)\left\{ {\begin{array}{*{20}{c}} {x\sin \frac{1}{x},} & {x\ne 0} \\ {0,} & {x=0} \end{array}} \right.$ , then $\displaystyle \underset{{x\to 0}}{\mathop{{\lim }}}\,f\left( x \right)$ equals.

a) 0

b) 2

c) 1

d) -1

The greatest value of sin x cos x is.

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

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

c) 1/2

d) 1

The smallest set A such that A U {1, 2, 3, 5, 9} is.

a) {1, 2, 5, 9}

b) {4, 5, 6}

c) {3, 5, 9}

d) {2, 3, 5}

{C₀ + 2C₁ + 3C₂ + … + (n+1)C_n) = ?.

a) n(n+1) . 2ⁿ

b) (n+2) . 2^(n-1)

c) (n+2) . 2ⁿ

d) n . 2^(n-1)

The integral part of $\displaystyle {{\left( {\sqrt{2}+1} \right)}^{6}}$ is.

a) 96

b) 98

c) 99

d) 100

If x and b are real numbers. If b > 0 and |x| > b, then.

a) x ∈ (-∞, b)

b) x ∈ (-b, ∞)

c) x ∈ (-∞, -b) U (b, ∞)

d) x ∈ (-∞, 4] U (b, ∞)

Let A = {x : x ∉R, x ≥ 4} and B = {x : x ∉ R, x < 5} then A ⋂ B is.

a) {5,4}

b) {4, 5}

c) {4}

d) {x : x ∈ R, 4 ≤ x < 5}

The value of $\displaystyle \sin \frac{\pi }{{10}}\sin \frac{{13\pi }}{{10}}$ is.

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

b) $\displaystyle \frac{1}{4}$

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

d) 1

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

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

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

c) 1+x²

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

In how many ways can 5 persons occupy 3 seats?.

a) 30

b) 15

c) 60

d) 20

Assertion (A): Let A = {1, 2, 3} and B = {1, 2, 3, 4}. Then, A C 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 first 6 terms of the GP 4, 16, 64, … is equal to 5460.

Reason (R): The sum of n terms of Geometric progression is $\displaystyle {{S}_{n}}=\frac{{a\left( {{{r}^{n}}-1} \right)}}{{r-1}}$ , where a = first term r = common ratio and n = number of terms.

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.

Write the value of $\displaystyle \cos ec\left( {\frac{{-33\pi }}{4}} \right)$ .

a) $\displaystyle \sqrt{2}$

b) $\displaystyle -\sqrt{2}$

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

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

Let A = {x ∈ R : -1 ≤ x ≤ 1} = B and C = {x ∈ R : x ≥ 0} and let S = {(x, y) ∈ A x B : x² + y² = 1} and S₀ = {(x, y) ∈ A x C : x² + y² = 1}. Then.

a) S defines a function from A to C

b) S₀ defines a function from A to B

c) S₀ defines a function from A to C

d) S defines a function from A to B

The geometric mean and harmonic mean of two non-negative observations are 10 and 8, respectively. Then, what is the arithmetic mean of the observations?.

a) 12.5

b) 9

c) 4

d) 25

$\displaystyle \underset{{x\to 0}}{\mathop{{\lim }}}\,\frac{{\left| {\sin x} \right|}}{x}$ is equal to.

a) None of these

b) -1

c) 1

d) 0

Area of the triangle formed by the points {(a + 3), (a + 4), (a + 3), ((a + 2) (a + 3)), (a + 2)) and ((a + 1) (a + 2), (a + 1))} is.

a) 25a²

b) 24a²

c) 5a²

d) None of these

A, B, C and D are four points in spaces such that AB = BC = CD = DA. Then ABCD is a.

a) nothing can be said

b) rectangle

c) rhombus

d) skew quadrilateral

$\displaystyle \frac{{1+2i+3{{i}^{2}}}}{{1-2i+3{{i}^{2}}}}$ equals.

a) 1

b) -1

c) -i

d) i

The product of r consecutive positive integers is divisible by.

a) (r + 1)!

b) r!

c) r! + 1

d) (r + 2)!

If $\displaystyle f\left( x \right)=\left\{ {\begin{array}{*{20}{c}} {{{x}^{3}},} & {\left| x \right|\le 1} \\ {x,} & {\left| x \right|>1} \end{array}} \right.$ , then f(x) is.

a) not continuous at -1 and 1

b) not continuous at x = 0

c) derivable at all x ∈ R

d) not derivable at -1 and 1

If tan 69° + tan 66°- tan 69° tan 66° = 2k, then k =.

a) -1

b) -1/2

c) 1/2

d) 0

Which of the following is a set?.

a) A collection of vowels in English alphabets is a set.

b) The collection of most talented writers of India is a set.

c) The collection of most difficult topics in Mathematics is a set.

d) The collection of good cricket players of India is a set.

In Pascal’s triangle, each row begins with 1 and ends in.

a) -1

b) 0

c) 2

d) 1

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

a) an irrational number

b) an odd positive integer

c) an even positive integer

d) a rational number

Solve the system of inequalities: $\displaystyle x-5>0,\frac{{2x-4}}{{x+2}}<2$ .

a) x > 5

b) x > -5

c) x < 2

d) x < -2

If A = {1, 2, 3, 4, 5, 6}, then the number of proper subsets is.

a) 63

b) 36

c) 64

d) 25

If cos(A – B) = 3/5 and tan A tan B = 2, then.

a) cos A cos B = -1/5

b) cos A cos B = 1/5

c) sin A sin B = -2/5

d) sin A sin B = 2/5

$\displaystyle \underset{{x\to 0}}{\mathop{{\lim }}}\,\frac{{\sin {{x}^{n}}}}{{{{{\left( {\sin x} \right)}}^{m}}}}$ , n> m > 0 is equal to.

a) m/n

b) 0

c) 1

d) n/m

In how many ways can 5 white balls and 3 black balls be arranged in a row so that no two black balls are together?.

a) 40

b) 120

c) 20

d) 192

Assertion (A): If A = set of letters in Alloy B = set of letters in LOYAL, then set A & B are equal sets.

Reason (R): If two sets have exactly the same elements, they is called equal sets.

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): A sequence is said to definite if it has finite no of terms.

Reason (R): The sequence whose n^th term if $\displaystyle \frac{{{{2}^{n}}}}{n}$ if 2,2, $\displaystyle \frac{8}{3}$ , 4

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.

In a right triangle ∆ABC, we have: sin² A + sin² B + sin² C = ?.

a) 2

b) 3

c) 0

d) 1

Let A = {1, 2, 3}, B = {1, 3, 5}. If relation R from A to B is given by R = {(1, 3), (2, 5), (3, 3)}. Then R^-1 is.

a) {(1, 3), (2, 5), (3, 3)}

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

c) {(1, 3), (2, 5), (3, 3)}

d) {(5, 2)}

A set of n values x₁, x₂, …, x_n has standard deviation σ. The standard deviation of n values x₁ + k, x₂ + k, …, x_n + k will be.

a) kσ

b) σ + k

c) σ

d) σ – k

$\displaystyle \underset{{x\to 3}}{\mathop{{\lim }}}\,\frac{{x-3}}{{\left| {x-3} \right|}}$ is equal to.

a) 1

b) -1

c) 0

d) None of these

The acute angle between the medians drawn from the acute angles of a right angled isosceles triangle is.

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

b) $\displaystyle {{\cos }^{{-1}}}\left( {\frac{4}{5}} \right)$

c) $\displaystyle {{\cos }^{{-1}}}\left( {\frac{5}{6}} \right)$

d) $\displaystyle {{\cos }^{{-1}}}\left( {\frac{2}{3}} \right)$

The locus of the first degree equation in x, y, z is a.

a) straight line

b) sphere

c) plane

d) Circle

If x is real and k = $\displaystyle \frac{{{{x}^{2}}-x+1}}{{{{x}^{2}}+x+1}}$ , then.

a) k ≥3

b) k ≤1/3

c) k ≤ 1/4

d) k ∈ [1/3, 3]

The number of four digit numbers having atleast one digit as 7 is.

a) 3168

b) 5976

c) 1254

d) 9000

If f be a function such that f(9) = 9 and f'(9) = 3, then $\displaystyle \underset{{x\to 9}}{\mathop{{\lim }}}\,\frac{{\sqrt{{f\left( x \right)}}-3}}{{\sqrt{x}-3}}$ is equal to.

a) 3

b) 9

c) 1

d) 0

cosec 150° = ?.

a) -2

b) $\displaystyle -\sqrt{2}$

c) 2

d) $\displaystyle \sqrt{2}$

Which of the following is a null set?.

a) C = φ

b) B = {x : x > 1 and x < 3}

c) D = {0}

d) A = {x : x > 1 and x < 3}

If C_r denotes ⁿC_r the coefficient of (1+x)ⁿ, then C₀ + C₁ + C₂ + … + C_n = ?.

a) 2n

b) 2ⁿ

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

d) 2ⁿ

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

The solution set of the inequations x ≥2, x ≤ – 3 is.

a) {}

b) [-3, 2]

c) (-3, 2)

d) [2, -3]

If A and B are two sets, then A ⋂ (A ⋃ B) equals.

a) A

b) φ

c) B

d) A ⋂ B

cos 18° = ?.

a) $\displaystyle \frac{{\left( {2\sqrt{5}+1} \right)}}{4}$

b) $\displaystyle \frac{{\left( {\sqrt{5}+1} \right)}}{4}$

c) $\displaystyle \frac{{\sqrt{{10+2\sqrt{5}}}}}{4}$

d) $\displaystyle \frac{{\sqrt{{10-2\sqrt{5}}}}}{4}$

$\displaystyle \underset{{x\to 0}}{\mathop{{\lim }}}\,\frac{{{{{\left( {1+x} \right)}}^{n}}-1}}{x}$ is equal to.

a) -n

b) 1

c) 0

d) n

In a room there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amounts of illumination is.

a) 2¹²

b) 12² – 1

c) 2¹² – 1

d) 2¹⁰– 1

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): 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.

cos θ + sin(270° + θ) – sin(270° – θ) + cos(180° + θ) is equal to.

a) 2 cos θ

b) 0

c) 2 sin θ

d) 1

Let R = {(x, y): x² + y² = 1 and x, y ∈ R} be a relation in R. The relation R is.

a) symmetric

b) anti – symmetric

c) reflexive

d) transitive

The mean of the series x₁, x₂, …, x_n is $\displaystyle \overline{X}$ . If x₂ is replaced by λ, then what is the new mean?.

a) $\displaystyle \frac{{\overline{X}-{{x}_{2}}-\lambda }}{n}$

b) $\displaystyle \frac{{n\overline{X}-{{x}_{2}}-\lambda }}{n}$

c) $\displaystyle \frac{{\overline{X}-{{x}_{2}}+\lambda }}{n}$

d) $\displaystyle \overline{X}-{{x}_{2}}+\lambda$

$\displaystyle \frac{d}{{dx}}\left( {\cos e{{c}^{{-1}}}x} \right)$ is equal to.

a) $\displaystyle \frac{{-1}}{{2x\sqrt{{{{x}^{2}}-1}}}}$ for |x| > 1

b) $\displaystyle \frac{1}{{x\sqrt{{{{x}^{3}}-2x}}}}$ for |x| > 1

c) $\displaystyle \frac{{-1}}{{\left| x \right|\sqrt{{{{x}^{2}}-1}}}}$ for |x| > 1

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

The triangle formed by the lines x + y = 1, 2x + 3y – 6 = 0 and 4x – y + 4 = 0 lies in.

a) 4^th quadrant

b) 2^nd quadrant

c) 1^st quadrant

d) 3^rd quadrant

A parallelogram is formed by planes drawn through the points (2, 3, 5) and (5, 9, 7), parallel to the coordinate planes. The length of a diagonal of the parallelogram is.

a) $\displaystyle \sqrt{{135}}$

b) $\displaystyle \sqrt{{38}}$

c) 7

d) $\displaystyle \sqrt{{155}}$

If p² + p + 1 = 0, then, the value of p³ⁿ is equal to.

a) 0

b) 1 or -1

c) 1

d) -1

If ⁿC₁ = ⁿC₂, then.

a) 2m = n(n+1)

b) 2m = n

c) 2m = n(n-1)

d) 2m = n(m-1)

If f(x) = 1 + x + x² + x³ + … + x¹⁰⁰, then f'(1) is equal to:.

a) 150

b) 50

c) -150

d) 50

(sin² 6x – sin² 4x) = ?.

a) sin 10x sin 2x

b) sin 3x

c) sin 2x

d) sin 10x

The number of subsets (Improper) of a set containing n elements is.

a) 2ⁿ

b) 2ⁿ – 1

c) 2ⁿ – 2

d) n

$\displaystyle \sum\limits_{{r=0}}^{n}{{{{4}^{r}}{{.}^{n}}{{C}_{r}}}}$ = ?.

a) 6ⁿ

b) 5^-n

c) 4ⁿ

d) 5ⁿ

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

a) ½ n(n+1)

b) 2n

c) 2^n-1

d) 2ⁿ

The solution set of the inequation 3x < 5, when x is a natural number is.

a) {1, 2}

b) {1}

c) {4}

d) {0, 1}

If a set A has n elements then the total number of subsets of A is.

a) 2n

b) n

c) 2ⁿ

d) n²

The value of cos 1° cos 2° cos 3° … cos 179° is.

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

b) 1

c) -1

d) 0

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

a) None of these

b) -1

c) 0

d) 1

The number of ways in which 8 different flowers can be strung to form a garland so that 4 particular flowers are never separated is.

a) 5!4!

b) 5!6!

c) 576

d) 288

Assertion (A): If A = set of letters in Alloy B = set of letters in LOYAL, then set A & B are equal sets.

Reason (R): If two sets have exactly the same elements, they are called equal sets.

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 = $\displaystyle \pm$ 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:

If 5 sin α = 3 sin (α + 2 β) ≠ 0, then tan (α + β) is equal to.

a) 4 tan β

b) 2 tan β

c) 6 tan β

d) 3 tan β

Let f : R -> R be defined by $\displaystyle f\left( x \right)=\left\{ {\begin{array}{*{20}{c}} {3x,} & {if} & {x>3} \\ {{{x}^{2}},} & {if} & {1<x\le 3} \\ {x,} & {if} & {x\le 1} \end{array}} \right.$ . Then f(-2) + f(0) + f(5) is equal to.

a) -17

b) 0

c) -4

d) 17

If the mean of the 3, 4, x, 7, 10 is 6, then the value of x is.

a) 5

b) 4

c) 7

d) 6

$\displaystyle \underset{{x\to \infty }}{\mathop{{\lim }}}\,\left( {\sqrt{{{{x}^{2}}+x+1}}-x} \right)$ is equal to.

a) 1/2

b) 0

c) 1

d) -1

Equation of the line passing through (1, 2) and parallel to the line y = 3x – 1 is.

a) y – 2 = 3(x – 1)

b) y + 2 = 3(x + 1)

c) y + 2 = x + 1

d) y – 2 = x – 1

The length of the foot of perpendicular drawn from the point P (3, 4, 5) on y-axis is.

a) $\displaystyle \sqrt{{34}}$

b) 10

c) $\displaystyle \sqrt{{113}}$

d) $\displaystyle 5\sqrt{2}$

If α and β are non real cube roots of unity, then which one of the following statements is incorrect:.

a) α² = β

b) β² = 1

c) αβ² = -1

d) β²= α

If ⁿC₁₈ = ⁿC₁₂, then ³²C_n = ?.

a) 938

b) 248

c) 992

d) 496

$\displaystyle \frac{d}{{dx}}\left( {{{{\sin }}^{{-1}}}x} \right)=\frac{1}{{\sqrt{{1-{{x}^{2}}}}}}$ holds true for.

a) all real x

b) all x ∈ [-1, 1]

c) all x ∈ (-1, 1)

d) all real x for which |x| > 1

$\displaystyle \sin \frac{\pi }{{12}}$ = ?.

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

b) $\displaystyle \frac{{\left( {\sqrt{3}-1} \right)}}{{2\sqrt{2}}}$

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

d) $\displaystyle \frac{{-\left( {\sqrt{3}-1} \right)}}{{2\sqrt{2}}}$

If A and B are two sets then A ⋂ (A ⋂B’) = ….

a) ∈

b) B

c) φ

d) 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

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

a) negative real number

b) an even positive integer

c) an odd positive integer

d) irrational number

Solve the system of inequalities -2 ≤ 6x – 1 < 2.

a) $\displaystyle -\frac{1}{6}\le x<\frac{1}{2}$

b) $\displaystyle -\frac{1}{6}<x<\frac{3}{2}$

c) $\displaystyle -\frac{1}{6}<x<\frac{5}{2}$

d) $\displaystyle -\frac{1}{7}\le x>\frac{1}{2}$

If A is {1, 5, 4, 7}. Then the total number subsets of A are.

a) 20

b) 32

c) 64

d) 40

$\displaystyle \left( {1+\sin \theta } \right)\left( {\frac{{\sin \theta +\cos \theta -1}}{{\sin \theta -\cos \theta +1}}} \right)$ = ?.

a) tan θ

b) sin θ

c) cot θ

d) cos θ

$\displaystyle \underset{{\theta \to 0}}{\mathop{{\lim }}}\,\frac{{1-\cos 4\theta }}{{1-\cos 6\theta }}$ is equal to.

a) 4/9

b) 1/2

c) -1

d) -1/2

If ⁿC₃ = 220, then n = ?.

a) 11

b) 10

c) 12

d) 9

Assertion (A): If A = set of letters in Alloy B = set of letters in LOYAL, then set A & B are equal sets.

Reason (R): If two sets have exactly the same elements, they are called equal sets.

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.

Maths MCQ’s of Class 11

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