1
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

The function $$y = {e^{kx}}$$ satisfies $$\left( {{{{d^2}y} \over {d{x^2}}} + {{dy} \over {dx}}} \right)\left( {{{dy} \over {dx}} - y} \right) = y{{dy} \over {dx}}$$. It is valid for

A
exactly one value of k.
B
two distinct values of k.
C
three distinct values of k.
D
infinitely many values of k.
2
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Given $${{{d^2}y} \over {d{x^2}}} + \cot x{{dy} \over {dx}} + 4y\cos e{c^2}x = 0$$. Changing the independent variable x to z by the substitution $$z = \log \tan {x \over 2}$$, the equation is changed to

A
$${{{d^2}y} \over {d{z^2}}} + {3 \over y} = 0$$
B
$$2{{{d^2}y} \over {d{z^2}}} + {e^y} = 0$$
C
$${{{d^2}y} \over {d{z^2}}} - 4y = 0$$
D
$${{{d^2}y} \over {d{z^2}}} + 4y = 0$$
3
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let $$f(x) = \left\{ {\matrix{ {x + 1,} & { - 1 \le x \le 0} \cr { - x,} & {0 < x \le 1} \cr } } \right.$$

A
f(x) is discontinuous in [$$-1,1$$] and so has no maximum value or minimum value in [$$-1,1$$].
B
f(x) is continuous in [$$-1,1$$] and so has maximum value and minimum value.
C
f(x) is discontinuous in [$$-1,1$$] but still has the maximum and minimum value.
D
f(x) is bounded in [$$-1,1$$] and does not attain maximum or minimum value.
4
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

A missile is fired from the ground level rises x meters vertically upwards in t sec, where $$x = 100t - {{25} \over 2}{t^2}$$. The maximum height reached is

A
100 m
B
300 m
C
200 m
D
125 m
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