The largest interval for which is
a)
b)
c)
d)
Your Answer
If g (f (x)) = |sin x| and f (g (x)) = (sin)2, then
a) f (x) = sin2 x, g (x) =
b) f (x) = sin x, g (x) =
c) f (x) = x2, g (x) = sin
d) f and g cannot be determined
The number of values of x where the function f (x) = cos x + cos () attains the maximum is
a) 0
b) 1
c) 2
d) Infinite
The domain of definition of the function f (x) given by the equation
2x + 2y = 2 is
a) 0 < x ≤ 1
b) 0 ≤ x ≤ 1
c) < x ≤ 0
d) < x ≤ 1
The domain of f (x) = is
a) R – {1, 2}
b) (2,
c) R – { 1, 2, 3}
d) (3,
Let g (x) = 1 + x – [ x ] and f (x) = then for all x, f (g (x)) is equal to
a) x
c) f ( x )
d) g ( x )
The range of the function f (x) = , x ε R is
a) ( 1, )
Multiple choices
Let g (x) be a function defined on [−1, 1]. If the area of the equilateral triangle with the area of its vertices at ( 0, 0) and ( x, g (x)) is then the function g (x) is
a) g (x) =
b) g (x) =
c) g (x) =
d) g (x) =
Multiple choices y = f ( x ) = then
a) x = f (y)
b) f (1) = 3
c) y is increasing with x for x < 1
d) f is a rational function of x
Subjective problem
Let y =
Find all real values of x for which y takes real values
a) for x ≥ 3, y is real
b) for 2 < x < 3, y is imaginary
c) for – 1 ≤ x < 2, y is real
d) for x < – 1, y is imaginary
Let R be the set of real numbers and f : R R such that for all x, y ε R, |f (x) – f (y)| ≤ | x – y |2. Then
b) f (x) is a constant
c) none of the above
Let {x} and [x] denote the fractional and integral part of a real number respectively. Solve 4 {x} = x + [x]
a) x = 0
True / False
If f (x) = ( a – xn )1/n where a > 0 and n is a positive integer then f ( f ( x ) ) = x.
a) True
b) False
Fill in the blank
The domain of the function f (x) = is
a) [− 2, − 1]
b) [1, 2]
c) [− 2, − 1] ⋃ [1, 2]
d) None of the above
Fill in the blank If f (x) = sin ln then the domain of f (x) is ………….
a) (−2, −1)
b) (−2, 1)
c) (0, 1)
d) (1, ∞)
If x, y, z are real and distinct then 8u = is always
a) Non–negative
b) Non–positive
c) Zero
d) None of these
Both roots of the equation
( x – b) ( x – c) + (x – c) ( x – a) + (x – a) (x – b) = 0 are always
a) positive
b) negative
c) real
d) none of these
The number of real solutions of the equation | x |2 – 3 | x | + 2 = 0 is
a) 4
c) 3
d) 2
If are any real numbers and n is any positive integer then
Two towns A and B are 60 meters apart. A school is to be built to serve 150 students in town A and 50 students in town B. If the total distance to be travelled by all the 200 students is to be as small as possible then the school should be built at
a) Town B
b) 45 km from town A
c) Town A
d) 45 km from town B
If p, q, r are any real numbers, then
a) Max ( p, q ) < max ( p, q, r )
b) Min ( p, q ) =
c) Max ( p, q ) < min ( p, q, r )
The equation has
a) No root
b) One root
c) Two equal roots
d) Infinitely many roots
If then ab + bc + ca lies in the interval
If α and β are roots of and are roots of then the equation has always
a) Two real roots
b) Two positive roots
c) Two negative roots
d) One positive and one negative root