1
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+2
-0

A line makes the same angle '$$\alpha$$' with each of the $$x$$ and $$y$$ axes. If the angle '$$\theta$$', which it makes with the $$z$$-axis, is such that $$\sin ^2 \theta=2 \sin ^2 \alpha$$, then the angle $$\alpha$$ is

A
$$\left(\frac{\pi}{4}\right)$$
B
$$\left(\frac{\pi}{2}\right)$$
C
$$\left(\frac{\pi}{3}\right)$$
D
$$\left(\frac{\pi}{6}\right)$$
2
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+2
-0

The negation of the statement pattern $$p \vee(q \rightarrow \sim r)$$ is

A
$$\sim p \wedge(q \wedge \sim r)$$
B
$$\sim p \wedge(q \wedge r)$$
C
$$\sim p \wedge(\sim q \wedge r)$$
D
$$\sim p \wedge(\sim q \wedge \sim r)$$
3
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $$\bar{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$\bar{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ be two vectors. If $$\bar{c}$$ is a vector such that $$\bar{b} \times \bar{c}=\bar{b} \times \bar{a}$$ and $$\bar{c} \cdot \bar{a}=0$$, then $$\bar{c} \cdot \bar{b}$$ is equal to

A
$$-\frac{1}{2}$$
B
$$\frac{3}{2}$$
C
$$\frac{1}{2}$$
D
$$-\frac{3}{2}$$
4
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+2
-0

The incidence of occupational disease in an industry is such that the workmen have a $$10 \%$$ chance of suffering from it. The probability that out of 5 workmen, 3 or more will contract the disease is

A
0.000856
B
0.856
C
0.0000856
D
0.00856
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