MHT CET 2026 20th April Evening Shift | Indefinite Integration Question 1 | Mathematics

If $f(x), g(x)$ be twice differentiable functions, satisfying $f''(x) = g''(x), f'(1) = 2g'(1) = 4$ and $f(2) = 3g(2) = 9$ then $f(x) - g(x)$ at $x = 4$ is equal to

$0$

$10$

$8$

$2$

MHT CET 2026 20th April Evening Shift

MCQ (Single Correct Answer)

-0

If $\int f(x)dx = g(x) + c$ then $\int f^{-1}(x)dx =$

$xf^{-1}(x) + c$

$f(g^{-1}(x)) + c$

$xf^{-1}(x) - g(f^{-1}(x)) + c$

$g^{-1}(x) + c$

MHT CET 2026 20th April Evening Shift

MCQ (Single Correct Answer)

-0

$\int\dfrac{\log x}{(1 + \log x)^2}dx =$

$\dfrac{1}{1 + \log x} + c$

$-\dfrac{1}{1 + \log x} + c$

$\dfrac{x}{1 + \log x} + c$

$-\dfrac{x}{1 + \log x} + c$

MHT CET 2026 20th April Evening Shift

MCQ (Single Correct Answer)

-0

$\int\dfrac{1}{\sqrt{2x - x^2}}dx =$

$\sin^{-1}(x - 1) + c$

$\cos^{-1}(x - 1) + c$

$\tan^{-1}(x - 1) + c$

$\sin^{-1}x + c$

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