1
WB JEE 2020
MCQ (Single Correct Answer)
+2
-0.5
Change Language
Let $$0 < \alpha < \beta < 1$$. Then, $$\mathop {\lim }\limits_{n \to \infty } \int\limits_{1/(k + \beta )}^{1/(k + \alpha )} {{{dx} \over {1 + x}}} $$ is
A
$${\log _e}{\beta \over \alpha }$$
B
$${\log _e}{1+\beta \over 1+\alpha }$$
C
$${\log _e}{1+\alpha \over 1+\beta }$$
D
$$\infty $$
2
WB JEE 2020
MCQ (Single Correct Answer)
+2
-0.5
Change Language
$$\mathop {\lim }\limits_{x \to 1} \left( {{1 \over {1nx}} - {1 \over {(x - 1)}}} \right)$$
A
Does not exist
B
1
C
$${1 \over 2}$$
D
0
3
WB JEE 2020
MCQ (Single Correct Answer)
+2
-0.5
Change Language
Let $$y = {1 \over {1 + x + lnx}}$$, then
A
$$x{{dy} \over {dx}} + y = x$$
B
$$x{{dy} \over {dx}} = y(y\ln x - 1)$$
C
$${x^2}{{dy} \over {dx}} = {y^2} + 1 - {x^2}$$
D
$$x{\left( {{{dy} \over {dx}}} \right)^2} = y - x$$
4
WB JEE 2020
MCQ (Single Correct Answer)
+2
-0.5
Change Language
Consider the curve $$y = b{e^{ - x/a}}$$, where a and b are non-zero real numbers. Then
A
$${x \over a} + {y \over b}$$ = 1 is tangent to the curve at (0, 0)
B
$${x \over a} + {y \over b}$$ = 1 is tangent to the curve, where the curve crosses the axis of y
C
$${x \over a} + {y \over b}$$ = 1 is tangent to the curve at (a, 0)
D
$${x \over a} + {y \over b}$$ = 1 is tangent to the curve at (2a, 0)
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