(1 + x)n ≥ ____ for all n ∈ N,where x > -1
1.1 + nx
2.1 – nx
3.1 + nx/2 (
4.1 – nx/2
(A’)’ = ?
1.∪ – A
2.A’
3.∪
4.A
(n² + n) is ____ for all n ∈ N.
1.Even
2.odd
3.Either even or odd
4.None of these
{ (A, B) : A² +B² = 1} on the sets has the following relation1.reflexive
2.symmetric
3.none
4.reflexive and transitive
{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
{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)}
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
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)
102n-1 + 1 is divisible by ____ for all N ∈ N
1.9
2.10
3.11
4.13
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
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
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
Empty set is a?
1. Finite Set
2. Invalid Set
3.None of the above
4.Infinite Set
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
For all n ∈ N, 3×52n+1 + 23n+1 is divisible by
1.19
2.17
3.23
4.25
For all n∈N, 72n − 48n−1 is divisible by :
1.25
2.2304
3.1234
4.26
For any natural number n, 7n – 2n is divisible by
1.3
2.4
3.5
4.7
How many rational and irrational numbers are possible between 0 and 1?
1. 0
2.Finite
3.Infinite
4.1
If 3 × tan(x – 15) = tan(x + 15), then the value of x is
1.30
2.45
3. 60
4.90
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
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
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
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)
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
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
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
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
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
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
If f(x) = log3 x and A = (3, 27) then f(A) =
1.(1, 1)
2.(3, 3)
3. (1, 3)
4. (2, 3)
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
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
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
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}
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
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
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
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
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
if z lies on |z| = 1, then 2/z lies on
1.a circle
2. an ellipse
3.a straight line
4. a parabola
In 2nd quadrant?
1. X < 0, Y < 0
2. X < 0, Y > 0
3.X > 0, Y > 0
4.X > 0, Y < 0
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
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
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
In last quadrant?
1.X < 0, Y > 0
2. X < 0, Y < 0
3. X > 0, Y < 0
4. X > 0, Y > 0
Let A = {-2, -1, 0} and f(x) = 2x – 3 then the range of f is1.{7, -5, -3}
2.{-7, 5, -3}
3.{-7, -5, 3}
4. {-7, -5, -3}
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
n(n + 1)(n + 5) is a multiple of ____ for all n ∈ N
1.2
2.3
3.5
4.7
The domain of tan-1 (2x + 1) is
1. R
2.R -{1/2}
3.R -{-1/2}
4.None of these
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
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}
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
The function f(x) = sin (πx/2) + cos (πx/2) is periodic with period
1.4
2.6
3.12
4.24
the function f(x) = x – [x] has period of
1.0
2.1
3.2
4.3
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)
The members of the set S = {x | x is the square of an integer and x < 100} is1. {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}
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
The number of binary operations on the set {a, b} are1.2
2.4
3.8
4.16
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°
The period of the function f(x) = sin4 3x + cos4 3x is
1.π/2
2.π/3
3. π/4
4.π/6
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
The range of the function f(x) = 3x – 2‚ is
1.(- ∞, ∞)
2.R – {3}
3.(- ∞, 0)
4.(0, – ∞)
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
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
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
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
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
The value of √(-144) is
1.12i
2.-12i
3. ±12i
4.None of these
The value of √(-16) is
1. -4i
2.4i
3.-2i
4.2i
The value of √(-25) + 3√(-4) + 2√(-9) is
1. 13i
2. -13i
3.17i
4. -17i
The value of cos 180° is
1.0
2.1
3. -1
4.infinite
The value of cos 20 + 2sin² 55 – √2 sin65 is
1.0
2.1
3.-1
4.None of these
The value of cos 5π is
1. 0
2.1
3.-1
4.None of these
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)
The value of tan 20 × tan 40 × tan 80 is
1. tan 30
2.tan 60
3.2 tan 30
4.2 tan 60
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
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
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}
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}