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Let f: [a, b] rarr R be such that f is d...

Let `f: [a, b] rarr R` be such that f is differentiable in (a,b). f is continuous at x=a & x= b and moreover f(a)= 0= f(b). Then

A

there exists at least one point c in (a,b) such that f'(c )= f(c )

B

f'(x)= f(x) does not hold at any point in(a,b)

C

at every point of (a, b), `f'(x) gt f(x)`

D

at everypoint of (a, b), `f'(x) lt f(x)`

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WB JEE PREVIOUS YEAR PAPER-QUESTION PAPER 2018-MULTIPLE CHOICE QUESTIONS
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  2. Let f(x)= 3x^(10)- 7x^(8) + 5x^(6)- 21x^(3) + 3x^(2)-7. Then underset(...

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  3. Let f: [a, b] rarr R be such that f is differentiable in (a,b). f is c...

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  4. Let f: R rarr R be a twice continuously differentiable function such t...

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  5. If int e^(sin x) [(x cos^(3)x - sin x)/(cos^(2)x)] dx= e^(sin x).f(x) ...

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  6. If int f(x) sin x cos x dx= (1)/(2(b^(2)-a^(2))) log f(x) + c, where c...

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  7. If M= underset(0)overset(pi//2)int (cos x)/(x +2) dx, N= underset(0)ov...

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  8. The value of the integral I= underset(1/2014)overset(2014)int (tan^(-1...

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  9. Let I= underset(pi /4)overset(pi /3)int (sin x)/(x) dx. Then

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  10. The value of I= underset(pi 2)overset(5pi//2)int (e^(tan^(-1) (sin x))...

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  11. The value of underset(n rarr oo)("lim") (1)/(n) {"sec"^(2) (pi)/(4n) ...

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  12. The differential equation representing the family of curves y^(2)= 2d(...

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  13. Let y(x) be a solution of (1-x^(2)) (dy)/(dx) + 2xy -4x^(2)= 0 and y(0...

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  14. The law of motion of a body moving along a straight line is x= (1)/(2)...

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  15. Find the equation of tangents at the point (1,2) of y= x^(2)

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  16. Given that n numbers of A.Ms are inserted between two sets of numbers ...

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  17. If x + log(10) (1 + 2^(x)) = x log(10) 5 + log(10)6 then the value of ...

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  18. If Z(r )= "sin" (2pi r)/(11)- "I cos" (2pi r)/(11) then underset(r = 0...

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  19. If z(1) and z(2) be two non zero complex numbers such that (z(1))/(z(2...

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  20. If b(1) b(2)= 2(c(1) +c(2))and b(1), b(2), c(1), c(2) are all real num...

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