1
MHT CET 2026 17th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
Which of the following function is discontinuous at $x = 0$ ?
A
$f(x) = (1 + x)^{\frac{2}{x}},$ for $x \neq 0$
$= e^2,$ for $x = 0$
B
$f(x) = \sin x - \cos x,$ for $x \neq 0$
$= -1,$ for $x = 0$
C
$f(x) = \dfrac{e^{\frac{1}{x}} - 1}{e^{\frac{1}{x}} + 1},$ for $x \neq 0$
$= -1,$ for $x = 0$
D
$f(x) = \dfrac{e^{5x} - e^{2x}}{\sin 3x},$ for $x \neq 0$
$= 1,$ for $x = 0$
2
MHT CET 2026 16th April Evening Shift
MCQ (Single Correct Answer)
+2
-0
If $\lim\limits_{x \to 0}\dfrac{45^x - 9^x - 5^x + 1}{(k^x - 1)(3^x - 1)} = 2$, then the value of $k$ is ...
A
$45$
B
$9$
C
$5$
D
$3$
3
MHT CET 2026 16th April Evening Shift
MCQ (Single Correct Answer)
+2
-0
If the function f is continuous at $x = \pi$, where $f(x) = \dfrac{1 - \cos[7(x - \pi)]}{5(x - \pi)^2}$, for $x \neq \pi$, then $f(\pi) = $
A
$\dfrac{49}{4}$
B
$\dfrac{4}{49}$
C
$\dfrac{49}{10}$
D
$\dfrac{10}{49}$
4
MHT CET 2026 16th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
$\displaystyle\lim_{x \to 0}\dfrac{(5^x - 1)^4\,\text{cosec}\,(x\log 5)}{\tan(x\log 5) \cdot \log(1 + x^2\log 25)} = \ldots\ldots$
A
$5\log 5$
B
$\log\sqrt{5}$
C
$(\log 5)^2$
D
$\dfrac{1}{4}\log 5$

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