1
JEE Main 2022 (Online) 25th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Water is being filled at the rate of 1 cm3 / sec in a right circular conical vessel (vertex downwards) of height 35 cm and diameter 14 cm. When the height of the water level is 10 cm, the rate (in cm2 / sec) at which the wet conical surface area of the vessel increases is

A
5
B
$${{\sqrt {21} } \over 5}$$
C
$${{\sqrt {26} } \over 5}$$
D
$${{\sqrt {26} } \over {10}}$$
2
JEE Main 2022 (Online) 25th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $${b_n} = \int_0^{{\pi \over 2}} {{{{{\cos }^2}nx} \over {\sin x}}dx,\,n \in N} $$, then

A
$${b_3} - {b_2},\,{b_4} - {b_3},\,{b_5} - {b_4}$$ are in A.P. with common difference $$-$$2
B
$${1 \over {{b_3} - {b_2}}},{1 \over {{b_4} - {b_3}}},{1 \over {{b_5} - {b_4}}}$$ are in an A.P. with common difference 2
C
$${b_3} - {b_2},\,{b_4} - {b_3},\,{b_5} - {b_4}$$ are in a G.P.
D
$${1 \over {{b_3} - {b_2}}},{1 \over {{b_4} - {b_3}}},{1 \over {{b_5} - {b_4}}}$$ are in an A.P. with common difference $$-$$2
3
JEE Main 2022 (Online) 25th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $$y = y(x)$$ is the solution of the differential equation

$$2{x^2}{{dy} \over {dx}} - 2xy + 3{y^2} = 0$$ such that $$y(e) = {e \over 3}$$, then y(1) is equal to :

A
$${1 \over 3}$$
B
$${2 \over 3}$$
C
$${3 \over 2}$$
D
3
4
JEE Main 2022 (Online) 25th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The value of 2sin (12$$^\circ$$) $$-$$ sin (72$$^\circ$$) is :

A
$${{\sqrt 5 (1 - \sqrt 3 )} \over 4}$$
B
$${{1 - \sqrt 5 } \over 8}$$
C
$${{\sqrt 3 (1 - \sqrt 5 )} \over 2}$$
D
$${{\sqrt 3 (1 - \sqrt 5 )} \over 4}$$
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