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JEE Questions for Maths Sets Relations And Functions Quiz 4 - MCQExams.com
JEE
Maths
Sets Relations And Functions
Quiz 4
The range of the function
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[0,3]
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[0,√3]
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(-∞,∞)
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None of these
The domain of the real valued function
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0%
2)
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0%
If f : R → R is defined by f(x)= [2x ]- 2[x], ∀ x ℇ R, where [x] is the greatest integer not exceeding x, then the range of f is
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{ x ℇ R :0 ≤ x ≤1}
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{0 ,1}
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{ x ℇ R : x > 0}
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{ x ℇ R : x ≤ 0}
The period of the function
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π
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2)
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2π
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1
The period of the function
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5π
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2π
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2)
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10π
The domain of the function
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[4, 6]
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(-∞,6)
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[2, 3)
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None of these
The domain of the function
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[--1, 2] - {0}
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[-2, -1, 1)
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[-2, 2] - {0}
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[1, 2]
The range of f(x) = cos x - sin x is
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[-1, 1]
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(-1, 2)
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0%
If f': R → S, defined by f(x)= sin x -√3 cos x + 1, is onto, then the interval of S is
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[0, 3]
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[-1, 1]
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[0, 1]
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[-I, 3]
The domain of the function
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[2, 3]
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[2,
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[1, 2]
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[ 1,
The period of the function f(x) = |sin x| + |cos x| is
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π
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2)
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2π
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None of these
If the function f : R → R defined by f(x) = [x]. where [x] is the greatest integer not exceeding x, for x ∈ R. then f is
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even
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odd
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neither even nor odd
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strictly increasing
The domain of the function
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[-1,∪ {1}
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[-1, 1]
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[-1, 1)
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None of these
The domain of the real valued function
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-5 ≤ x ≤ 1
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-5 ≤ x and x ≥ 1
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- 4 < x ≤ 1
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∅
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0 ≤ x ≤ 1
The largest possible set of real numbers which can be the domain of
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(0,∪ (0,∝ )
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(-1,∪ ( I,∝)
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(-∝ ,-∪ (0,∝)
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(-∝. 0 ) ∪ [1,∝)
The domain of the function
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[1,3,2}
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(-∝,1]
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(1,3,2}
The period of the function f(x) = sin
4
x + cos
4
x is
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π
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2)
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2π
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None of these
The domain of definition of the function
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[1, 4]
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[1, 0]
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[0, 5]
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[5, 0]
If f(x) =2x
6
+3x
4
+ 4x
2
, then f'(x)is
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even function
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an odd function
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neither even nor odd
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None of these
The range of the function
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[0, 1]
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(-1, 1)
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(-3,
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(-3, 1)
Let f(x) = (x + 1)
2
for x ≥ -1. If g(x) is a unction whose graph is the reflection of the graph of f(x) in the line y = x, then g(x) is equal to
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0%
2)
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0%
If f(x) = √x and g(x) = -2x - 3, then domain of (fog) (x) is
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(-∞,-3)
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2)
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0%
0%
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x
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-x
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0%
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0
If R is the set of all real numbers and f : R → R is given by f(x) = 3x
2
+ 1. Then, the set f
-1
([1, 6]) is
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0%
2)
0%
0%
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x2- 1
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x2-2
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x2
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x4
If the function
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f(x) - f(y)
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f(y)
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2f(x) f(y)
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None of these
If f(x) = (x +2)
2
- 2, x ≥ - 2 . Then f
-1
(x) is equal to
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0%
2)
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0%
If F : (-1,→ R be such that
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0%
2)
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0%
If f(x) = x
2
+ 2bx + 2c
2
and g(x) = - x
2
- 2cx + bx
2
are such that min f (x) > max g(x), then relation between b and C is
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no relation
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0 < c < b/2
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|c| < √2|b|
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|c| > √2|b|
If f : R → R is defined by f(x) = 2x + 3, then f
-1
(x)
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0%
2)
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does not exist because f is not injective
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does not exist because f is not surjective
If f(x) = x
2
and g (x) = sin x, ∀ x ε R. Then, the set of all x satisfying ( fogogof)(x)= (gogof)(x), where (fog) (x) = f(g (x)), is
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±√nπ, n ε {0,1,2...}
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±√nπ, n ε {1,2...}
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π/2+2nπ, n ε {...-2,-1,01,2...}
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2nπ, n ε {...,-2,-1,0,1,2...}
if f : (0,→ R is defined by
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f-1 is not invertible on (0,1)
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2)
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f-1 is differentiable on (0,1)
If f (x) = 4x
3
+ 3x
2
+ 3x + 4, then x
3
f(1/x) is equal to
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f(- x)
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2)
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0%
f(x)
If the function f : [1, ∝) → [1, ∝) is defined by f (x)= 2x
(x-1)
, then f
-1
(x) is equal to
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0%
2)
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0%
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Not defined
If .f = {(0, - 1), (- 1, - 3), (2, 3), (3, 5)} is a function from z to z defined by f (x) = ax + b. Then,
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a = 1, b = - 2
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a = 2, b = 1
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a = 2, b = - 1
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a = 1, b = 2
If g(x) is the inverse of f (x) and f
-1
(x) = cos x, then g' (x) is equal to
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sec x
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sec [g(x)]
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cos [g(x)]
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- sin [g(x)]
if f(x) = αx
2
/x+1, x ≠ -1, the the value of α for which F(a) = α where α ≠ 0, is
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0%
2)
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0%
If f (x) = x
2
- 1 and g (x)= (x + 1)
2
, then (gof )(x) is equal to
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(x + 1)4 - 1
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x4 - 1
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x4
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(x+ 1)4
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(x -1)4 -1
If f is a real valued function such that f(x + y) = f (x) + f( y) and f(= 5, then the value of f (is
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200
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300
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350
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400
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500
If f is a real numbers and the mappings f : R → R, g : R → R are defined by f(x) = 5-x
2
and g(x) = 3x-4. then the value of (f0g)(-is
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-44
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-54
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-32
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-64
if f : [4,∞] → [4,∞] is defined by f(x) = 5
x(x-4)
then f
-1
(x) is equal to
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0%
2)
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not defined
If D
30
is the set of the divisors of 30, x, y ϵ D
30
, we define x+ y =LCM (x,y), x•y = GCD (x,y) x' = 30/x and f(x, y, z ) = (x + y ) • (y' + z ), then f(2, 5,is equal to
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2
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5
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10
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15
if the function f : N → N is defined by f(x) = √x, then
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0%
2)
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0%
1
If a function f satisfies f {f(x)} = x + 1 for all real values of x and f(= 1/2, then f(is equal to
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0%
1
0%
0%
2
0%
0
If f(x) satisfies the relation 2f(x) + f(1-x) = x
2
for all real x, then f(x) is
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0%
2)
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0%
0%
if f(x) = sin
2
x + sin
2
(x + π/+ cos x cos(x + π/and g(5/= 1, then gof (x) is equal to
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1
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-1
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2
0%
-2
If
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1
0%
48
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-48
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-1
if f(x + 2y, x - 2y) = xy, then f(x,y) is equal to
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0%
2)
0%
0%
If a and b are two integers such that 10a + b = 5 and P(x) = x + ax + b. Then, integer n such that P(10).P(= P(n) is
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15
0%
65
0%
115
0%
165
if f(x) = 2x
4
- 13x
2
+ ax + b is divisible by x
2
- 3x +2, then(a,b) is equal to
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(-9,-2)
0%
(6,4)
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(9,2)
0%
(2,9)
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