1
MHT CET 2023 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If truth value of logical statement $$(p \leftrightarrow \sim q) \rightarrow(\sim p \wedge q)$$ is false, then the truth values of $$p$$ and $$q$$ are respectively

A
$$\mathrm{F}, \mathrm{T}$$
B
$$\mathrm{T}, \mathrm{T}$$
C
$$\mathrm{T}, \mathrm{F}$$
D
$$\mathrm{F,F}$$
2
MHT CET 2023 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The teacher wants to arrange 5 students on the platform such that the boy $$B_1$$ occupies second position and the girls $$G_1$$ and $$G_2$$ are always adjacent to each other, then the number of such arrangements is

A
24
B
12
C
8
D
16
3
MHT CET 2023 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\overline{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \overline{\mathrm{b}}=4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}$$ and $$\overline{\mathrm{c}}=\hat{\mathrm{i}}+\alpha \hat{\mathrm{j}}+\beta \hat{\mathrm{k}}$$ are linearly dependent vectors and $$|\bar{c}|=\sqrt{3}$$, then the values of $$\alpha$$ and $$\beta$$ are respectively.

A
$$1,1$$
B
$$2,1$$
C
$$0,1$$
D
$$1,2$$
4
MHT CET 2023 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

At present a firm is manufacturing 1000 items. It is estimated that the rate of change of production $$\mathrm{P}$$ w.r.t. additional number of worker $$x$$ is given by $$\frac{\mathrm{dp}}{\mathrm{d} x}=100-12 \sqrt{x}$$. If the firm employees 9 more workers, then the new level of production of items is

A
1684
B
1648
C
2116
D
1116
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