1
WB JEE 2022
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let $$f(x) = \int\limits_{\sin x}^{\cos x} {{e^{ - {t^2}}}dt} $$. Then $$f'\left( {{\pi \over 4}} \right)$$ equals

A
$$\sqrt {{1 \over e}} $$
B
$$ - \sqrt {{2 \over e}} $$
C
$$\sqrt {{2 \over e}} $$
D
$$ - \sqrt {{1 \over e}} $$
2
WB JEE 2022
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $$x{{dy} \over {dx}} + y = x{{f(xy)} \over {f'(xy)}}$$, then $$|f(xy)|$$ is equal to

A
$$C{e^{{{{x^2}} \over 2}}}$$ (where C is the constant of integration)
B
$$C{e^{{x^2}}}$$ (where C is the constant of integration)
C
$$C{e^{2{x^2}}}$$ (where C is the constant of integration)
D
$$C{e^{{{{x^2}} \over 3}}}$$ (where C is the constant of integration)
3
WB JEE 2022
MCQ (Single Correct Answer)
+1
-0.25
Change Language

A curve passes through the point (3, 2) for which the segment of the tangent line contained between the co-ordinate axes is bisected at the point of contact. The equation of the curve is

A
$$y = {x^2} - 7$$
B
$$x = {{{y^2}} \over 2} + 2$$
C
$$xy = 6$$
D
$${x^2} + {y^2} - 5x + 7y + 11 = 0$$
4
WB JEE 2022
MCQ (Single Correct Answer)
+1
-0.25
Change Language

The solution of

$$\cos y{{dy} \over {dx}} = {e^{x + \sin y}} + {x^2}{e^{\sin y}}$$ is $$f(x) + {e^{ - \sin y}} = C$$ (C is arbitrary real constant) where f(x) is equal to

A
$${e^x} + {1 \over 2}{x^3}$$
B
$${e^{ - x}} + {1 \over 3}{x^3}$$
C
$${e^{ - x}} + {1 \over 2}{x^3}$$
D
$${e^x} + {1 \over 3}{x^3}$$
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