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Let `f(x)` be a function such that `f''(x) = f'(x) + e^x` and `f'(0) =1` ,`f(0) = 0` then (1)`ln((f(2))^2/4)=4` (2) Range of `f(x)` is `[-1/e,oo)` (3) for `xgt-2`, tangent at any point of f(x) lies below the curve (4) for `x<-1` `f(x)` is decreasing function

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RESONANCE DPP-JEE MAINS-All Questions
  1. The system of equations 'alpha' x+y+z=1,x+2y+4z=alpha and x+4y+10 z=...

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  2. If alpha,beta be the roots of the equation (x-a)(x-b)+c=0(c!=0), then ...

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  3. Let f(x) be a function such that f''(x) = f'(x) + e^x and f'(0) =1 ,f(...

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  4. If |x^2-5x+3 2x-5 3 3x^2+x+4 6x+1 9 7x^2-6x+9 14 x-6 21| =a x^3+b x^...

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  5. If y = x^3-3x + 2, then draw the graph of the followings (i) y=|x^3-3x...

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  6. The equation of a line which is parallel to the line common to the pai...

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  7. If y = x^3-3x + 2, then draw the graph of the followings (i) y=|x^3-3x...

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  8. If point (a ,a) lies in between the lines |x+y|=6 , then ' a ' may sat...

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  9. If sintheta+costheta=1/5"and"0 le theta ltpi, thentantheta is

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  10. ) Six points(x,yi),i=1,2, ,.., 6 are taken on the circle x4 such that ...

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  11. If a x ^2+b x+c=0 has imaginary roots and a-b+c >0 then the set of p...

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  12. From a point "P" on the line 2x y 4 which is nearest to the circle x2 ...

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  13. If a, b and c are in AP and if the equations (b-c)x^2 + (c -a)x+(a-b)=...

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  14. ABC is a right triangle, right - angled at the vertex A. A circle is d...

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  15. All the values of ' a ' for which the quadratic expression a x^2+(a-2...

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  16. The base of triangle passes through a fixed point (f,g) and its other ...

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  17. Sn=3/(1^2)+3/(1^2+2^2)+7/(1^2+2^2+3^2)+ upto n terms, then Sn=(6n)/(n+...

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  18. Let A (-2, 0) and B(2, 0), then the number of integral values of a, a ...

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  19. Find the sum of the series 1+2(1-x)+3(1-x)(1-2x)++n(1-x)(1-2x)(1-3x)[1...

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  20. [2x]-2[x]=lambda where [.] represents greatest integer function and {....

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