1
WB JEE 2021
MCQ (Single Correct Answer)
+1
-0.25
Change Language
If $$\int\limits_{{{\log }_e}2}^x {{{({e^x} - 1)}^{ - 1}}dx = {{\log }_e}{3 \over 2}} $$, then the value of x is
A
1
B
e2
C
log 4
D
$${1 \over e}$$
2
WB JEE 2021
MCQ (Single Correct Answer)
+1
-0.25
Change Language
The normal to a curve at P(x, y) meets the X-axis at G. If the distance of G from the origin is twice the abscissa of P then the curve is
A
a parabola
B
a circle
C
a hyperbola
D
an ellipse
3
WB JEE 2021
MCQ (Single Correct Answer)
+1
-0.25
Change Language
The differential equation of all the ellipses centred at the origin and have axes as the co-ordinate axes is where $$y^{\prime}\equiv{{{dx}\over {dy}}},y^{\prime\prime}\equiv{{{d^2}y\over {dx^2}}}$$
A
y2 + xy'2 $$-$$ yy' = 0
B
xyy'' + xy'2 $$-$$ yy' = 0
C
yy' + xy'2 $$-$$ xy' = 0
D
x2y' + xy'' $$-$$ 3y = 0
4
WB JEE 2021
MCQ (Single Correct Answer)
+1
-0.25
Change Language
If $$x{{dy} \over {dx}} + y = {{xf(xy)} \over {f'(xy)'}}$$, then | f(xy) | is equal to (where k is an arbitrary positive constant).
A
$$k{e^{{x^2}/2}}$$
B
$$k{e^{{y^2}/2}}$$
C
$$k{e^{{x^2}}}$$
D
$$k{e^{{y^2}}}$$
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