1
MHT CET 2025 23rd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \begin{aligned} & f(x)=\left\{\begin{array}{ll} 3-x, & -1 \leqslant x<0 \\ 1+\frac{5 x}{3}, & -3 \leqslant x \leqslant 2 \end{array}\right. \text { and } \\ & g(x)=\left\{\begin{aligned} -x, & -2 \leqslant x \leqslant 3 \\ x, & 0 \leqslant x \leqslant 1 \end{aligned}\right. \end{aligned} $$

then range of (fog) $(x)$ is

A
$\left[1, \frac{8}{3}\right]$
B
$\left[-4, \frac{8}{3}\right]$
C
$\left[-4, \frac{13}{3}\right]$
D
$\left[\frac{8}{3}, \frac{10}{3}\right]$
2
MHT CET 2025 23rd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

The foci of the conic $25 x^2+16 y^2-150 x=175$ are

A
$(0, \pm 3)$
B
$(3, \pm 3)$
C
$(0, \pm 5)$
D
$(5, \pm 5)$
3
MHT CET 2025 23rd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $\mathrm{A}=\mathop {\lim }\limits_{x \to {0^ + }}\left(1+\tan ^2 \sqrt{x}\right)^{\frac{1}{2 x}}$, then $\log _{\mathrm{e}} \mathrm{A}=$

A
2
B
1
C
$\frac{1}{2}$
D
$\frac{1}{4}$
4
MHT CET 2025 23rd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

The function $\mathrm{f}(x)=2 x-\left|x-x^2\right|$ is

A
continuous at $x=1$
B
discontinuous at $x=1$
C
not defined at $x=1$
D
discontinuous at $x=0$

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