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Let f(x) be a differentiable function su...

Let `f(x)` be a differentiable function such that `f(x)=x^2 +int_0^x e^-t f(x-t) dt` then `int_0^1 f(x) dx=`

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RESONANCE DPP-JEE MAINS-All Questions
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  2. Make the following expressions free from modulus sign : (x in R) (...

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  3. Let f(x) be a differentiable function such that f(x)=x^2 +int0^x e^-t ...

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  4. let |{:(1+x,x,x^(2)),(x,1+x,x^(2)),(x^(2),x,1+x):}|=(1)/(6)(x-alpha(1)...

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  5. The sum of first p -terms of a sequence is p(p+1)(p+2)dot the 10th ter...

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  6. Lines whose equation are (x-3)/2=(y-2)/3=(z-1)/(lamda) and (x-2)/3=(y-...

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  7. The solution set of the inequation 3^(72)(1/3)^x(1/3)^(sqrt(x))>1 is [...

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  8. If the curves C1 : y= (In x)/x and C2 : y=lambdax^2 (where lambda is c...

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  9. A die is rolled and showing any number is directly proportional to tha...

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  10. If A=[{:(1,-1,1),(0,2,-3),(2,1,0):}] and B=(adjA) and C=5A, then find ...

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  11. If the roots of the equation (x^2-b x)/(a x-c)=(m-1)/(m+1) are equal ...

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  12. The value of ' a ' for which the sum of the squares of the roots of th...

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  13. Lines whose equation are (x-3)/2=(y-2)/3=(z-1)/(lamda) and (x-2)/3=(y-...

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  14. Let f(x)a n dg(x) be differentiable functions such that f^(prime)(x)g(...

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  15. Let f(x) =4x^2-4ax+a^2-2a+2 be a quadratic polynomial in x,a be any re...

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  16. Suppose that E1 and E2 are two events of a random experiment such that...

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  17. If 1/3(log)3M+3(log)3N=1+(log)(0. 008)5, then M^9 9/N b. N^9=9/M c. M^...

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  18. Consider the quadratic equation az^(2)+bz+c=0 where a,b,c are non-zero...

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  19. Value of [2/((log)4(2000)^6)+3/((log)5(2000)^6)] is 4^(1/3). 5^(1//2) ...

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  20. Find the whole area included between the curve x^2)y^(2) = a^(2)(y^(2)...

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