1
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A wet substance in the open air loses its moisture at a rate proportional to the moisture content. If a sheet hung in the open air loses half its moisture during the first hour, then the time t , in which $99 \%$ of the moisture will be lost, is

A
$\frac{2 \log 10}{\log 2}$
B
$\frac{\log 10}{\log 2}$
C
$\frac{3 \log 10}{\log 2}$
D
$\frac{1}{2} \frac{\log 10}{\log 2}$
2
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$\lim _\limits{x \rightarrow 0} \frac{(1-\cos 2 x)(3+\cos x)}{x \tan 4 x}$ has the value

A
2
B
$\frac{1}{2}$
C
4
D
3
3
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $a, b \in(a \neq 0)$. If the function $f$ is defined as

$$f(x)=\left\{\begin{array}{cc} \frac{2 x^2}{\mathrm{a}} & , 0 \leq x<1 \\ \mathrm{a} & , 1 \leq x<\sqrt{2} \\ \frac{2 \mathrm{~b}^2-4 b}{x} & , \sqrt{2} \leq x<\infty \end{array}\right.$$

is continuous in the interval $[0, \infty)$, then an ordered pair $(a, b)$ is

A
$(-\sqrt{2}, 1-\sqrt{3})$
B
$(\sqrt{2},-1+\sqrt{3})$
C
$(\sqrt{2}, 1-\sqrt{3})$
D
$(-\sqrt{2}, 1+\sqrt{3})$
4
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $(p \wedge \sim q) \wedge(p \wedge r) \rightarrow \sim p \vee q$ is false, then the truth values of $p, q$ and $r$ are respectively

A
$\mathrm{T}, \mathrm{T}, \mathrm{T}$
B
$\mathrm{F, F, F}$
C
$\mathrm{T, F, T}$
D
$\mathrm{F, T, F}$
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