The standard deviation of 20 numbers is 30. If each of the numbers is increased by 4, then the new standard deviation will be
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The area of the triangle formed by the vertices whose position vectors are $3\widehat{i}+\widehat{j}$ , $5\widehat{i}+2…
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The general value of $\theta$, satisfying the equation $\sin \theta=\frac{-1}{2},\, \tan \theta=\frac{1}{\sqrt[]{3}}$
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If the position vector of A and B relative to O be $\widehat{i}\, -4\widehat{j}+3\widehat{k}$ and $-\widehat{…
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The locus of the point of intersection of tangents to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ which meet right …
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If $\frac{n!}{2!(n-2)!}$ and $\frac{n!}{4!(n-4)!}$ are in the ratio 2:1, then the value of n is
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If $F(\theta)=\begin{bmatrix}{\cos \theta} & {-\sin \theta} & {0} \\ {\sin \theta} & {\cos \theta} & {0} \\ {0} & {0} &…
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For what value of p, the polynomial $x^4-3x^3+2px^2-6$ is exactly divisible by $(x-1)$
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Let $\vec{a}=2\widehat{i}\, +\widehat{j}\, +2\widehat{k}$ , $\vec{b}=\widehat{i}-\widehat{j}+2\widehat{k}$ and $\vec{c…
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In a ΔABC, if $\tan ^2\frac{A}{2}+\tan ^2\frac{B}{2}+\tan ^2\frac{C}{2}=k$ , then k is always
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The number of common tangents to the circle $x^2+y^2=4$ and $x^2+y^2-6x-8y=24$ is
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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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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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A polygon has 44 diagonals, the number of sides are
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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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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 value of $\tan 9{^{\circ}}-\tan 27{^{\circ}}-\tan 63{^{\circ}}+\tan 81{^{\circ}}$ is equal to
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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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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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If $y=\sin ^{-1}(\frac{{x}^2+1}{\sqrt[]{1+3{x}^2+{x}^4}}),\, (x>0),$ then $\frac{dy}{dx}$=
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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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