A tower subtends angles $\alpha, 2\alpha$ and $3\alpha$ respectively at points A, B and C which are lying on a horizontal line through the foot of the tower. Then $\frac{AB}{BC}$ is equal to
Previous 10 Questions — NIMCET 2025
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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…
Topic: NIMCET 2025
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
If x, y and z are three cube roots of 27, then the determinant of the matrix $\begin{bmatrix}{x} & {y} &…
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If $\vec{a}, \vec{b}$ and $\vec{c} $ are three vectors such that $\vec{a} \times \vec{b}=\vec{c}$ , $\vec{a}.\vec{c} = …
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Let A = {1,2,3, ... , 20}. Let $R\subseteq A\times A$ such that R = {(x,y): y = 2x - 7}. Then the number
of elements in…
Topic: NIMCET 2025
The number of all even integers between 99 and 999 which are not multiple of 3 and 5 is
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There are two coins, say blue and red. For blue coin, probability of getting head is 0.99 and
for red coin, it is 0.01.…
Topic: NIMCET 2025
The value of $\frac{d}{dx}\int ^{2\sin x}_{\sin {x}^2}{e}^{{t}^2}dt$ at $x=\pi$
Topic: NIMCET 2025
The captains of five cricket teams, including India and Australia, are lined up randomly
next to one other for a group …
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Let A and B be two square matrices of same order satisfying $A^2+5A+5I =0$ and $B^2+3B+I=0$ repectively. Where I is the…
Topic: NIMCET 2025
Next 10 Questions — NIMCET 2025
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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…
Topic: NIMCET 2025
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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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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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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Which one of the following is NOT a correct statement?
Topic: NIMCET 2025
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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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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The number of accidents per week in a town follows Poisson distribution with mean 3 (In Exam Given 2, which is incorrec…
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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…
Topic: NIMCET 2025
