A spherical iron ball of radius $10\ \text{cm}$ is coated with a layer of ice of uniform thickness that melts at a rate of $50\ \text{cm}^3/\text{min}$. When the thickness of the ice is $5\ \text{cm}$, the rate at which the thickness (in cm/min) of the ice decreases is:

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Let f(x) = loge(sin x), (0 < x < $\pi $) and g(x) = sin–1 (e–x ), (x $ \ge $ 0). If $\alpha $ is a positive real …

Topic: JEE Main 2019 (10 April Evening Shift)

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The number of real roots of the equation $5+\lvert 2^{x}-1\rvert=2^{x},(2^{x}-2)$ is:

Topic: JEE Main 2019 (10 April Evening Shift)

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If $\displaystyle \lim_{x\to1}\frac{x^{2}-ax+b}{x-1}=5$, then $a+b$ is equal to:

Topic: JEE Main 2019 (10 April Evening Shift)

3

Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than $9…

Topic: JEE Main 2019 (10 April Evening Shift)

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If $\displaystyle \int x^{5}e^{-x^{2}},dx=g(x)e^{-x^{2}}+c$, where $c$ is a constant of integration, then $g(-1)$ is eq…

Topic: JEE Main 2019 (10 April Evening Shift)

5

Let $a_1,a_2,a_3,\ldots$ be an A.P. with $a_6=2$. Then the common difference of this A.P., which maximises the product …

Topic: JEE Main 2019 (10 April Evening Shift)

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The distance of the point having position vector $-\hat{i}+2\hat{j}+6\hat{k}$ from the straight line passing through th…

Topic: JEE Main 2019 (10 April Evening Shift)

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If $\cos^{-1}x-\cos^{-1}\left(\dfrac{y}{2}\right)=\alpha$, where $-1\le x\le1,\ -2\le y\le2,\ x\le\dfrac{y}{2}$, then f…

Topic: JEE Main 2019 (10 April Evening Shift)

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If both the mean and the standard deviation of $50$ observations $x_{1},x_{2},\ldots,x_{50}$ are equal to $16$, then th…

Topic: JEE Main 2019 (10 April Evening Shift)

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Lines are drawn parallel to the line $4x-3y+2=0$, at a distance $\dfrac{3}{5}$ from the origin. Then which one of the f…

Topic: JEE Main 2019 (10 April Evening Shift)

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Let $y=y(x)$ be the solution of the differential equation $\dfrac{dy}{dx}+y\tan x=2x+x^{2}\tan x,\ x\in\left(-\dfrac{\p…

Topic: JEE Main 2019 (10 April Evening Shift)