JEE Advanced questions
3844 published questions with worked solutions.
- Let f(x) be a continuous function in R such that f(x) + f(y) = f(x + y). If _0^3 f(x) ,dx = k then _ -3 ^ 3 f(x) ,dx is equal to
- Let f(x) be a continuous function such that f(x) does not vanish for all x R. If _2^3 f(x) ,dx= _ -2 ^3 f(x) ,dx then f(x), x R,...
- Let I= _ -a ^ a (p ^3x+q ^2x+r x) ,dx, where p,q,r are arbitrary constants. The numerical value of I depends on
- Let I_1= _0^1 e^ -x^2 dx, I_2= _0^1 e^ -x ^2x ,dx and I_3= _0^1 e^ -x^2 ^2x ,dx. Then
- If _ -2 ^ 3 f(x) ,dx=5 and _1^3 2-f(x) ,dx=6 then the value of _ -2 ^ 1 f(x) ,dx is
- Let f(x) be a continuous function such that _n^ n+1 f(x) ,dx=n^3, n Z. Then the value of _ -3 ^ 3 f(x) ,dx is
- If I= _0^1 x ,dx 8+x^3 then the smallest interval in which I lies is
- If _0^1xe^ x^2 dx= _0^1e^ x^2 dx then
- _ 1/2 ^ 2 ( e^x-1 e^x+1 )dx is equal to
- Let _0^a f(x) ,dx= and _0^a f(2a-x) ,dx= . Then _0^ 2a f(x) ,dx is equal to
- If f(-x)+f(x)=0 then _a^x f(t) ,dt is
- If f(x) and g(x) be continuous functions over the closed interval [0,a] such that f(x)=f(a-x) and g(x)+g(a-x)=2. Then _0^a f(x)...
- If f(x)=f(a+x) and _0^a f(x) ,dx=p then _a^ na f(x) ,dx is equal to
- Let f(x) be a given integrable function such that f(x+k)=f(x) for all x R. Then _a^ a+k f(x) ,dx depends for its value on
- The value of _ /4 ^ 3 /4 x 1+ x ,dx is equal to
- The value of _0^ /2 dx 1+ ^3x is
- Let f and g be two continuous functions. Then _ - /2 ^ /2 f(x)+f(-x) g(x)-g(-x) ,dx is equal to
- Let _a^b f(x) ,dx=p and _a^b|f(x)| ,dx=q. Then
- If f(x)= _0^x (1+t^2) ,dt then the value of f''(1) is equal to
- If f(x)= _x^ x^2 dt 1+t^3 then f'(2) is equal to