R4RIN – MCQs, Mock Tests | NCERT Class 11 MCQ Questions for Class 11 Maths sets 2

If ω is an imaginary cube root of unity, then (1 + ω – ω²)7 equalsx

1. 128 ω
2. -128 ω
3. 128 ω²
4. -128 ω²

✅ Correct Answer: 4

The least value of n for which {(1 + i)/(1 – i)}n is real, is

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

✅ Correct Answer: 2

Let z be a complex number such that |z| = 4 and arg(z) = 5π/6, then z =

1. -2√3 + 2i
2. 2√3 + 2i
3. 2√3 – 2i
4. -√3 + i

✅ Correct Answer: 1

The value of i-999 is

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

✅ Correct Answer: 3

Let z1 and z2 be two roots of the equation z² + az + b = 0, z being complex. Further assume that the origin, z1 and z1 form an equilateral triangle. Then

1. a² = b
2. a² = 2b
3. a² = 3b
4. a² = 4b

✅ Correct Answer: 3

The complex numbers sin x + i cos 2x are conjugate to each other for

1. x = nπ
2. x = 0
3. x = (n + 1/2) π
4. no value of x

✅ Correct Answer: 4

The curve represented by Im(z²) = k, where k is a non-zero real number, is

1. a pair of striaght line
2. an ellipse
3. a parabola
4. a hyperbola

✅ Correct Answer: 4

The value of x and y if (3y – 2) + i(7 – 2x) = 0

1. x = 7/2, y = 2/3
2. x = 2/7, y = 2/3
3. x = 7/2, y = 3/2
4. x = 2/7, y = 3/2

✅ Correct Answer: 1

Find real θ such that (3 + 2i × sin θ)/(1 – 2i × sin θ) is imaginary

1. θ = nπ ± π/2 where n is an integer
2. θ = nπ ± π/3 where n is an integer
3. θ = nπ ± π/4 where n is an integer
4. None of these

✅ Correct Answer: 2

If {(1 + i)/(1 – i)}n = 1 then the least value of n is

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

✅ Correct Answer: 4

If arg (z) < 0, then arg (-z) – arg (z) =

1. π
2. -π
3. -π/2
4. π/2

✅ Correct Answer: 1

if x + 1/x = 1 find the value of x2000 + 1/x2000 is

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

✅ Correct Answer: 3

If the cube roots of unity are 1, ω, ω², then the roots of the equation (x – 1)³ + 8 = 0 are

1. -1, -1 + 2ω, – 1 – 2ω²
2. – 1, -1, – 1
3. – 1, 1 – 2ω, 1 – 2ω²
4. – 1, 1 + 2ω, 1 + 2ω²

✅ Correct Answer: 3

(1 – w + w²)×(1 – w² + w4)×(1 – w4 + w8) × …………… to 2n factors is equal to

1. 2n
2. 22n
3. 23n
4. 24n

✅ Correct Answer: 2

The modulus of 5 + 4i is

1. 41
2. -41
3. √41
4. -√41

✅ Correct Answer: 3

Sum of two rational numbers is ______ number

1. rational
2. irrational
3. Integer
4. Both 1, 2 and 3

✅ Correct Answer: 1

if x² = -4 then the value of x is

1. (-2, 2)
2. (-2, ∞)
3. (2, ∞)
4. No solution

✅ Correct Answer: 4

Solve: (x + 1)² + (x² + 3x + 2)² = 0

1. x = -1, -2
2. x = -1
3. x = -2
4. None of these

✅ Correct Answer: 2

If (x + 3)/(x – 2) > 1/2 then x lies in the interval

1. (-8, ∞)
2. (8, ∞)
3. (∞, -8)
4. (∞, 8)

✅ Correct Answer: 1

The region of the XOY-plane represented by the inequalities x ≥ 6, y ≥ 2, 2x + y ≤ 10 is

1. unbounded
2. a polygon
3. exterior of a triangle
4. None of these

✅ Correct Answer: 4

The interval in which f(x) = (x – 1) × (x – 2) × (x – 3) is negative is

1. x > 2
2. 2 < x and x < 1
3. 2 < x < 1 and x < 3
4. 2 < x < 3 and x < 1

✅ Correct Answer: 4

If -2 < 2x – 1 < 2 then the value of x lies in the interval

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

✅ Correct Answer: 2

The solution of the inequality |x – 1| < 2 is

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

✅ Correct Answer: 2

If | x − 1| > 5, then

1. x∈(−∞, −4)∪(6, ∞]
2. x∈[6, ∞)
3. x∈(6, ∞)
4. x∈(−∞, −4)∪(6, ∞)

✅ Correct Answer: 4

The solution of |2/(x – 4)| > 1 where x ≠ 4 is

1. (2, 6)
2. (2, 4) ∪ (4, 6)
3. (2, 4) ∪ (4, ∞)
4. (-∞, 4) ∪ (4, 6)

✅ Correct Answer: 2

If (|x| – 1)/(|x| – 2) ‎≥ 0, x ∈ R, x ‎± 2 then the interval of x is

1. (-∞, -2) ∪ [-1, 1]
2. [-1, 1] ∪ (2, ∞)
3. (-∞, -2) ∪ (2, ∞)
4. (-∞, -2) ∪ [-1, 1] ∪ (2, ∞)

✅ Correct Answer: 4

The solution of the -12 < (4 -3x)/(-5) < 2 is

1. 56/3 < x < 14/3
2. -56/3 < x < -14/3
3. 56/3 < x < -14/3
4. -56/3 < x < 14/3

✅ Correct Answer: 4

Solve: |x – 3| < 5

1. (2, 8)
2. (-2, 8)
3. (8, 2)
4. (8, -2)

✅ Correct Answer: 2

The graph of the inequations x ≥ 0, y ≥ 0, 3x + 4y ≤ 12 is

1. interior of a triangle including the points on the sides
2. in the 2nd quadrant
3. exterior of a triangle
4. None of these

✅ Correct Answer: 1

If |x| < 5 then the value of x lies in the interval

1. (-∞, -5)
2. (∞, 5)
3. (-5, ∞)
4. (-5, 5)

✅ Correct Answer: 4

Solve: f(x) = {(x – 1)×(2 – x)}/(x – 3) ≥ 0

1. (-∞, 1] ∪ (2, ∞)
2. (-∞, 1] ∪ (2, 3)
3. (-∞, 1] ∪ (3, ∞)
4. None of these

✅ Correct Answer: 2

If x² = 4 then the value of x is

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

✅ Correct Answer: 3

The solution of the 15 < 3(x – 2)/5 < 0 is

1. 27 < x < 2
2. 27 < x < -2
3. -27 < x < 2
4. -27 < x < -2

✅ Correct Answer: 1

Solve: 1 ≤ |x – 1| ≤ 3

1. [-2, 0]
2. [2, 4]
3. [-2, 0] ∪ [2, 4]
4. None of these

✅ Correct Answer: 3

There are 12 points in a plane out of which 5 are collinear. The number of triangles formed by the points as vertices is

1. 185
2. 210
3. 220
4. 175

✅ Correct Answer: 2

The number of combination of n distinct objects taken r at a time be x is given by

1. n/2Cr
2. n/2Cr/2
3. nCr/2
4. nCr

✅ Correct Answer: 4

Four dice are rolled. The number of possible outcomes in which at least one dice show 2 is

1. 1296
2. 671
3. 625
4. 585

✅ Correct Answer: 2

Four dice are rolled. The number of possible outcomes in which at least one dice show 2 is

1. 1296
2. 671
3. 625
4. 585

✅ Correct Answer: 2

If repetition of the digits is allowed, then the number of even natural numbers having three digits is

1. 250
2. 350
3. 450
4. 550

✅ Correct Answer: 3

The number of ways in which 8 distinct toys can be distributed among 5 children is

1. 58
2. 85
3. 8P5
4. 5P5

✅ Correct Answer: 1

The value of P(n, n – 1) is

1. n
2. 2n
3. n!
4. 2n!

✅ Correct Answer: 3

In how many ways can 4 different balls be distributed among 5 different boxes when any box can have any number of balls?

1. 54 – 1
2. 54
3. 45 – 1
4. 45

✅ Correct Answer: 2

The number of ways of painting the faces of a cube with six different colors is

1. 1
2. 6
3. 6!
4. None of these

✅ Correct Answer: 1

Out of 5 apples, 10 mangoes and 13 oranges, any 15 fruits are to be distributed among 2 persons. Then the total number of ways of distribution is

1. 1800
2. 1080
3. 1008
4. 8001

✅ Correct Answer: 3

6 men and 4 women are to be seated in a row so that no two women sit together. The number of ways they can be seated is

1. 604800
2. 17280
3. 120960
4. 518400

✅ Correct Answer: 1

The number of ways can the letters of the word ASSASSINATION be arranged so that all the S are together is

1. 152100
2. 1512
3. 15120
4. 151200

✅ Correct Answer: 4

Let Tn denote the number of triangles which can be formed using the vertices of a regular polygon on n sides. If Tn+1 – Tn = 21, then n equals

1. 5
2. 7
3. 6
4. 4

✅ Correct Answer: 2

How many ways are here to arrange the letters in the word GARDEN with the vowels in alphabetical order?

1. 120
2. 240
3. 360
4. 480

✅ Correct Answer: 3

How many factors are 25 × 36 × 52 are perfect squares

1. 24
2. 12
3. 16
4. 22

✅ Correct Answer: 1

A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is

1. 40
2. 196
3. 280
4. 346

✅ Correct Answer: 2

In how many ways in which 8 students can be sated in a line is

1. 40230
2. 40320
3. 5040
4. 50400

✅ Correct Answer: 2

The number of squares that can be formed on a chess board is

1. 64
2. 160
3. 224
4. 204

✅ Correct Answer: 4

How many 3-letter words with or without meaning, can be formed out of the letters of the word, LOGARITHMS, if repetition of letters is not allowed

1. 720
2. 420
3. 5040
4. None of these

✅ Correct Answer: 1

The coefficient of y in the expansion of (y² + c/y)5 is

1. 10c
2. 10c²
3. 10c³
4. None of these

✅ Correct Answer: 3

The coefficient of y in the expansion of (y² + c/y)5 is

1. 10c
2. 10c²
3. 10c³
4. None of these

✅ Correct Answer: 3

(1.1)10000 is _____ 1000

1. greater than
2. less than
3. equal to
4. None of these

✅ Correct Answer: 1

The fourth term in the expansion (x – 2y)12 is

1. -1670 x9 × y³
2. -7160 x9 × y³
3. -1760 x9 × y³
4. -1607 x9 × y³

✅ Correct Answer: 3

If n is a positive integer, then (√3+1)2n+1 + (√3−1)2n+1 is

1. an even positive integer
2. a rational number
3. an odd positive integer
4. an irrational number

✅ Correct Answer: 4

If the third term in the binomial expansion of (1 + x)m is (-1/8)x² then the rational value of m is

1. 2
2. 1/2
3. 3
4. 4

✅ Correct Answer: 2

The greatest coefficient in the expansion of (1 + x)10 is

1. 10!/(5!)
2. 10!/(5!)²
3. 10!/(5! × 4!)²
4. 10!/(5! × 4!)

✅ Correct Answer: 2

The coefficient of xn in the expansion of (1 – 2x + 3x² – 4x³ + ……..)-n is

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

✅ Correct Answer: 2

The value of n in the expansion of (a + b)n if the first three terms of the expansion are 729, 7290 and 30375, respectively is

1. 2
2. 4
3. 6
4. 8

✅ Correct Answer: 3

If α and β are the roots of the equation x² – x + 1 = 0 then the value of α2009 + β2009 is

1. 0
2. 1
3. -1
4. 10

✅ Correct Answer: 2

The general term of the expansion (a + b)n is

1. Tr+1 = nCr × ar × br
2. Tr+1 = nCr × ar × bn-r
3. Tr+1 = nCr × an-r × bn-r
4. Tr+1 = nCr × an-r × br

✅ Correct Answer: 4

The coefficient of xn in the expansion (1 + x + x² + …..)-n is

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

✅ Correct Answer: 2

If n is a positive integer, then (√5+1)2n + 1 − (√5−1)2n + 1 is

1. an odd positive integer
2. not an integer
3. an even positive integer
4. none of these

✅ Correct Answer: 2

In the expansion of (a + b)n, if n is even then the middle term is

1. (n/2 + 1)th term
2. (n/2)th term
3. nth term
4. (n/2 – 1)th term

✅ Correct Answer: 1

In the expansion of (a + b)n, if n is odd then the number of middle term is/are

1. 0
2. 1
3. 2
4. More than 2

✅ Correct Answer: 3

if n is a positive ineger then 23nn – 7n – 1 is divisible by

1. 7
2. 9
3. 49
4. 81

✅ Correct Answer: 3

In the binomial expansion of (71/2 + 51/3)37, the number of integers are

1. 2
2. 4
3. 6
4. 8

✅ Correct Answer: 3

The number of ordered triplets of positive integers which are solution of the equation x + y + z = 100 is

1. 4815
2. 4851
3. 8451
4. 8415

✅ Correct Answer: 2

In the binomial expansion of (a + b)n, the coefficient of fourth and thirteenth terms are equal to each other, then the value of n is

1. 10
2. 15
3. 20
4. 25

✅ Correct Answer: 2

If a, b, c are in G.P., then the equations ax² + 2bx + c = 0 and dx² + 2ex + f = 0 have a common root if d/a, e/b, f/c are in

1. AP
2. GP
3. HP
4. None of these

✅ Correct Answer: 1

If a, b, c are in AP then

1. b = a + c
2. 2b = a + c
3. b² = a + c
4. 2b² = a + c

✅ Correct Answer: 2

If a, b, c are in AP then

1. b = a + c
2. 2b = a + c
3. b² = a + c
4. 2b² = a + c

✅ Correct Answer: 2

Three numbers form an increasing GP. If the middle term is doubled, then the new numbers are in Ap. The common ratio of GP is

1. 2 + √3
2. 2 – √3
3. 2 ± √3
4. None of these

✅ Correct Answer: 1

The sum of n terms of the series (1/1.2) + (1/2.3) + (1/3.4) + …… is

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

✅ Correct Answer: 1

If 1/(b + c), 1/(c + a), 1/(a + b) are in AP then

1. a, b, c are in AP
2. a², b², c² are in AP
3. 1/1, 1/b, 1/c are in AP
4. None of these

✅ Correct Answer: 2