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

For the following shaded region, the linear constraints are

MHT CET 2024 11th May Morning Shift Mathematics - Linear Programming Question 7 English

A
$x-y \leq 0,-x+3 y \leq 3, x \geq 0, y \geq 0$
B
$x-y \geq 0,-x+3 y \geq 3, x \geq 0, y \geq 0$
C
$x-y \geq 0,-x+3 y \leq 3, x \geq 0, y \geq 0$
D
$x-y \leq 0,-x+3 y=3, x \geq 0, y \geq 0$
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

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

(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
$\frac{14}{45}, \frac{-40}{27}$
4
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
$-2$
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