1
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\mathrm{a} \cos 2 \theta+\mathrm{b} \sin 2 \theta=\mathrm{c}$$ has $$\alpha$$ and $$\beta$$ as its roots, then the value of $$\tan \alpha+\tan \beta$$ is

A
$$\frac{2 b}{c+a}$$
B
$$\frac{2 a}{b+c}$$
C
$$\frac{b}{c+a}$$
D
$$\frac{a}{b+c}$$
2
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A lot of 100 bulbs contains 10 defective bulbs. Five bulbs are selected at random from the lot and are sent to retail store. Then the probability that the store will receive at most one defective bulb is

A
$$\frac{7}{5}\left(\frac{9}{10}\right)^4$$
B
$$\frac{7}{5}\left(\frac{9}{10}\right)^5$$
C
$$\frac{6}{5}\left(\frac{9}{10}\right)^4$$
D
$$\frac{6}{5}\left(\frac{9}{10}\right)^5$$
3
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Given $$0 \leq x \leq \frac{1}{2}$$, then the value of $$\tan \left(\sin ^{-1}\left(\frac{x}{\sqrt{2}}+\frac{\sqrt{1-x^2}}{\sqrt{2}}\right)-\sin ^{-1} x\right)$$ is

A
1
B
$$\sqrt{3}$$
C
$$-1$$
D
$$\frac{1}{\sqrt{3}}$$
4
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A vector parallel to the line of intersection of the planes $$\bar{r} \cdot(3 \hat{i}-\hat{j}+\hat{k})=1$$ and $$\bar{r} \cdot(\hat{i}+4 \hat{j}-2 \hat{k})=2$$ is

A
$$-2 \hat{i}+7 \hat{j}+13 \hat{k}$$
B
$$2 \hat{i}-7 \hat{j}+13 \hat{k}$$
C
$$-\hat{i}+4 \hat{j}+7 \hat{k}$$
D
$$\hat{\mathrm{i}}-4 \hat{\mathrm{j}}+7 \hat{\mathrm{k}}$$
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