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

If $f(1)=1, f^{\prime}(1)=3$, then the derivative of $\mathrm{f}(\mathrm{f}(\mathrm{f}(x)))+(\mathrm{f}(x))^2$ at $x=1$ is

A
12
B
30
C
15
D
33
2
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$ y=[(x+1)(2 x+1)(3 x+1) \ldots \ldots \ldots(n x+1)]^2 $$ then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=0$ is

A
$2 \mathrm{n}(\mathrm{n}+1)$
B
$\mathrm{n}(\mathrm{n}+1)$
C
 $\frac{\mathrm{n}(\mathrm{n}+1)}{2}$
D
$\left(\frac{\mathrm{n}(\mathrm{n}+1)}{2}\right)^2$
3
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $(a+\sqrt{2} b \cos x)(a-\sqrt{2} b \cos y)=a^2-b^2$, where $\mathrm{a}>\mathrm{b}>0$, then $\frac{\mathrm{d} x}{\mathrm{~d} y}$ at $\left(\frac{\pi}{4}, \frac{\pi}{4}\right)$ is

A
$\frac{a-b}{a+b}$
B
$\frac{a+b}{a-b}$
C
$\frac{2 a+b}{2 a-b}$
D
$\frac{a-2 b}{a+2 b}$
4
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $x=2 \cos \theta-\cos 2 \theta$ and $y=2 \sin \theta-\sin 2 \theta$, then $\frac{\mathrm{d}^2 y}{d x^2}$ is equal to

A
$\frac{3}{2} \tan \frac{3 \theta}{2}$
B
$\frac{3}{2} \sec \frac{3 \theta}{2} \tan \frac{3 \theta}{2}$
C
$\frac{3}{2} \sec ^2 \frac{3 \theta}{2}$
D
$\sec ^2 \frac{3 \theta}{2}$
MHT CET Subjects
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