1
MHT CET 2021 22th September Morning Shift
+2
-0

If $$y^2=a x^2+b x+c$$, where $$a, b, c$$ are constants, then $$y^3 \frac{d^2 y}{d x^2}$$ is equal to

A
function of $$y$$
B
function of both $$\mathrm{x}$$ and $$\mathrm{y}$$
C
constant
D
function of $$x$$
2
MHT CET 2021 22th September Morning Shift
+2
-0

$$x=\frac{1-t^2}{1+t^2}$$ and $$y=\frac{2 a t}{1+t^2}$$, then $$\frac{d y}{d x}=$$

A
$$\frac{a\left(t^2+1\right)}{2 t}$$
B
$$\frac{a\left(t^2-1\right)}{t}$$
C
$$\frac{a\left(1-t^2\right)}{2 t}$$
D
$$\frac{a\left(t^2-1\right)}{2 t}$$
3
MHT CET 2021 21th September Evening Shift
+2
-0

If y = 2 sin x + 3 cos x and y + A$$\mathrm{\frac{d^2y}{dx^2}}$$ = B, then the values of A, B are respectively

A
0, 1
B
0, $$-$$1
C
$$-$$1, 0
D
1, 0
4
MHT CET 2021 21th September Evening Shift
+2
-0

If $$y = {\tan ^{ - 1}}\left\{ {{{a\cos x - b\sin x} \over {b\cos x + a\sin x}}} \right\}$$, then $${{dy} \over {dx}}$$

A
$${1 \over {1 + {x^2}}}$$
B
$${1 \over {\sqrt {1 - {x^2}} }}$$
C
$$- 1$$
D
None of these
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