JEE Advanced questions
3844 published questions with worked solutions.
- If f(2a-x)=f(x) and _0^a f(x) ,dx= then _0^ 2a f(x) ,dx is
- Let f(x) be a continuous function such that the area bounded by the curve y=f(x), the x-axis, and the lines x=0 and x=a is 1+ a^2...
- If y= _0^x x ,dx then the value of dy dx at x= 2 is
- If y= _x^ x^2 5-t^2 ,dt then the value of dy dx at x= 2 is
- The function f(x)= _ -1 ^ x t(e^t-1)(t-2)^3(t-3)^5 ,dt has a local minimum at x which is equal to
- Let f(x) be a differentiable function and f(1)=2. If _ x 1 _2^ f(x) 2t x-1 ,dt=4 then the value of f'(1) is
- If (x)= _x^ x^2 (t-1) ,dt, 1 x 2, then the greatest value of (x) is
- If _0^1(1+ ^4x)(ax^2+bx+c) ,dx= _0^2(1+ ^4x)(ax^2+bx+c) ,dx then the quadratic equation ax^2+bx+c=0 has
- Let f(x) be a function defined by f(x)= _1^x x(x^2-3x+2) ,dx, 1 x 3. Then the range of f(x) is
- If A= _0^ x x+ x ,dx, B= _0^ x x- x ,dx then
- Let f(a)>0, and let f(x) be a nondecreasing continuous function in [a,b]. Then 1 b-a _a^b f(x) ,dx has the
- The value of _0^ nx x ,dx, n N, is
- If f(x)= _x^ x^2 dt ( t)^2 , x 0, x 1, then f(x) is
- Let f(x)=ax^3+bx^2+cx have relative extrema x=1 and at x=5. If _ -1 ^ 1 f(x) ,dx=6 then
- Let f(x)= _0^x|x-1| ,dx, x 0. Then f'(x) is
- P( , f( )) and Q( , f( )) are ends of an arc in the first quadrant. The area bounded by the arc, ordinates through P and Q, and...
- The area bounded by the lines y = |x-2|, |x| = 3 and y = 0 is
- The area bounded by the curve y= 4-x^2 and the line y=0 is
- The area bounded by the curve y^2=4x and the double ordinate x=2 is
- The area bounded by the curve x^2=ky, k>0 and the line y=3 is 12 unit^2. Then k is