A particle is at rest at the origin. It moves along the x −axis with an acceleration $x-x^2$ , where x is the distance of the particle at time t. The particle next comes to rest after it has covered a distance
Previous 10 Questions — NIMCET 2022
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If the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{b^2}=1$ and the hyperbola $\frac{x^2}{144}-\frac{y^2}{81}=\frac{1…
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Angles of elevation of the top of a tower from
three points (collinear) A, B and C on a road
leading to the foot of t…
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The 10th and 50th percentiles of the observation 32, 49, 23, 29, 118 respectively are
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Suppose that the temperature at a point (x,y), on a metal plate is $T(x,y)=4x^2-4xy+y^2$, An ant, walking on the plate…
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The correct expression for $cos^{-1} (-x)$ is
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Let $\vec{a}, \vec{b}, \vec{c} $ be distinct non-negative numbers. If the vectors $a\hat{i}+a\hat{j}+c\hat{k}$ , $\hat{…
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Inverse of the function $f(x)=\frac{10^x-10^{-x}}{10^{x}+10^{-x}}$ is
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If $a{\lt}b$ then $\int ^b_a\Bigg{(}|x-a|+|x-b|\Bigg{)}dx$ is equal to
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The domain of the function $f(x)=\frac{{\cos }^{-1}x}{[x]}$ is
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If the volume of the parallelepiped whose adjacent edges are $\vec{a}=2\hat{i}+3\hat{j}+4\hat{k}$, $\vec{b}=\hat{i}+\al…
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Let $a$ be the distance between the lines $−2x + y = 2$ and $2x − y = 2$, and $b$ be the distance between the lines $4x…
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If $cosec\theta-cot \theta=2$, then the value of $cosec\theta$ is
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The solution of the equation ${4\cos }^2x+6{\sin }^2x=5$ are
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The function $f(x)=\begin{cases}{{(1+2x)}^{1/x}} & {,x\ne0} \\ {{e}^2} & {,x=0}\end{cases}$, is
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Let $\vec{a}=2\hat{i}+2\hat{j}+\hat{k}$ and $\vec{b}$ be another vector such that $\vec{a}.\vec{b}=14$ and $\vec{a} \ti…
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Which term of the series $\frac{\sqrt[]{5}}{3},\, \frac{\sqrt[]{5}}{4},\frac{1}{\sqrt[]{5}},\, ...$ is $\frac{\sqrt{5}}…
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The first three moments of a distribution about 2 are 1, 16, -40 respectively. The mean and variance of the distributio…
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