1
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

From the following options, the nearest line to the origin is ….

A
$\quad 3 x-4 y+4=0$
B
$2 x-3 y=5$
C
$\quad 4 x-3 y+12=0$
D
$\quad 5 x-2 y=3$
2
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the truth value of the statement pattern $[p \wedge \sim r] \rightarrow \sim r \wedge q$ is False, then which of the following has truth value False?

A
$(p \vee r) \rightarrow \sim r$
B
$\quad(\mathrm{r} \vee \mathrm{q}) \rightarrow \sim \mathrm{p}$
C
$\sim(p \vee q) \rightarrow \sim r$
D
$\quad \sim(r \vee q) \rightarrow \sim p$
3
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

$\bar{a}=\hat{i}-\hat{j}, \bar{b}=\hat{j}-\hat{k}, \bar{c}=\hat{k}-\hat{i}$ then a unit vector $\bar{d}$ such that $\overline{\mathrm{a}} \cdot \overline{\mathrm{d}}=0=[\overline{\mathrm{b}} \overline{\mathrm{c}} \overline{\mathrm{d}}]$ is

A
$\pm\left(\frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}+3 \hat{\mathrm{k}}}{\sqrt{11}}\right)$
B
$\pm\left(\frac{-\hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{2}}\right)$
C
$\pm\left(\frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{3}}\right)$
D
$\pm\left(\frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}}{\sqrt{6}}\right)$
4
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

In $\triangle A B C$, with usual notations, if $\mathrm{a}^4+\mathrm{b}^4+\mathrm{c}^4-2 \mathrm{a}^2 \mathrm{c}^2-2 \mathrm{c}^2 \mathrm{~b}^2=0$, then $\angle \mathrm{C}=\ldots$

A
$135^{\circ}$
B
$120^{\circ}$
C
$150^{\circ}$
D
$125^{\circ}$
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