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Let f and g be differentiable on the int...

Let f and g be differentiable on the interval I and let a, `b in I, a lt b`. Then

A

If f(a) = 0 - f(b), the equation f'(x) + f(x)g'(x) = 0 is solvable in (a, b)

B

If f(a) = 0 = f(b), the equation f'(x) + f(x)g'(x) = 0 may not be solvable in (a, b)

C

If g(a) = 0 = g(b), the equation g'(x) + kg(x) = 0 is solvable in (a, b), `k in R`

D

If g(a) = 0 = g(b), the equation g'(x) = kg(x) = 0 may not be solvable in (a, b), `k in R`

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WB JEE PREVIOUS YEAR PAPER-QUESTION PAPER 2019-MULTIPLE CHOICE QUESTIONS
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  2. Let f(x) = x^(4) - 4x^(3) + 4x^(2) + c, c in R. Then

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  3. The graphs of the polynomial x^(2)-1 and cos x intersect

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  4. A point is in motion along a hyperbola y = (10)/(x) so that its abscis...

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  5. Let a = min {x^(2) + 2x + 3 : x in R} and b = lim(theta rarr 0)(1-cos...

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  6. Let a gt b gt 0 and I(n) = a^(1//n) - b^(1//n), J(n) = (a-b)^(1//n) fo...

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  7. Let hat(alpha), hat(beta), hat(gamma)be three unit vectors such that h...

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  8. The position vectors of the points A, B, C and D are 3hat(i) - 2hat(j)...

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  9. A particle starts at the origin and moves 1 unit horizontally to the r...

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  10. For any non-zero complex number z, the minimum value of |z| + |z-1| is

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  11. Let A = ((3, 0, 3), (0, 3, 0), (3,0,3)). Then the roots of the equatio...

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  12. If A and B are (-2, -2) and (2, -4) respectively, find the coordinates...

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  13. Equation of a tangent to the hyperbola 5x^(2) - y^(2) = 5 and which pa...

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  14. Let f and g be differentiable on the interval I and let a, b in I, a l...

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  15. Consider the function f(x) = (x^(3))/(4) - sin pi x + 3

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  16. Let I(n) = int(0)^(1) x^(n) tan^(-1) x dx. If a(n) I(n+2) + b(n)I(n) =...

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  17. Two particles A and B move from rest along a straight line with consta...

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  18. The area bounded by y = x + 1 and y = cos x and the x-axis, is

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  19. Let x(1), x(2) be the roots of x^(2) - 3x + a = 0 and x(3), x(4) be th...

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  20. If theta in RR and (1 +i cos theta)/(1-2 i cos theta) is real number,...

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