1
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\lim _\limits{x \rightarrow 2}\left(\frac{5^x+5^{3-x}-30}{5^{3-x}-5^{\frac{x}{2}}}\right)=$$

A
$\frac{-16}{3}$
B
$\frac{8}{3}$
C
$\frac{-8}{3}$
D
$\frac{16}{3}$
2
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\begin{aligned} & \text { If } \\ & \int(7 x-2) \sqrt{3 x+2} \mathrm{~d} x=\mathrm{A}(3 x+2)^{\frac{5}{2}}+\mathrm{B}(3 x+2)^{\frac{3}{2}}+\mathrm{c} \end{aligned}$$

(where c is a constant of integration), then the values of $A$ and $B$ are respectively

A
$\frac{14}{45}, \frac{40}{27}$
B
$\frac{14}{15}, \frac{-40}{9}$
C
$\frac{14}{15}, \frac{40}{9}$
D
$\frac{14}{45}, \frac{-40}{27}$
3
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $y=\sin ^{-1}\left(\frac{\log x^2}{1+(\log x)^2}\right)$, then $\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)_{\mathrm{at ~} x=1}=$

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

If $f(x)=\left\{\begin{array}{cc}\frac{a}{2}(x-|x|) & , \\ 0, & \text { for } x<0 \\ 0, & \text { for } x=0 \\ b x^2 \sin \left(\frac{1}{x}\right) & \text { for } x>0\end{array}\right.$

is continuous at $x=0$, then

A
a is any real value and b is any real value
B
a is only rational value and b is any real value
C
a is only irrational value and b is any real value
D
a is only rational value and b is only rational value
MHT CET Papers
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12