The number of accidents per week in a town follows Poisson distribution with mean 3 (In Exam Given 2, which is incorrect). If the probability that there are three accidents in two weeks time is $ke^{-6}$, then the value of k is
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The angles of depression of the top and bottom of an 8m tall building from the top of a multi storied building are 30° …
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An equilateral triangle is inscribed in the parabola $y^2 = x$. One vertex of the triangle is at
the vertex of the para…
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Which one of the following is NOT a correct statement?
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Let the line $\frac{x}{4}+\frac{y}{2}=1$ meets the x-axis and y-axis at A and B, respectively. M is the midpoint
of sid…
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Consider the sample space $\Omega={\{(x,y):x,y\in{\{1,2,3,4\}\}}}$ where each outcome is equally likely.
Let A = {x ≥ 2…
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If $\vec{a}=\hat{i}+\hat{j}+\hat{k}$, $\vec{b}=2\hat{i}-\hat{j}+3\hat{k}$ and $\vec{c}=\hat{i}-2\hat{j}+\hat{k}$, then …
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If $\vec{a}$ and $\vec{b}$ are twp vectors such that |$\vec{a}$|=3, |$\vec{b}$|=4 and |$\vec{a}+\vec{b}$|=1, then the v…
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A tower subtends angles $\alpha, 2\alpha$ and $3\alpha$ respectively at points A, B and C which are lying on a horizont…
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Let $\vec{a}$, $\vec{b}$ and $\vec{c}$ be unit vectors such that the angle between them is ${\cos }^{-1}\Bigg…
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Let $A=\{{5}^n-4n-1\colon n\in N\}$ and $B=\{{}16(n-1)\colon n\in N\}$ be sets. Then
Topic: NIMCET 2025
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If $B=sin^2 y+cos^4 y$, then for all real y
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Let $F_1, F_2$ be foci of hyperbola $\frac{{x}^2}{{a}^2}-\frac{{y}^2}{{b}^2}=1$, a>0, b>0, and let O be…
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A circle with its center in the first quadrant touches both the coordinate axes and the line
x-y-2=0. Then the area of …
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If $\alpha$ and $\beta$ are the two roots of the quadratic equation $x^2 + ax + b = 0, (ab \ne 0)$ then the quadratic r…
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The maximum value of $\sin x+\sin(x+1)$ is $k \cos \frac{1}{2}$. Then the value of k is
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Let $\mathbb{R}\rightarrow\mathbb{R}$ be any function defined as $f(x)=\begin{cases}{{x}^{\alpha}\sin \frac{1}{{x}…
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The number of 3-digit integers that are multiple of 6 which can be formed by using the
digits 1,2,3,4,5,6 without repet…
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The circle $x^2 + y^2+ \alpha x+ \beta y+ \gamma=0$ is the image of the circle $x^2 + y^2- 6x- 10y+ 30=0$ across
the li…
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Let $\vec{a}=2\hat{i}-3\hat{j}+4\hat{k}$, $\vec{b}=\hat{i}+2\hat{j}-\hat{k}$ and $\vec{c}=3\hat{i}+\hat{j}+\lambda \hat…
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The area enclosed between the curve y = sin x, y = cosx, $0\leq x\leq\frac{\pi}{2}$ is
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