Practice questions
88551 published questions with worked solutions.
- If f(x)=x^2-1 and g(x)=(x+1)^2, then (g f)(x) is
- If f(x)=2x^4-13x^2+ax+b is divisible by x^2-3x+2, then (a,b) is equal to
- If f(x)=ax+b and g(x)=cx+d, then f g(x) =g f(x) is equivalent to
- If f:R R is given by f(x)= cases -1, & x rational 1, & x irrational cases , then (f f)(1- 3) is equal to
- Let R be the set of real numbers and the mappings f:R R and g:R R be defined by f(x)=5-x^2 and g(x)=3x-4, then the value of (f...
- Let a>2 be a constant. If there are just 18 positive integers satisfying the inequality (x-a)(x-2a)(x-a^2)<0, then the value of a...
- If 4^x-2^ x+2 +5+ ||b-1|-3 |=| y|, x,y,b R, then the positive value of b is
- If f(x)= 4-x^2 + x^2-1 , then the maximum value of (f(x))^2 is
- Number of integral values of x for which (2^ / ^ -1 x -4 )(x-4)(x-10) x!-(x-1)! <0 is
- If is the fundamental period of the function f(x)= ^ 99 x+ ^ 99 (x+ 2 3 )+ ^ 99 (x+ 4 3 ), then the complex number z=|z|( +i )...
- Number of integral values of x for which the function x+ x + 7x-x^2-6 is defined is
- Let f be a real-valued invertible function such that f ( 2x-3 x-2 )=5x-2, x 2. Then the value of f^ -1 (13) is
- If x= 49 satisfies the inequality _a(x^2-x+2)> _a(-x^2+2x+3), then the sum of all possible distinct values of [x] is (where [ ]...
- Let E= 1,2,3,4 and F= 1,2 . If N is the number of onto functions from E to F, then the value of N/2 is
- If T is the period of the function f(x)=[8x+7]+| 2 x+ 2 x|-8x (where [ ] denotes the greatest integer function), then the value...
- If a, b and c are non-zero rational numbers, the sum of all the possible values of |a| a + |b| b + |c| c is
- Let f:R R be a continuous onto function satisfying f(x)+f(-x)=0, x R. If f(-3)=2 and f(5)=4, then the minimum number of roots of...
- Suppose that f is an even, periodic function with period 2, and that f(x)=x for all x in the interval [0,1]. The value of...
- Suppose that f(x) is a function of the form f(x)= ax^8+bx^6+cx^4+dx^2+15x+1 x (x 0). If f(5)=2, then the value of |f(-5)/4| is
- If f:N N, x_2>x_1 f(x_2)>f(x_1) x_1,x_2 N and f(f(n))=3n, n N, then f(2)=