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

Let f be twice differentiable function such that $\mathrm{f}^{\prime \prime}(x)=-\mathrm{f}(x), \mathrm{f}^{\prime}(x)=\mathrm{g}(x)$ and $\mathrm{h}(x)=(\mathrm{f}(x))^2+(\mathrm{g}(x))^2$. If $\mathrm{h}(5)=1$, then the value of $h(10)$ is

A
2
B
1
C
$\frac{1}{2}$
D
$-1$
2
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
$\frac{16}{3}$
3
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
4
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The approximate value of $(3.978)^{\frac{3}{2}}$ is

A
7.934
B
8.934
C
7.022
D
8.866
MHT CET Subjects
EXAM MAP