1
MHT CET 2021 20th September Morning Shift
+2
-0

If $$y=\log \tan \left(\frac{x}{2}\right)+\sin ^{-1}(\cos x)$$, then $$\frac{d y}{d x}=$$

A
$$\operatorname{cosec} x$$
B
$$\sin x+1$$
C
$$x$$
D
$$\operatorname{cosec} x-1$$
2
MHT CET 2021 20th September Morning Shift
+2
-0

If $$h(x)=\sqrt{4 f(x)+3 g(x)}, f(1)=4, g(1)=3, f^{\prime}(1)=3, g^{\prime}(1)=4$$, then $$h^{\prime}(1)=$$

A
$$\frac{5}{12}$$
B
$$\frac{12}{5}$$
C
$$\frac{-5}{12}$$
D
$$\frac{-12}{7}$$
3
MHT CET 2021 20th September Morning Shift
+2
-0

If $$x=a \cos \theta, y=b \sin \theta$$, then $$\left[\frac{d^2 y}{d x^2}\right]_{\theta=\frac{\pi}{4}}=$$

A
$$2\left(\frac{a^2}{b}\right)$$
B
$$\sqrt{2}\left(\frac{\mathrm{a}^2}{\mathrm{~b}}\right)$$
C
$$-2 \sqrt{2}\left(\frac{b}{a^2}\right)$$
D
$$2 \sqrt{2}\left(\frac{\mathrm{b}}{\mathrm{a}^2}\right)$$
4
MHT CET 2020 16th October Morning Shift
+2
-0

If $$\frac{x}{\sqrt{1+x}}+\frac{y}{\sqrt{1+y}}=0, x \neq y$$, then $$(1+x)^2 \frac{d y}{d x}=$$

A
1
B
$$\frac{1}{2}$$
C
$$-$$1
D
0
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