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If f(x)a n dg(x) are continuous function...

If `f(x)a n dg(x)` are continuous functions in `[a , b]` and are differentiable in`(a , b)` then prove that there exists at least one `c in (a , b)` for which. `|f(a)f(b)g(a)g(b)|=(b-a)|f(a)f^(prime)(c)g(a)g^(prime)(c)|,w h e r ea

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RESONANCE DPP-JEE MAINS-All Questions
  1. Let f(x)=x^(3)+ax^(2)+bx+c be the given cubic polynomial and f(x)=0 be...

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  2. |(2x-1)/(x-1)|>2

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  3. If f(x)a n dg(x) are continuous functions in [a , b] and are different...

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  4. |x-1|+|x-2|+|x-3|geq6

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  5. If sum(r=1)^n r(r+1)(2r+3)=a n^4+b n^3+c n^2+d n+e , then a-b=d-c ...

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  6. For a family circles passing through the points A(3,7)B(6,5) which o...

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  7. If sn=(1-4/1)(1-4/9)(1-4/25)......(1-4/((2n-1)^2)), where n in N, th...

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  8. If {.} represents fractional part function and {x}+{-x}=x^2+x-6 , then...

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  9. If there are three square matrix A, B, C of same order satisfying the...

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  10. The quadratic equation, a (x -b)(x-c) + b (x-c)(x-a) + c (x-a) (x-b)=0...

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  11. Let g(x) be the inverse of an invertible function f(x), which is dif...

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  12. The product of all values of t , for which the system of equations (a-...

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  13. The Fibonacci sequence is defined by 1=a1=a2 and an=a(n-1)+a(n-2,)n > ...

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  14. Let A and B are square matrices of same order satisfying A B=A ,a n dB...

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  15. If the graph of the function y = f(x) is as shown : The graph of ...

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  16. If p ,q ,r are in A.P. then value of determinant |a^2+2^(n+1)+2p b^2+2...

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  17. Let A=[-3-7-5 2 4 3 1 2 2]&B=[a b1] If AB is a scalar multipl...

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  18. If f(x)=x+t a n xa n df(x) is inverse of g(x), then g^(prime)(x) is eq...

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  19. If 3x+4y=12 intersect the ellipse x^2/25+y^2/16=1 at P and Q , then p...

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  20. sin^4(pi/16)+sin^4(3pi/16)+sin^4(5pi/16)+sin^4(7pi/16)=3/2

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