1
MHT CET 2023 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A curve passes through the point $$\left(1, \frac{\pi}{6}\right)$$. Let the slope of the curve at each point $$(x, y)$$ be $$\frac{y}{x}+\sec \left(\frac{y}{x}\right), x>0$$, then, the equation of the curve is

A
$$\sin \left(\frac{y}{x}\right)=\log (x)+\frac{1}{2}$$
B
$$\operatorname{cosec}\left(\frac{y}{x}\right)=\log (x)+2$$
C
$$\sec \left(\frac{2 y}{x}\right)=\log (x)+2$$
D
$$\cos \left(\frac{2 y}{x}\right)=\log (x)+\frac{1}{2}$$
2
MHT CET 2023 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

For the following shaded area, the linear constraints except $$x,y \ge 0$$ are

MHT CET 2023 11th May Morning Shift Mathematics - Linear Programming Question 38 English

A
$$2 x+y \leq 2, x-y \leq 1, x+2 y \leq 8$$
B
$$2 x+y \geq 2, x-y \leq 1, x+2 y \leq 8$$
C
$$2 x+y \geq 2, x-y \geq 1, x+2 y \leq 8$$
D
$$2 x+y \geq 2, x-y \geq 1, x+2 y \geq 8$$
3
MHT CET 2023 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $$\omega \neq 1$$ be a cube root of unity and $$S$$ be the set of all non-singular matrices of the form $$\left[\begin{array}{ccc}1 & a & b \\ \omega & 1 & c \\ \omega^2 & \omega & 1\end{array}\right]$$ where each of $$a, b$$ and $$c$$ is either $$\omega$$ or $$\omega^2$$, then the number of distinct matrices in the set $$\mathrm{S}$$ is

A
2
B
6
C
4
D
8
4
MHT CET 2023 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of $$2 \tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{1}{7}$$

A
$$\tan ^{-1}\left(\frac{17}{31}\right)$$
B
$$\tan ^{-1}\left(\frac{19}{31}\right)$$
C
$$\tan ^{-1}\left(\frac{31}{17}\right)$$
D
$$\tan ^{-1}\left(\frac{31}{19}\right)$$
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