1
WB JEE 2021
+2
-0.5 The differential of $$f(x) = {\log _e}(1 + {e^{10x}}) - {\tan ^{ - 1}}({e^{5x}})$$ at x = 0 and for dx = 0.2 is
A
0.5
B
0.3
C
$$-$$ 0.2
D
$$-$$ 0.5
2
WB JEE 2020
+1
-0.25 Let cos$$^{ - 1}\left( {{y \over b}} \right) = \log {\left( {{x \over n}} \right)^n}$$. Then
A
$${x^2}{y^2} + x{y_1} + {n^2}y = 0$$
B
$$x{y_{^2}} - x{y_1} + 2{n^2}y = 0$$
C
$${x^2}{y_{^2}} + 3x{y_1} - {n^2}y = 0$$
D
$$x{y_{^2}} + 5x{y_1} - 3y = 0$$

$$\left( {Here,\,{y_2} = {{{d^2}y} \over {d{x^2}}},\,{y_1} = {{dy} \over {dx}}} \right)$$
3
WB JEE 2020
+1
-0.25 Let f be a differentiable function with $$\mathop {\lim }\limits_{x \to \infty } f(x) = 0.$$ If $$y' + yf'(x) - f(x)f'(x) = 0$$, $$\mathop {\lim }\limits_{x \to \infty } y(x) = 0$$, then (where $$y \equiv {{dy} \over {dx}})$$
A
$$y + 1 = {e^{f(x)}} + f(x)$$
B
$$y - 1 = {e^{f(x)}} + f(x)$$
C
$$y + 1 = {e^{ - f(x)}} + f(x)$$
D
$$y - 1 = {e^{ - f(x)}} + f(x)$$
4
WB JEE 2020
+1
-0.25 If $$x\sin \left( {{y \over x}} \right)dy = \left[ {y\sin \left( {{y \over x}} \right) - x} \right]dx,\,x > 0$$ and $$y(1) = {\pi \over 2}$$, then the value of $$\cos \left( {{y \over x}} \right)$$ is
A
1
B
log x
C
e
D
0
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Physics
Mechanics
Electricity
Optics
Modern Physics
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Physical Chemistry
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Organic Chemistry
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