1
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $y$ is a function of $x$ and $\log (x+y)=2 x y$, then the value of $y^{\prime}(0)$ is

A
1
B
$-$1
C
2
D
0
2
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $x^2 y^2=\sin ^{-1} x+\cos ^{-1} x$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=1$ and $y=2$ is

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

If $\frac{\mathrm{d}}{\mathrm{d} x} \mathrm{f}(x)=4 x^3-\frac{3}{x^4}$ such that $\mathrm{f}(2)=0$, then $\mathrm{f}(x)$ is equal to

A
$x^4+\frac{1}{x^3}+\frac{129}{8}$
B
$x^4+\frac{1}{x^3}-\frac{129}{8}$
C
$x^3+\frac{1}{x^4}+\frac{129}{8}$
D
  $x^3+\frac{1}{x^4}-\frac{129}{8}$
4
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0
If $$y = {{\sin x} \over {1 + {{\cos x} \over {1 + {{\sin x} \over {1 + {{\cos x} \over {...}}}}}}}}$$, then $\frac{dy}{dx}$ is given by
A
$\frac{y \sin x+(1+y) \cos x}{1+2 y+\cos x-\sin x}$
B
$\frac{y \cos x+(1+y) \sin x}{1+2 y+\cos x-\sin x}$
C
$\frac{y \sin x-(1+y) \cos x}{1+2 y+\cos x-\sin x}$
D
$\frac{y \cos x-(1+y) \sin x}{1+2 y+\cos x-\sin x}$
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