1
JEE Main 2019 (Online) 9th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is $${\tan ^{ - 1}}\left( {{1 \over 2}} \right)$$. Water is poured into it at a constant rate of 5 cubic meter per minute. The the rate (in m/min.), at which the level of water is rising at the instant when the depth of water in the tank is 10m; is :-
A
$${1 \over {15\pi }}$$
B
$${1 \over {5\pi }}$$
C
$${1 \over {10\pi }}$$
D
$${2 \over \pi }$$
2
JEE Main 2019 (Online) 9th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If f : R $$ \to $$ R is a differentiable function and f(2) = 6,
then $$\mathop {\lim }\limits_{x \to 2} {{\int\limits_6^{f\left( x \right)} {2tdt} } \over {\left( {x - 2} \right)}}$$ is :-
A
2f'(2)
B
24f'(2)
C
0
D
12f'(2)
3
JEE Main 2019 (Online) 9th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If the system of equations 2x + 3y – z = 0, x + ky – 2z = 0 and 2x – y + z = 0 has a non-trival solution (x, y, z), then $${x \over y} + {y \over z} + {z \over x} + k$$ is equal to :-
A
-4
B
$${3 \over 4}$$
C
$${1 \over 2}$$
D
$$-{1 \over 4}$$
4
JEE Main 2019 (Online) 9th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
A thin smooth rod of length L and mass M is rotating freely with angular speed $$\omega $$0 about an axis perpendicular to the rod and passing through its center. Two beads of mass m and negligible size are at the center of the rod initially. The beads are free to slide along the rod. The angular speed of the system , when the beads reach the opposite ends of the rod, will be :-
A
$${{M{\omega _0}} \over {M + 3m}}$$
B
$${{M{\omega _0}} \over {M + m}}$$
C
$${{M{\omega _0}} \over {M + 6m}}$$
D
$${{M{\omega _0}} \over {M + 2m}}$$
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