R4RIN – MCQs, Mock Tests | NCERT Class 11 MCQ Questions for Class 11 Maths sets 1

If A, B and C are any three sets, then A – (B ∪ C) is equal to

1. (A – B) ∪ (A – C)
2. (A – B) ∪ C
3. (A – B) ∩ C
4. (A – B) ∩ (A – C)

✅ Correct Answer: 4

(A’)’ = ?

1. ∪ – A
2. A’
3. ∪
4. A

✅ Correct Answer: 4

A – B is read as?

1. Difference of A and B of B and A
2. None of the above
3. Difference of B and A
4. Both a and b

✅ Correct Answer: 1

If A, B and C are any three sets, then A × (B ∪ C) is equal to

1. (A × B) ∪ (A × C)
2. (A ∪ B) × (A ∪ C)
3. (A × B) ∩ (A × C)
4. None of these

✅ Correct Answer: 1

IF A = [5, 6, 7] and B = [7, 8, 9] then A ∪ B is equal to

1. [5, 6, 7, 8, 9]
2. [5, 6, 7]
3. [7, 8, 9]
4. None of these

✅ Correct Answer: 1

Which of the following sets are null sets

1. {x: |x |< -4, x ?N}
2. 2 and 3
3. Set of all prime numbers between 15 and 19
4. {x: x < 5, x > 6}

✅ Correct Answer: 2

IF R = {(2, 1),(4, 3),(4, 5)}, then range of the function is?

1. Range R = {2, 4}
2. Range R = {1, 3, 5}
3. Range R = {2, 3, 4, 5}
4. Range R {1, 1, 4, 5}

✅ Correct Answer: 2

The members of the set S = {x | x is the square of an integer and x < 100} is

1. {0, 2, 4, 5, 9, 58, 49, 56, 99, 12}
2. {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}
3. {1, 4, 9, 16, 25, 36, 64, 81, 85, 99}
4. {0, 1, 4, 9, 16, 25, 36, 49, 64, 121}

✅ Correct Answer: 2

In a class of 120 students numbered 1 to 120, all even numbered students opt for Physics, whose numbers are divisible by 5 opt for Chemistry and those whose numbers are divisible by 7 opt for Math. How many opt for none of the three subjects?

1. 19
2. 41
3. 21
4. 57

✅ Correct Answer: 2

{ (A, B) : A² +B² = 1} on the sets has the following relation

1. reflexive
2. symmetric
3. none
4. reflexive and transitive

✅ Correct Answer: 2

Two finite sets have N and M elements. The number of elements in the power set of first set is 48 more than the total number of elements in power set of the second test. Then the value of M and N are

1. 7, 6
2. 6, 4
3. 7, 4
4. 6, 3

✅ Correct Answer: 2

The range of the function f(x) = 3x – 2‚ is

1. (- ∞, ∞)
2. R – {3}
3. (- ∞, 0)
4. (0, – ∞)

✅ Correct Answer: 1

If A, B, C be three sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C, then,

1. B = C
2. A = C
3. A = B = C
4. A = B

✅ Correct Answer: 1

In 2nd quadrant?

1. X < 0, Y < 0
2. X < 0, Y > 0
3. X > 0, Y > 0
4. X > 0, Y < 0

✅ Correct Answer: 2

How many rational and irrational numbers are possible between 0 and 1?

1. 0
2. Finite
3. Infinite
4. 1

✅ Correct Answer: 3

Empty set is a?

1. Finite Set
2. Invalid Set
3. None of the above
4. Infinite Set

✅ Correct Answer: 1

If A = [5, 6, 7] and B = [7, 8, 9] then A U B is equal to

1. [5, 6, 7, 8, 9]
2. [5, 6, 7]
3. [7, 8, 9]
4. None of these

✅ Correct Answer: 1

Which of the following two sets are equal

1. A = {1, 2} and B = {1}
2. A = {1, 2} and B = {1, 2, 3}
3. A = {1, 2, 3} and B = {2, 1, 3}
4. A = {1, 2, 4} and B = {1, 2, 3}

✅ Correct Answer: 3

In a class of 50 students, 10 did not opt for math, 15 did not opt for science and 2 did not opt for either. How many students of the class opted for both math and science.

1. 24
2. 25
3. 26
4. 27

✅ Correct Answer: 4

In last quadrant?

1. X < 0, Y > 0
2. X < 0, Y < 0
3. X > 0, Y < 0
4. X > 0, Y > 0

✅ Correct Answer: 4

If f(x) = (a – x)1/n, a > 0 and n ∈ N, then the value of f(f(x)) is

1. 1/x
2. x
3. x²
4. x1/2

✅ Correct Answer: 2

The domain of the definition of the real function f(x) = √(log12 x² ) of the real variable x is

1. x > 0
2. |x| ≥ 1
3. |x| > 4
4. x ≥ 4

✅ Correct Answer: 2

If f(x) = ex and g(x) = loge x then the value of fog(1) is

1. 0
2. 1
3. -1
4. None of these

✅ Correct Answer: 2

Two functions f and g are said to be equal if f

1. the domain of f = the domain of g
2. the co-domain of f = the co-domain of g
3. f(x) = g(x) for all x
4. All of the above

✅ Correct Answer: 4

A function f(x) is said to be an odd function if

1. f(-x) = f(x)
2. f(-x) = -f(x)
3. f(-x) = k * f(x) where k is a constant
4. None of these

✅ Correct Answer: 2

If f(x) is an odd differentiable function on R, then df(x)/dx is a/an

1. Even function
2. Odd function
3. Either even or odd function
4. Neither even nor odd function

✅ Correct Answer: 1

The function f(x) = sin (‎πx/2) + cos (πx/2) is periodic with period

1. 4
2. 6
3. 12
4. 24

✅ Correct Answer: 1

If f(x) = log3 x and A = (3, 27) then f(A) =

1. (1, 1)
2. (3, 3)
3. (1, 3)
4. (2, 3)

✅ Correct Answer: 3

The domain of tan-1 (2x + 1) is

1. R
2. R -{1/2}
3. R -{-1/2}
4. None of these

✅ Correct Answer: 1

the function f(x) = x – [x] has period of

1. 0
2. 1
3. 2
4. 3

✅ Correct Answer: 2

If f(x) =(3x – 2)/(2x – 3) then the value of f(f(x)) is

1. x
2. x²
3. x³
4. None of these

✅ Correct Answer: 1

Let R be the set of real numbers. If f(x) = x² and g(x) = 2x + 1, then fog(x) is equal to

1. 2x + 1
2. 2x² + 1
3. (2x + 1)²
4. None of these

✅ Correct Answer: 2

A relation R is defined from the set of integers to the set of real numbers as (x, y) = R if x² + y² = 16 then the domain of R is

1. (0, 4, 4)
2. (0, -4, 4)
3. (0, -4, -4)
4. None of these

✅ Correct Answer: 2

The number of binary operations on the set {a, b} are

1. 2
2. 4
3. 8
4. 16

✅ Correct Answer: 4

If f is an even function and g is an odd function the fog is a/an

1. Even function
2. Odd function
3. Either even or odd function
4. Neither even nor odd function

✅ Correct Answer: 1

The domain of the function f(x) = 1/(x² – 3x + 2) is

1. {1, 2}
2. R
3. R – {1, 2}
4. R – {1, -2}

✅ Correct Answer: 3

The domain of the function f(x) = sin-1 (tan x) is

1. -π/4 ≤ x ≤ π/4
2. nπ – π/4 ≤ x ≤ nπ + π/4
3. nπ – π/3 ≤ x ≤ nπ + π/3
4. -π/3 ≤ x ≤ π/3

✅ Correct Answer: 2

Let A = {-2, -1, 0} and f(x) = 2x – 3 then the range of f is

1. {7, -5, -3}
2. {-7, 5, -3}
3. {-7, -5, 3}
4. {-7, -5, -3}

✅ Correct Answer: 4

The range of the function 7-xPx-3 is

1. {1, 2, 3, 4, 5}
2. {3, 4, 5}
3. {1, 2, 3}
4. None of these

✅ Correct Answer: 3

The period of the function f(x) = sin4 3x + cos4 3x is

1. π/2
2. π/3
3. π/4
4. π/6

✅ Correct Answer: 4

The value of cos² x + cos² y – 2cos x × cos y × cos (x + y) is

1. sin (x + y)
2. sin² (x + y)
3. sin³ (x + y)
4. sin4 (x + y)

✅ Correct Answer: 2

If a×cos x + b × cos x = c, then the value of (a × sin x – b²cos x)² is

1. a² + b² + c²
2. a² – b² – c²
3. a² – b² + c²
4. a² + b² – c²

✅ Correct Answer: 4

If cos a + 2cos b + cos c = 2 then a, b, c are in

1. 2b = a + c
2. b² = a × c
3. a = b = c
4. None of these

✅ Correct Answer: 1

The value of cos 5π is

1. 0
2. 1
3. -1
4. None of these

✅ Correct Answer: 3

In a triangle ABC, cosec A (sin B cos C + cos B sin C) equals

1. c/a
2. 1
3. a/c
4. None of these

✅ Correct Answer: 2

If the angles of a triangle be in the ratio 1 : 4 : 5, then the ratio of the greatest side to the smallest side is

1. 4 : (√5 – 1)
2. 5 : 4
3. (√5 – 1) : 4
4. None of these

✅ Correct Answer: 1

The value of cos 180° is

1. 0
2. 1
3. -1
4. infinite

✅ Correct Answer: 3

The perimeter of a triangle ABC is 6 times the arithmetic mean of the sines of its angles. If the side b is 2, then the angle B is

1. 30°
2. 90°
3. 60°
4. 120°

✅ Correct Answer: 2

If 3 × tan(x – 15) = tan(x + 15), then the value of x is

1. 30
2. 45
3. 60
4. 90

✅ Correct Answer: 2

If the sides of a triangle are 13, 7, 8 the greatest angle of the triangle is

1. π/3
2. π/2
3. 2π/3
4. 3π/2

✅ Correct Answer: 3

The value of tan 20 × tan 40 × tan 80 is

1. tan 30
2. tan 60
3. 2 tan 30
4. 2 tan 60

✅ Correct Answer: 2

The general solution of √3 cos x – sin x = 1 is

1. x = n × π + (-1)n × (π/6)
2. x = π/3 – n × π + (-1)n × (π/6)
3. x = π/3 + n × π + (-1)n × (π/6)
4. x = π/3 – n × π + (π/6)

✅ Correct Answer: 3

If tan² θ = 1 – e², then the value of sec θ + tan³ θ × cosec θ is

1. 2 – e²
2. (2 – e²)1/2
3. (2 – e²)²
4. (2 – e²)3/2

✅ Correct Answer: 4

The value of cos 20 + 2sin² 55 – √2 sin65 is

1. 0
2. 1
3. -1
4. None of these

✅ Correct Answer: 2

If the radius of the circumcircle of an isosceles triangle PQR is equal to PQ ( = PR), then the angle P is

1. 2π/3
2. π/3
3. π/2
4. π/6

✅ Correct Answer: 1

The value of 4 × sin x × sin(x + π/3) × sin(x + 2π/3) is

1. sin x
2. sin 2x
3. sin 3x
4. sin 4x

✅ Correct Answer: 3

If tan A – tan B = x and cot B – cot A = y, then the value of cot (A – B) is

1. x + y
2. 1/x + y
3. x + 1/y
4. 1/x + 1/y

✅ Correct Answer: 4

The value of (sin 7x + sin 5x) /(cos 7x + cos 5x) + (sin 9x + sin 3x) / (cos 9x + cos 3x) is

1. tan 6x
2. 2 tan 6x
3. 3 tan 6x
4. 4 tan 6x

✅ Correct Answer: 2

The value of (sin 7x + sin 5x) /(cos 7x + cos 5x) + (sin 9x + sin 3x) / (cos 9x + cos 3x) is

1. tan 6x
2. 2 tan 6x
3. 3 tan 6x
4. 4 tan 6x

✅ Correct Answer: 2

The sum of the series 1³ + 2³ + 3³ + ………..n³ is

1. {(n + 1)/2}²
2. {n/2}²
3. n(n + 1)/2
4. {n(n + 1)/2}²

✅ Correct Answer: 4

If n is an odd positive integer, then an + bn is divisible by :

1. a² + b²
2. a + b
3. a – b
4. None of these

✅ Correct Answer: 2

1/(1 ∙ 2) + 1/(2 ∙ 3) + 1/(3 ∙ 4) + ….. + 1/{n(n + 1)}

1. n(n + 1)
2. n/(n + 1)
3. 2n/(n + 1)
4. 3n/(n + 1)

✅ Correct Answer: 2

The sum of the series 1² + 2² + 3² + ………..n² is

1. n(n + 1)(2n + 1)
2. n(n + 1)(2n + 1)/2
3. n(n + 1)(2n + 1)/3
4. n(n + 1)(2n + 1)/6

✅ Correct Answer: 4

{1 – (1/2)}{1 – (1/3)}{1 – (1/4)} ……. {1 – 1/(n + 1)} =

1. 1/(n + 1) for all n ∈ N.
2. 1/(n + 1) for all n ∈ R
3. n/(n + 1) for all n ∈ N
4. n/(n + 1) for all n ∈ R

✅ Correct Answer: 1

For any natural number n, 7n – 2n is divisible by

1. 3
2. 4
3. 5
4. 7

✅ Correct Answer: 3

1/(1 ∙ 2 ∙ 3) + 1/(2 ∙ 3 ∙ 4) + …….. + 1/{n(n + 1)(n + 2)} =

1. {n(n + 3)}/{4(n + 1)(n + 2)}
2. (n + 3)/{4(n + 1)(n + 2)}
3. n/{4(n + 1)(n + 2)}
4. None of these

✅ Correct Answer: 1

The nth terms of the series 3 + 7 + 13 + 21 +………. is

1. 4n – 1
2. n² + n + 1
3. n + 2
4. None of these

✅ Correct Answer: 2

n(n + 1)(n + 5) is a multiple of ____ for all n ∈ N

1. 2
2. 3
3. 5
4. 7

✅ Correct Answer: 2

Find the number of shots arranged in a complete pyramid the base of which is an equilateral triangle, each side containing n shots.

1. n(n+1)(n+2)/3
2. n(n+1)(n+2)/6
3. n(n+2)/6
4. (n+1)(n+2)/6

✅ Correct Answer: 2

(n² + n) is ____ for all n ∈ N.

1. Even
2. odd
3. Either even or odd
4. None of these

✅ Correct Answer: 1

For all n ∈ N, 3×52n+1 + 23n+1 is divisible by

1. 19
2. 17
3. 23
4. 25

✅ Correct Answer: 2

(1 + x)n ≥ ____ for all n ∈ N,where x > -1

1. 1 + nx
2. 1 – nx
3. 1 + nx/2 (
4. 1 – nx/2

✅ Correct Answer: 1

102n-1 + 1 is divisible by ____ for all N ∈ N

1. 9
2. 10
3. 11
4. 13

✅ Correct Answer: 3

For all n∈N, 72n − 48n−1 is divisible by :

1. 25
2. 2304
3. 1234
4. 26

✅ Correct Answer: 2

{1/(3 ∙ 5)} + {1/(5 ∙ 7)} + {1/(7 ∙ 9)} + ……. + 1/{(2n + 1)(2n + 3)} =

1. n/(2n + 3)
2. n/{2(2n + 3)}
3. n/{3(2n + 3)}
4. n/{4(2n + 3)}

✅ Correct Answer: 3

The value of √(-16) is

1. -4i
2. 4i
3. -2i
4. 2i

✅ Correct Answer: 2

The value of √(-144) is

1. 12i
2. -12i
3. ±12i
4. None of these

✅ Correct Answer: 1

The value of √(-25) + 3√(-4) + 2√(-9) is

1. 13i
2. -13i
3. 17i
4. -17i

✅ Correct Answer: 3

if z lies on |z| = 1, then 2/z lies on

1. a circle
2. an ellipse
3. a straight line
4. a parabola

✅ Correct Answer: 1