MHT CET 2026 19th April Morning Shift | Limits, Continuity and Differentiability Question 7 | Mathematics

If the function $f(x) = \dfrac{2\sqrt{2} - (\cos x + \sin x)^3}{1 - \sin 2x}$ is continuous at $x = \dfrac{\pi}{4}$, then the value of $f\left(\dfrac{\pi}{4}\right)$ is ...

$\dfrac{3\sqrt{2}}{2}$

$\dfrac{5\sqrt{2}}{2}$

$0$

$\sqrt{2}$

MHT CET 2026 19th April Morning Shift

MCQ (Single Correct Answer)

-0

The value of $\lim\limits_{x \to 0}\left(\dfrac{8}{x^8}\right)\left[1 - \cos\dfrac{x^2}{2} - \cos\dfrac{x^2}{4} + \cos\dfrac{x^2}{2}\cdot\cos\dfrac{x^2}{4}\right]$ is equal to ...

$\dfrac{1}{8}$

$\dfrac{1}{32}$

$\dfrac{1}{16}$

$0$

MHT CET 2025 5th May Evening Shift

MCQ (Single Correct Answer)

-0

If $\quad f(x)=\left\{\begin{array}{cc}\frac{9^x-2 \cdot 3^x+1}{\log (1+3 x) \cdot \tan 2 x} & , \text { if } x \neq 0 \\ a(\log b)^c & , \text { if } x=0\end{array}\right.$ is continuous at $x=0$, then $\mathrm{a}+\mathrm{b}+\mathrm{c}=$

$\frac{31}{6}$

$\frac{1}{6}$

$\frac{5}{6}$

$\frac{3}{20}$

MHT CET 2025 5th May Evening Shift

MCQ (Single Correct Answer)

-0

Define $f(x)=\left\{\begin{array}{cl}b-a x & , \text { if } x<2 \\ 3 & , \text { if } x=2 \\ a+2 b x & , \text { if } x>2\end{array}\right.$ and if $\lim _{x \rightarrow 2} f(x)$ exists, then $\frac{a}{b}=$

-1

$\frac{2}{3}$

$\frac{3}{2}$

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