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
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The coefficient of x101 in the expression ${(5 + x)^{500}} + x{(5 + x)^{499}} + {x^2}{(5 + x)^{498}} + \,\,.....\,\, + …
Topic: JEE Main 2022 (25 June Evening Shift)
The area of the region enclosed between the parabolas y2 = 2x $-$ 1 and y2 = 4x $-$ 3 is
Topic: JEE Main 2022 (25 June Evening Shift)
$\mathop {\lim }\limits_{x \to {\pi \over 2}} \left( {{{\tan }^2}x\left( {{{(2{{\sin }^2}x + 3\sin x + 4)}^{{1 \over 2…
Topic: JEE Main 2022 (25 June Evening Shift)
The system of equations$ - kx + 3y - 14z = 25$$ - 15x + 4y - kz = 3$$ - 4x + y + 3z = 4$is consistent for all k in the …
Topic: JEE Main 2022 (25 June Evening Shift)
Let z1 and z2 be two complex numbers such that ${\overline z _1} = i{\overline z _2}$ and $\arg \left( {{{{z_1}} \over …
Topic: JEE Main 2022 (25 June Evening Shift)
Let a, b $\in$ R be such that the equation $a{x^2} - 2bx + 5 = 0$ has a repeated root $\alpha$. If $\alpha$ and $\beta$…
Topic: JEE Main 2022 (25 June Evening Shift)
Let $A = \{ x \in R:|x + 1| < 2\} $ and $B = \{ x \in R:|x - 1| \ge 2\} $. Then which one of the following statements i…
Topic: JEE Main 2022 (25 June Evening Shift)
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If ${b_n} = \int_0^{{\pi \over 2}} {{{{{\cos }^2}nx} \over {\sin x}}dx,\,n \in N} $, then
Topic: JEE Main 2022 (25 June Evening Shift)
If $y = y(x)$ is the solution of the differential equation $2{x^2}{{dy} \over {dx}} - 2xy + 3{y^2} = 0$ such that $y(e)…
Topic: JEE Main 2022 (25 June Evening Shift)
The value of 2sin (12$^\circ$) $-$ sin (72$^\circ$) is :
Topic: JEE Main 2022 (25 June Evening Shift)
A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its faces and the probability of getting a face with mark n …
Topic: JEE Main 2022 (25 June Evening Shift)
The value of ${\tan ^{ - 1}}\left( {{{\cos \left( {{{15\pi } \over 4}} \right) - 1} \over {\sin \left( {{\pi \over 4}}…
Topic: JEE Main 2022 (25 June Evening Shift)
The line y = x + 1 meets the ellipse ${{{x^2}} \over 4} + {{{y^2}} \over 2} = 1$ at two points P and Q. If r is the rad…
Topic: JEE Main 2022 (25 June Evening Shift)
