1
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

Calculate the pH of buffer solution containing 0.027 M weak acid and 0.054 M of its salt with strong base if $\mathrm{pK}_{\mathrm{a}}$ is 4.2.

A
4.5
B
3.2
C
5.6
D
6.4
2
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\int \frac{\mathrm{d} x}{\cos ^3 x \sqrt{2 \sin 2 x}}=(\tan x)^A+C(\tan x)^B+K$, where K is a constant of integration, then the value of $5(A+B+C)$ is equal to

A
25
B
14
C
16
D
20
3
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{2 x^2-1}{\left(x^2+4\right)\left(x^2-3\right)} d x=$$

A
$\frac{9}{14} \tan ^{-1}\left(\frac{x}{2}\right)+\frac{5}{14 \sqrt{3}} \log \left(\frac{x-\sqrt{3}}{x+\sqrt{3}}\right)+\mathrm{c}$, (where c is constant of integration)
B
$\frac{9}{7} \tan ^{-1}\left(\frac{x}{2}\right)+\frac{5}{7 \sqrt{3}} \log \left(\frac{x-\sqrt{3}}{x+\sqrt{3}}\right)+c$, (where c is constant of integration)
C
$\frac{9}{7} \tan ^{-1}\left(\frac{x}{2}\right)-\frac{5}{7 \sqrt{3}} \log \left(\frac{x-\sqrt{3}}{x+\sqrt{3}}\right)+\mathrm{c}$, (where c is constant of integration)
D
$\frac{9}{14} \tan ^{-1}\left(\frac{x}{2}\right)+\frac{5}{7} \log \left(\frac{x-\sqrt{3}}{x+\sqrt{3}}\right)+\mathrm{c}$, (where c is constant of integration)
4
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $\mathrm{f}(x)=\frac{1-\tan x}{4 x-\pi}, x \neq \frac{\pi}{4}, x \in\left[0, \frac{1}{2}\right], \quad \mathrm{f}(x)$ is continuous in $\left[0, \frac{\pi}{2}\right]$, then $\mathrm{f}\left(\frac{\pi}{4}\right)$ is

A
$-\frac{1}{2}$
B
$\frac{1}{2}$
C
1
D
$-1$
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