$\theta={\cos }^{-1}\Bigg{(}\frac{3}{\sqrt[]{10}}\Bigg{)}$ is the angle between $\vec{a}=\hat{i}-2x\hat{j}+2y\hat{k}$ & $\vec{b}=x\hat{i}+\hat{j}+y\hat{k}$ then possible values of (x,y) that lie on the locus
Previous 10 Questions — NIMCET 2023
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Let a, b, c, d be no zero numbers. If the point of intersection of the line 4ax + 2ay + c = 0 & 5bx + 2by + d=0 lie…
Topic: NIMCET 2023
If $\int x\, \sin x\, sec^3x\, dx=\frac{1}{2}\Bigg{[}f(x){se}c^2x+g(x)\Bigg{(}\frac{\tan x}{x}\Bigg{)}\Bigg{]}+C$, then…
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A point P in the first quadrant, lies on $y^2 = 4ax$, a > 0, and keeps a distance of 5a units from its focus. Which …
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The negation of $\sim S\vee(\sim R\wedge S)$ is equivalent to
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If n1 and n2 are the number of real valued solutions x = | sin–1 x | & x = sin (x) respectively, then the valu…
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Number of point of which f(x) is not differentiable $f(x)=|cosx|+3$ in $[-\pi, \pi]$
Topic: NIMCET 2023
If ${{x}}_k=\cos \Bigg{(}\frac{2\pi k}{n}\Bigg{)}+i\sin \Bigg{(}\frac{2\pi k}{n}\Bigg{)}$ , then $\sum ^n_{k=1}({{…
Topic: NIMCET 2023
The coefficient of $x^{50}$ in the expression of ${(1 + x)^{1000} + 2x(1 + x)^{999} + 3x^2(1 + x)^{998} + ...... + 1001…
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The maximum value of $f(x) = (x – 1)^2 (x + 1)^3$ is equal to $\frac{2^p3^q}{3125}$
then the ordered pair of (p, …
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If f(x) is a polynomial of degree 4, f(n) = n + 1 & f(0) = 25, then find f(5) = ?
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Next 10 Questions — NIMCET 2023
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Let R be reflexive relation on the finite set a having 10 elements and if m is the number of ordered pair in R, then
Topic: NIMCET 2023
If $| x - 6|= | x - 4x | -| x^2- 5x +6 |$ , where x is a real variable
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The range of values of θ in the interval (0, π) such that the points (3,5) and
(sinθ, cosθ) lie on the same side of t…
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Which of the following number is the coefficient of $x^{100}$ in the expansion of $\log _e\Bigg{(}\frac{1+x}{1+{x}^2}\B…
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A real valued function f is defined as $f(x)=\begin{cases}{-1} & {-2\leq x\leq0} \\ {x-1} & {0\leq x\leq2}\end{…
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A line segment AB of length 10 meters is passing through the foot of the perpendicular of a pillar, which is standing a…
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If a vector having magnitude of 5 units, makes equal angle with each of the three mutually perpendicular axes, then the…
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Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ballsis trans…
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Let $f(x)=\frac{x^2-1}{|x|-1}$. Then the value of $lim_{x\to-1} f(x)$ is
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If yellow is called white, white is called black, black is called green, green is called pink, pink is called blue and …
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