1
MHT CET 2025 19th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

The last column in the truth table of the statement pattern $[\mathrm{p} \rightarrow(\mathrm{q} \wedge \sim \mathrm{p})] \vee[(\mathrm{p} \vee \sim \mathrm{q}) \wedge \mathrm{p}]$ is

A
TTTF
B
TFFF
C
TTTT
D
FFTT
2
MHT CET 2025 19th April Evening Shift
MCQ (Single Correct Answer)
+2
-0
Which of the following are pairs of equivalent circuitsMHT CET 2025 19th April Evening Shift Mathematics - Mathematical Reasoning Question 15 English
A
(A) and (B)
B
(B) and (D)
C
(C) and (E)
D
(A) and (C)
3
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
The statement pattern $[(p \rightarrow q) \wedge \sim q] \rightarrow r$ is a tautology when $r$ is equivalent to
A
$\mathrm{p} \wedge \sim \mathrm{q}$
B
$q \vee p$
C
$p \wedge q$
D
$\sim q$
4
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

Consider the three statements

$\mathrm{p}: \forall \mathrm{n} \in \mathbb{N}, 10 \mathrm{n}-3$ is a prime number, when n is not divisible by 3.

$\mathrm{q}: \frac{2}{\sqrt{3}}, \frac{-2}{\sqrt{3}}, \frac{-1}{\sqrt{3}}$ are the direction cosines of a directed line.

$\mathrm{r}: \sin x$ is an increasing function in the interval $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$.

Then which of the following statement pattern has truth value true?

A
$\quad(p \wedge q) \leftrightarrow r$
B
$(p \rightarrow q) \rightarrow \sim r$
C
$(\sim p \vee q) \wedge r$
D
$\quad(\sim p \wedge \sim q) \leftrightarrow \sim r$
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