(1 – w + w²)×(1 – w² + w4)×(1 – w4 + w8) × …………… to 2n factors is equal to
1. 2n
2.22n
3.23n
4.24n
(1.1)10000 is _____ 1000
1.greater than
2. less than
3. equal to
4.None of these
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
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
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
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
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
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
How many factors are 25 × 36 × 52 are perfect squares
1.24
2.12
3.16
4.22
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
If (x + 3)/(x – 2) > 1/2 then x lies in the interval
1.(-8, ∞)
2. (8, ∞)
3.(∞, -8)
4. (∞, 8)
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, ∞)
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)
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
If a, b, c are in AP then
1.b = a + c
2.2b = a + c
3.b² = a + c
4.2b² = a + c
If a, b, c are in AP then
1.b = a + c
2.2b = a + c
3.b² = a + c
4.2b² = a + c
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
If arg (z) < 0, then arg (-z) – arg (z) =
1.Ï€
2.-Ï€
3.-Ï€/2
4. π/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
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
if n is a positive ineger then 23nn – 7n – 1 is divisible by
1. 7
2.9
3.49
4.81
if n is a positive ineger then 23nn – 7n – 1 is divisible by
1. 7
2.9
3.49
4.81
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
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
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
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
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
if x + 1/x = 1 find the value of x2000 + 1/x2000 is
1. 0
2.1
3. -1
4.None of these
if x² = -4 then the value of x is
1.(-2, 2)
2. (-2, ∞)
3.(2, ∞)
4.No solution
If x² = 4 then the value of x is
1. -2
2.2
3.-2, 2
4.None of these
If {(1 + i)/(1 – i)}n = 1 then the least value of n is1.1
2.2
3.3
4.4
If | x − 1| > 5, then
1. x∈(−∞, −4)∪(6, ∞]
2.x∈[6, ∞)
3.x∈(6, ∞)
4.x∈(−∞, −4)∪(6, ∞)
If |x| < 5 then the value of x lies in the interval
1.(-∞, -5)
2. (∞, 5)
3. (-5, ∞)
4. (-5, 5)
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
In how many ways in which 8 students can be sated in a line is
1. 40230
2.40320
3.5040
4.50400
In the binomial expansion of (71/2 + 51/3)37, the number of integers are
1.2
2.4
3.6
4.8
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
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
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
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
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
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
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
Solve: (x + 1)² + (x² + 3x + 2)² = 0
1. x = -1, -2
2.x = -1
3. x = -2
4.None of these
Solve: 1 ≤ |x – 1| ≤ 3
1.[-2, 0]
2.[2, 4]
3.[-2, 0] ∪ [2, 4]
4.None of these
Solve: f(x) = {(x – 1)×(2 – x)}/(x – 3) ≥ 01. (-∞, 1] ∪ (2, ∞)
2. (-∞, 1] ∪ (2, 3)
3.(-∞, 1] ∪ (3, ∞)
4.None of these
Solve: |x – 3| < 5
1.(2, 8)
2.(-2, 8)
3.(8, 2)
4.(8, -2)
Sum of two rational numbers is ______ number
1.rational
2.irrational
3.Integer
4.Both 1, 2 and 3
The coefficient of xn in the expansion (1 + x + x² + …..)-n is
1. 1
2.(-1)n
3.n
4.n+1
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
The coefficient of y in the expansion of (y² + c/y)5 is
1. 10c
2.10c²
3.10c³
4.None of these
The coefficient of y in the expansion of (y² + c/y)5 is
1. 10c
2.10c²
3.10c³
4.None of these
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
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
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
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
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
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
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!)
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
The least value of n for which {(1 + i)/(1 – i)}n is real, is1.1
2.2
3.3
4.4
The modulus of 5 + 4i is
1. 41
2.-41
3. √41
4.-√41
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
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
The number of squares that can be formed on a chess board is
1.64
2.160
3.224
4.204
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
The number of ways in which 8 distinct toys can be distributed among 5 children is
1.58
2.85
3.8P5
4.5P5
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
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
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
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
The solution of the inequality |x – 1| < 2 is
1. (1, ∞)
2. (-1, 3)
3.(1, -3)
4.(∞, 1)
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)
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
The value of i-999 is
1. 1
2.-1
3.i
4.-i
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
The value of P(n, n – 1) is
1. n
2. 2n
3.n!
4. 2n!
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
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
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