1
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

In a triangle ABC , with usual notations, $\frac{\cos \mathrm{B}+\cos \mathrm{C}}{\mathrm{b}+\mathrm{c}}+\frac{\cos \mathrm{A}}{\mathrm{a}}$ has the value

A
$\frac{1}{\mathrm{~b}+\mathrm{c}}$
B
$\frac{1}{\mathrm{~b}}$
C
$\frac{1}{\mathrm{c}}$
D
$\frac{1}{\mathrm{a}}$
2
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{f}(x)=\frac{x}{x+1}, x \neq-1$ and (fof) $(x)=\mathrm{F}(x)$, then $\int \mathrm{F}(x) \mathrm{d} x$ is

A
$\frac{x}{2}+\frac{1}{2} \log (2 x+1)+\mathrm{c}$, where c is a constant of integration.
B
$\frac{x}{2}-\frac{1}{4} \log (2 x+1)+\mathrm{c}$, where c is a constant of integration.
C
$\frac{x}{2}-\frac{1}{2} \log (2 x+1)+\mathrm{c}$, where c is a constant of integration.
D
$\frac{x}{2}+\frac{1}{4} \log (2 x+1)+\mathrm{c}$, where c is a constant of integration.
3
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If p : The total prime numbers between 2 to 100 are 26.

q : Zero is a complex number.

$r$ : Least common multiple (L.C.M.) of 6 and 7 is 6 .

Then which of the following is correct?

A
$(p \wedge q) \rightarrow r$ has truth value False.
B
$(p \rightarrow q) \rightarrow r$ has truth value True.
C
$(p \vee q) \leftrightarrow r$ has truth value False.
D
$(\mathrm{p} \rightarrow \mathrm{q}) \rightarrow(\mathrm{q} \rightarrow \mathrm{p})$ has truth value True.
4
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\lim _\limits{x \rightarrow 2} \frac{3^x+3^{3-x}-12}{3^{3-x}-3^{\frac{x}{2}}}=$$

A
$-\frac{4}{3}$
B
$\frac{4}{3}$
C
$\frac{2}{3}$
D
$-\frac{4}{9}$
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