If $32\, \tan ^8\theta=2\cos ^2\alpha-3\cos \alpha$ and $3\, \cos \, 2\theta=1$, then the general value of $\alpha$ =
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If $y=\sin ^{-1}(\frac{{x}^2+1}{\sqrt[]{1+3{x}^2+{x}^4}}),\, (x>0),$ then $\frac{dy}{dx}$=
Topic: NIMCET 2021
If $H_1,H_2,\ldots,H_n$ are n harmonic means between a and b $(b\ne a)$;,then $\frac{{{H}}_n+a}{{{H}}_n-a}+\frac{{{H}}_…
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In a triangle, if the sum of two sides is x and their product is y such that (x+z)(x-z)=y, where z is the third side of…
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The value of $\tan 9{^{\circ}}-\tan 27{^{\circ}}-\tan 63{^{\circ}}+\tan 81{^{\circ}}$ is equal to
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If $y={\tan }^{-1}\lgroup{\frac{3x-{x}^3}{1-3{x}^2}}\rgroup\, ,\, \frac{-1}{\sqrt[]{3}}{\lt}x{\lt}\frac{1}{\sqrt[]{3}}$…
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The probability of occurrence of two events E and F are 0.25 and 0.50, respectively. the probability of their simultane…
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A polygon has 44 diagonals, the number of sides are
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If $f\colon R\rightarrow R$ is defined by $f(x)=\begin{cases}{\frac{x+2}{{x}^2+3x+2}} & {,\, if\, x\, \in R-\{-1,-2\}} …
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The function $f(x)=\frac{x}{1+x\tan x}$ , $0\leq x\leq\frac{\pi}{2}$ is maximum when
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The standard deviation of 20 numbers is 30. If each of the numbers is increased by 4, then the new standard deviation w…
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In a triangle ABC, $a\cos ^2\frac{C}{2}+\, c\, \, {\cos }^2\frac{A}{2}=\frac{3b}{2}$ then the sides of the triangle are…
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If θ is acute angle between the pair of lines $x^2-7xy+12y^2=0$, then $\frac{2\cos \theta+3\sin \theta}{4\sin \theta+5\…
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The four geometric means between 2 and 64 are
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The lines $px+qy=1$ and $qx+py=1$ are respectively the sides AB, AC of the triangle ABC and the bas…
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If the vectors $a\hat{i}+\hat{j}+\hat{k},\hat{i}+b\hat{j}+\hat{k},\hat{i}+\hat{j}+c\hat{k}$ , $(a,b,c\ne1)$ are coplana…
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Let $\vec{a}=\hat{i}+\hat{j}$ and $\vec{b}=2\hat{i}-\hat{k}$, the point of intersection of the lines $\vec{r}\times\ve…
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If the system of equations $3x-y+4z=3$ , $x+2y-3z=-2$ , $6x+5y+λz=-3 $ has atleast one solution, then $λ=$
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If a variable takes values 0, 1, 2,…, 50 with frequencies $1,\, {{50}}_{{{C}}_1},{{50}}_{{{C}}_2},\ldots..,{{50}}_…
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If A={1,2,3,4} and B={3,4,5}, then the number of elements in (A∪B)×(A∩B)×(AΔB)
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If n is an integer between 0 to 21, then find a value of n for which the value of $n!(21-n)!$ is minimum
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