1
MHT CET 2023 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

In $$\triangle \mathrm{ABC}$$, with usual notations, $$\mathrm{m} \angle \mathrm{C}=\frac{\pi}{2}$$, if $$\tan \left(\frac{A}{2}\right)$$ and $$\tan \left(\frac{B}{2}\right)$$ are the roots of the equation $$a_1 x^2+b_1 x+c_1=0\left(a_1 \neq 0\right)$$, then

A
$$a_1+b_1=c_1$$
B
$$b_1+c_1=a_1$$
C
$$a_1+c_1=b_1$$
D
$$b_1=c_1$$
2
MHT CET 2023 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\int \frac{\sin x}{3+4 \cos ^2 x} \mathrm{~d} x=\mathrm{A} \tan ^{-1}(\mathrm{~B} \cos x)+\mathrm{c}$$, (where $$\mathrm{c}$$ is a constant of integration), then the value of $$\mathrm{A}+\mathrm{B}$$ is

A
$$\frac{5}{2 \sqrt{3}}$$
B
$$\frac{-1}{2 \sqrt{3}}$$
C
$$\frac{-2}{\sqrt{3}}$$
D
$$\frac{\sqrt{3}}{2}$$
3
MHT CET 2023 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Vectors $$\overline{\mathrm{a}}$$ and $$\overline{\mathrm{b}}$$ are such that $$|\overline{\mathrm{a}}|=1 ;|\overline{\mathrm{b}}|=4$$ and $$\bar{a} \cdot \bar{b}=2$$. If $$\bar{c}=2 \bar{a} \times \bar{b}-3 \bar{b}$$, then the angle between $$\bar{b}$$ and $$\bar{c}$$ is

A
$$\frac{\pi}{6}$$
B
$$\frac{5 \pi}{6}$$
C
$$\frac{\pi}{3}$$
D
$$\frac{2 \pi}{3}$$
4
MHT CET 2023 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$y$$ is a function of $$x$$ and $$\log (x+y)=2 x y$$, then the value of $$y^{\prime}(0)$$ is

A
1
B
$$-$$1
C
2
D
0
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