If $\alpha$ and $\beta$ are the two roots of the quadratic equation $x^2 + ax + b = 0, (ab \ne 0)$ then the quadratic roots whose roots $\frac{1}{\alpha^3+\alpha}$ and $\frac{1}{\beta^3+\beta}$ is
Previous 10 Questions — NIMCET 2025
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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 …
Topic: NIMCET 2025
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
If $B=sin^2 y+cos^4 y$, then for all real y
Topic: NIMCET 2025
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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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…
Topic: NIMCET 2025
Which one of the following is NOT a correct statement?
Topic: NIMCET 2025
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…
Topic: NIMCET 2025
Consider the sample space $\Omega={\{(x,y):x,y\in{\{1,2,3,4\}\}}}$ where each outcome is equally likely.
Let A = {x ≥ 2…
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 …
Topic: NIMCET 2025
Next 10 Questions — NIMCET 2025
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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
Topic: NIMCET 2025
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…
Topic: NIMCET 2025
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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Given the equation $x+y =1$, $x^2+y^2 =2$, $x^5 +y^5 =A$. Let N be the number
of solution pairs (x,y) to this system of…
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Number of three digit numbers that can be formed using 0, 1, 2, 3 and 5 where these digits
are allowed to repeat any nu…
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Let $g:\mathbb{R}\rightarrow \mathbb{R}$ and $h:\mathbb{R}\rightarrow \mathbb{R}$, be two functions such that $h(x) = s…
Topic: NIMCET 2025
An airplane, when 4000m high from the ground, passes vertically above another airplane at
an instant when the angles of…
Topic: NIMCET 2025
