1
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

With usual notations in $$\triangle$$ABC, if $$\frac{\sin A}{\sin C}=\frac{\sin (A-B)}{\sin (B-C)}$$, then $$a^2, b^2, c^2$$ are in

A
Not in AP
B
HP
C
AP
D
GP
2
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

The general solution of the differential equation $$\cos (x+y) \frac{d y}{d x}=1$$ is

A
$$y=\tan (x+y)+c$$
B
$$y=\sec (x+y)+c$$
C
$$y=\tan \left(\frac{x+y}{2}\right)+c$$
D
$$y=\cot \left(\frac{x+y}{2}\right)+c$$
3
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

The derivative of the function $$\cot ^{-1}\left[(\cos 2 x)^{1 / 2}\right]$$ at $$x=\pi / 6$$ is

A
$$\left(\frac{1}{3}\right)^{1 / 2}$$
B
$$\left(\frac{2}{3}\right)^{1 / 2}$$
C
$$\left(\frac{3}{2}\right)^{1 / 2}$$
D
$$(3)^{1 / 2}$$
4
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

The domain of the function $$\log _{10}\left(x^2-5 x+6\right)$$ is

A
$$(-\infty, \infty)$$
B
$$(-\infty, 2) \cup(3, \infty)$$
C
$$(2,3)$$
D
None of these
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