1
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
$${e^x} + {1 \over 3}{x^3}$$
2
WB JEE 2022
MCQ (Single Correct Answer)
+1
-0.25
Change Language

The point of contact of the tangent to the parabola y2 = 9x which passes through the point (4, 10) and makes an angle $$\theta$$ with the positive side of the axis of the parabola where tan$$\theta$$ > 2, is

A
$$\left( {{4 \over 9},2} \right)$$
B
(4, 6)
C
(4, 5)
D
$$\left( {{1 \over 4},{1 \over 6}} \right)$$
3
WB JEE 2022
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let $$f(x) = {(x - 2)^{17}}{(x + 5)^{24}}$$. Then

A
f does not have a critical point at x = 2
B
f has a minimum at x = 2
C
f has neither a maximum nor a minimum at x = 2
D
f has a minimum at x = 2
4
WB JEE 2022
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $$\overrightarrow a = \widehat i + \widehat j - \widehat k$$, $$\overrightarrow b = \widehat i - \widehat j + \widehat k$$ and $$\overrightarrow c $$ is unit vector perpendicular to $$\overrightarrow a $$ and coplanar with $$\overrightarrow a $$ and $$\overrightarrow b $$, then unit vector $$\overrightarrow d $$ perpendicular to both $$\overrightarrow a $$ and $$\overrightarrow c $$ is

A
$$ \pm {1 \over {\sqrt 6 }}\left( {2\widehat i - \widehat j + \widehat k} \right)$$
B
$$ \pm {1 \over {\sqrt 2 }}\left( {\widehat j + \widehat k} \right)$$
C
$$ \pm {1 \over {\sqrt 6 }}\left( {\widehat i - 2\widehat j + \widehat k} \right)$$
D
$$ \pm {1 \over {\sqrt 2 }}\left( {\widehat j - \widehat k} \right)$$
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