Let $f: R \rightarrow R$ be defined by $f(x) = \begin{cases} x + 2 & \text{if } x < 0 \\ |x - 2| & \text{if } x \geq 0 \end{cases}$. Find $\int_{-2}^{3} f(x)\, dx$
Previous 10 Questions — NIMCET 2018
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$\int_0^{\pi} x\, f(\sin x)\, dx$ is equal to
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The set of points, where $f(x)=\frac{x}{1+|x|}$ is differentiable in
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If the mean of the squares of first n natural numbers be 11, then n is equal to?
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If A is an invertible skew-symmetric matrix, then is a
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Suppose that m and n are fixed numbers such that the mth term of an HP is equal to n and the nth term is equal to m, (m…
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Sum to infinity of a geometric is twice the sum of the first two terms. Then what are the possible values of common rat…
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The quadratic equation whose roots are $\sin^218^o$ and $\cos^236^o$ is
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A and B play a game where each is asked to select a number from 1 to 25. If the two number match, both of them win a pr…
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Three numbers a,b and c are chosen at random (without replacement) from among the numbers 1, 2, 3, ..., 99. The probabi…
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Two person A and B agree to meet 20 april 2018 between 6pm to 7pm with understanding that they will wait no longer…
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The slope of two-lines $6x^2-xy-2y^2=0$ differ by
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If the radius of the circle changes at the rate of $-\dfrac{2}{\pi}$ m/s, at what rate does the circle's area change wh…
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The point of intersection os circle $x^2+y^2+10x-12y+51=0$ and the line $3y+x=3$ is
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The number of solutions of the equation sinx + sin5x = sin3x lying in the interval $[0, \pi]$ is
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In an acute-angled ΔABC the least value of secA+secB+secC is
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Let $P = \{\theta : \sin\theta - \cos\theta = \sqrt{2}\cos\theta \}$ and
$Q = \{\theta : \sin\theta + \cos\theta = \s…
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If $\dfrac{\tan x}{2} = \dfrac{\tan y}{3} = \dfrac{\tan z}{5}$ and $x + y + z = \pi$, then the value of $\tan^2 x + \ta…
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The circles whose equations are $x^2+y^2+c^2=2ax$ and $x^2+y^2+x^2-2by=0$ will touch one another externally, if
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The locus of the orthocentre of the triangle formed by the lines (1+p)x-py+p(1+p)=0, (1+p)(x-q)+q(1+ q)=0 and y=0 where…
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Equation of the common tangents with a positive slope to the circle $x^2+y^2-8x=0$ and$\dfrac{x^2}{9}-\dfrac{y^2}{4}=1$…
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