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if f(x)=4x^3-x^2-2x+1 and g(x)={min f(t)...

if `f(x)=4x^3-x^2-2x+1` and `g(x)={min f(t): 0<=t<=x; 0<=x<=1, 3-x : 1}` then `g(1/4)+g(3/4)+g(5/4)` is equal to

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Let f (x) = x^3-x^2-x+1 and g(x) = {max{f(t); 0<=t<=x}, 0<=x<=1, 3-x, 1<=x<=2 Discuss the continuity and differentiability of the function g (x) in the interval (0, 2).

If f(x) = 2x^(3)-15x^(2)+24x and g(x) = int_(0)^(x)f(t) dt + int_(0)^(5-x) f(t) dt (0 lt x lt 5) . Find the number of integers for which g(x) is increasing.

Let f(x) = x^(3) - x^(2) + x + 1 and g(x) = {{:(max f(t)",", 0 le t le x,"for",0 le x le 1),(3-x",",1 lt x le 2,,):} Then, g(x) in [0, 2] is

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If f(x)=x^3+2x^2+3x+4 and g(x) is the inverse of f(x) then g^(prime)(4) is equal to- 1/4 (b) 0 (c) 1/3 (d) 4

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RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. If t a n y=(2^x)/(1+2^(2x+1)),t h e n(dy)/(dx) at x=0 is

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  2. The least value of x satisfying the equation 2^(|x+1|)-2^x=|2^x-1|+1...

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  3. if f(x)=4x^3-x^2-2x+1 and g(x)={min f(t): 0<=t<=x; 0<=x<=1, 3-x : 1...

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  4. Let a and b be the number of solutions and sum of solutions of (2x)/(x...

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  5. If xcosy+ycosx=pi then the value of y' '(0) is equal to pi (b) -pi (...

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  6. The simultaneous equations, y=x+2|x| & y=4+x-|x| have the solution se...

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  7. If f''(x)=-f(x) and g(x)=f^(prime)(x) and F(x)=(f(x/2))^2+(g(x/2))^2 a...

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  8. Minimum vlaue of |x-p| + |x-15| +|x-p-15|. If p le x le 15 and 0 lt p ...

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  9. if sqrt(x^2+y^2)=e^t where t=sin^-1 (y/sqrt(x^2+y^2)) then (dy)/(dx) i...

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  10. Solution set of inequality ((e^x-1)(2x-3)(x^2+x+2))/((sinx-2)(x+1)^2x)...

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  11. If the sum of first 16 terms of the series s=cot^(-1)(2^2+1/2)+cot^(-1...

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  12. If two chords of circle x^2+y^2-a x-b y=0 , drawn from the point (a, b...

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  13. Let y=tan^(-1)((2cos(3x^2-2)+5sin(3x^2-2))/(5cos(3x^2-2)-2sin(3x^2-2))...

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  14. Let cos(alpha+beta)""=4/5 and let sin (alpha+beta)""=5/(13) where 0lt=...

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  15. If y is a function of x and log(x+y)-2x y=0, then the value of y^(prim...

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  16. If (log)(10)(1025)/(1024)=alphaa n d(log)(10)2=beta , then the value o...

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  17. The vector hat i+x hat j+3 hat k is rotated through an angle theta an...

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  18. Leg P(x)=|7 6x-10 2x-10 5x-10 3 4|, sum of zeroes of P(x) is (a) 30...

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  19. The value of a for which the function f(x)=(4a-3)(x+log5)+2(a-7)cot(x/...

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  20. The solution set of inequality ((e^(x)-1)(2x-3)(x^(2)+x+2))/((sinx-...

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