JEE Main questions
34495 published questions with worked solutions.
- The domain of the function ^ -1 ( _2 x^2 2 ) is
- The domain of the real valued function f(x)= 1-2x +2 ^ -1 ( 3x-1 2 ) is
- If the function f:R R is defined by f(x)=[x], where [x] is the greatest integer not exceeding x, for x R, then f is
- The range of the function f(x)=x^2-6x+7 is
- If f(x)= x+ x and g(x)=x^2-1, then g(f(x)) is invertible in the domain
- If f(x) is an odd periodic function with period 2, then f(4) equals
- The period of the function f(x)= ( x 5 ) is
- The domain of the real valued function f(x)= 5-4x-x^2 +x^2 (x+4) is
- If f(x+y,x-y)=xy, then the arithmetic mean of f(x,y) and f(y,x) is
- The function f(x)= ( 1+x 1-x ) satisfies the equation
- If Q denotes the set of all rational numbers and f ( p q )= p^2-q^2 for any p q Q with p,q integers, q>0 and (p,q)=1, then...
- If f is a real valued function such that f(x+y)=f(x)+f(y) and f(1)=5, then the value of f(100) is
- If f:R R is defined as f(x)=(1-x)^ 1/3 , then f^ -1 (x) is
- If f:R R and g:R R are defined by f(x)=x-[x] and g(x)=[x] for x R, where [x] is the greatest integer not exceeding x, then for...
- If f(x)= 2x-1 x+5 (x -5), then f^ -1 (x) is equal to
- If f:[-6,6] R is defined by f(x)=x^2-3 for x R, then (f f f)(-1)+(f f f)(0)+(f f f)(1) is equal to
- If D_ 30 is the set of the divisors of 30, for x,y D_ 30 we define x+y= LCM (x,y), x y= GCD (x,y), x'= 30 x and f(x,y,z)=(x+y)...
- If X and Y are two non-empty sets and f:X Y is a function such that f(C)= f(x):x C for C X and f^ -1 (D)= x:f(x) D for D Y, then...
- Let f:N Y be a function defined as f(x)=4x+3, where Y= y N:y=4x+3 for some x N . Then f is invertible and its inverse is
- Suppose f:[-2,2] R is defined by f(x)= cases -1, & -2 x 0 x-1, & 0 x 2 cases , then x [-2,2]:x 0 and f(|x|)=x is equal to