1
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\lim _\limits{x \rightarrow 2} \frac{3^x+3^{3-x}-12}{3^{3-x}-3^{\frac{x}{2}}}=$$

A
$-\frac{4}{3}$
B
$\frac{4}{3}$
C
$\frac{2}{3}$
D
$-\frac{4}{9}$
2
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int_0^{\frac{\pi}{4}} \frac{\sec ^2 x}{(1+\tan x)(2+\tan x)} d x=$$

A
$\log \left(\frac{3}{4}\right)$
B
$\frac{1}{3} \log \left(\frac{4}{3}\right)$
C
$\log \left(\frac{4}{3}\right)$
D
$\frac{1}{4} \log \left(\frac{3}{4}\right)$
3
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If two fair dice are rolled, then the probability that the sum of the numbers on the upper faces is at least 9, is

A
$\frac{1}{3}$
B
$\frac{4}{11}$
C
$\frac{5}{18}$
D
$\frac{5}{36}$
4
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

After $t$ seconds, the acceleration of a particle, which starts from rest and moves in a straight line is $\left(8-\frac{\mathrm{t}}{5}\right) \mathrm{cm} / \mathrm{s}^2$, then velocity of the particle at the instant, when the acceleration is zero, is

A
$160 \mathrm{~cm} / \mathrm{s}$
B
$80 \mathrm{~cm} / \mathrm{s}$
C
$320 \mathrm{~cm} / \mathrm{s}$
D
$480 \mathrm{~cm} / \mathrm{s}$
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