(1 – w + w²)×(1 – w² + w4)×(1 – w4 + w8) × …………… to 2n factors is equal to
1. 2n
2.22n
3.23n
4.24n
Posted Date:-2021-12-25 13:30:50
(1.1)10000 is _____ 1000
1.greater than
2. less than
3. equal to
4.None of these
Posted Date:-2021-12-25 14:15:35
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
Posted Date:-2021-12-25 13:58:00
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
Posted Date:-2021-12-25 14:01:55
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
Posted Date:-2021-12-25 13:26:44
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
Posted Date:-2021-12-25 13:52:00
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
Posted Date:-2021-12-25 13:53:02
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
Posted Date:-2021-12-25 14:05:20
How many factors are 25 × 36 × 52 are perfect squares
1.24
2.12
3.16
4.22
Posted Date:-2021-12-25 14:01:16
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
Posted Date:-2021-12-25 14:00:42
If (x + 3)/(x – 2) > 1/2 then x lies in the interval
1.(-8, ∞)
2. (8, ∞)
3.(∞, -8)
4. (∞, 8)
Posted Date:-2021-12-25 13:35:22
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, ∞)
Posted Date:-2021-12-25 13:42:03
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)
Posted Date:-2021-12-25 13:37:32
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
Posted Date:-2021-12-25 15:26:55
If a, b, c are in AP then
1.b = a + c
2.2b = a + c
3.b² = a + c
4.2b² = a + c
Posted Date:-2021-12-25 15:23:42
If a, b, c are in AP then
1.b = a + c
2.2b = a + c
3.b² = a + c
4.2b² = a + c
Posted Date:-2021-12-25 15:24:17
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
Posted Date:-2021-12-25 14:33:06
If arg (z) < 0, then arg (-z) – arg (z) =
1.Ï€
2.-Ï€
3.-Ï€/2
4. π/2
Posted Date:-2021-12-25 13:27:54
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
Posted Date:-2021-12-25 13:20:43
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
Posted Date:-2021-12-25 14:21:46
if n is a positive ineger then 23nn – 7n – 1 is divisible by
1. 7
2.9
3.49
4.81
Posted Date:-2021-12-25 14:28:23
if n is a positive ineger then 23nn – 7n – 1 is divisible by
1. 7
2.9
3.49
4.81
Posted Date:-2021-12-25 14:28:23
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
Posted Date:-2021-12-25 14:17:28
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
Posted Date:-2021-12-25 14:23:56
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
Posted Date:-2021-12-25 13:53:51
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
Posted Date:-2021-12-25 13:30:00
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
Posted Date:-2021-12-25 14:18:08
if x + 1/x = 1 find the value of x2000 + 1/x2000 is
1. 0
2.1
3. -1
4.None of these
Posted Date:-2021-12-25 13:28:37
if x² = -4 then the value of x is
1.(-2, 2)
2. (-2, ∞)
3.(2, ∞)
4.No solution
Posted Date:-2021-12-25 13:33:48
If x² = 4 then the value of x is
1. -2
2.2
3.-2, 2
4.None of these
Posted Date:-2021-12-25 13:47:03
If {(1 + i)/(1 – i)}n = 1 then the least value of n is1.1
2.2
3.3
4.4
Posted Date:-2021-12-25 13:27:15
If | x − 1| > 5, then
1. x∈(−∞, −4)∪(6, ∞]
2.x∈[6, ∞)
3.x∈(6, ∞)
4.x∈(−∞, −4)∪(6, ∞)
Posted Date:-2021-12-25 13:38:56
If |x| < 5 then the value of x lies in the interval
1.(-∞, -5)
2. (∞, 5)
3. (-5, ∞)
4. (-5, 5)
Posted Date:-2021-12-25 13:45:27
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
Posted Date:-2021-12-25 13:55:57
In how many ways in which 8 students can be sated in a line is
1. 40230
2.40320
3.5040
4.50400
Posted Date:-2021-12-25 14:03:55
In the binomial expansion of (71/2 + 51/3)37, the number of integers are
1.2
2.4
3.6
4.8
Posted Date:-2021-12-25 14:29:19
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
Posted Date:-2021-12-25 14:32:11
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
Posted Date:-2021-12-25 14:24:51
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
Posted Date:-2021-12-25 14:27:22
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
Posted Date:-2021-12-25 14:00:02
Let z be a complex number such that |z| = 4 and arg(z) = 5Ï€/6, then z =
1. -2√3 + 2i
2.2√3 + 2i
3.2√3 – 2i
4.-√3 + i
Posted Date:-2021-12-25 13:22:06
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
Posted Date:-2021-12-25 13:23:35
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
Posted Date:-2021-12-25 13:57:26
Solve: (x + 1)² + (x² + 3x + 2)² = 0
1. x = -1, -2
2.x = -1
3. x = -2
4.None of these
Posted Date:-2021-12-25 13:34:31
Solve: 1 ≤ |x – 1| ≤ 3
1.[-2, 0]
2.[2, 4]
3.[-2, 0] ∪ [2, 4]
4.None of these
Posted Date:-2021-12-25 13:48:26
Solve: f(x) = {(x – 1)×(2 – x)}/(x – 3) ≥ 01. (-∞, 1] ∪ (2, ∞)
2. (-∞, 1] ∪ (2, 3)
3.(-∞, 1] ∪ (3, ∞)
4.None of these
Posted Date:-2021-12-25 13:46:22
Solve: |x – 3| < 5
1.(2, 8)
2.(-2, 8)
3.(8, 2)
4.(8, -2)
Posted Date:-2021-12-25 13:43:55
Sum of two rational numbers is ______ number
1.rational
2.irrational
3.Integer
4.Both 1, 2 and 3
Posted Date:-2021-12-25 13:32:59
The coefficient of xn in the expansion (1 + x + x² + …..)-n is
1. 1
2.(-1)n
3.n
4.n+1
Posted Date:-2021-12-25 14:23:04
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
Posted Date:-2021-12-25 14:20:07
The coefficient of y in the expansion of (y² + c/y)5 is
1. 10c
2.10c²
3.10c³
4.None of these
Posted Date:-2021-12-25 14:14:39
The coefficient of y in the expansion of (y² + c/y)5 is
1. 10c
2.10c²
3.10c³
4.None of these
Posted Date:-2021-12-25 14:15:04
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
Posted Date:-2021-12-25 13:24:25
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
Posted Date:-2021-12-25 13:25:14
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
Posted Date:-2021-12-25 13:25:14
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
Posted Date:-2021-12-25 14:16:39
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
Posted Date:-2021-12-25 14:22:25
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
Posted Date:-2021-12-25 13:44:36
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!)
Posted Date:-2021-12-25 14:19:17
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
Posted Date:-2021-12-25 13:36:51
The least value of n for which {(1 + i)/(1 – i)}n is real, is1.1
2.2
3.3
4.4
Posted Date:-2021-12-25 13:21:20
The modulus of 5 + 4i is
1. 41
2.-41
3. √41
4.-√41
Posted Date:-2021-12-25 13:32:03
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
Posted Date:-2021-12-25 13:50:13
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
Posted Date:-2021-12-25 14:30:47
The number of squares that can be formed on a chess board is
1.64
2.160
3.224
4.204
Posted Date:-2021-12-25 14:04:30
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
Posted Date:-2021-12-25 13:58:48
The number of ways in which 8 distinct toys can be distributed among 5 children is
1.58
2.85
3.8P5
4.5P5
Posted Date:-2021-12-25 13:54:31
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
Posted Date:-2021-12-25 13:56:36
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
Posted Date:-2021-12-25 13:36:04
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
Posted Date:-2021-12-25 13:42:46
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
Posted Date:-2021-12-25 13:47:45
The solution of the inequality |x – 1| < 2 is
1. (1, ∞)
2. (-1, 3)
3.(1, -3)
4.(∞, 1)
Posted Date:-2021-12-25 13:38:16
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)
Posted Date:-2021-12-25 13:41:18
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
Posted Date:-2021-12-25 15:25:57
The value of i-999 is
1. 1
2.-1
3.i
4.-i
Posted Date:-2021-12-25 13:22:46
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
Posted Date:-2021-12-25 14:20:36
The value of P(n, n – 1) is
1. n
2. 2n
3.n!
4. 2n!
Posted Date:-2021-12-25 13:55:17
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
Posted Date:-2021-12-25 13:25:58
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
Posted Date:-2021-12-25 13:49:20
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
Posted Date:-2021-12-25 15:25:04