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The two curves $x^2+p{y}^2=1$ and $q{x}^2+y^2=1$ are orthogonal to each other then

Find the value of [2 - h] + [2 + h], where h is really small. $(h\to 0orhtendstozero)$ and [x] is the greatest integer function

If a set $A$ has ${}^{\prime }{n}^{\prime }$ distinct elements, then the number of all relations on $A$ is

In $△OAB,$ if $\overrightarrow{OA}=\overrightarrow{a},\overrightarrow{OB}=\overrightarrow{b},L$ is mid point of $\overrightarrow{OA}$ and $M$ is a point on $\overrightarrow{OB}$ such that $\overrightarrow{OM}:\overrightarrow{MB}=2:1.$ If $P$ is the mid point of $\overrightarrow{LM},$ then $\overrightarrow{AP}=$

Solve the given unique solution equations and arrange the equations in descending order to the values of $y$.

If I < x < I +1, Find [-x], where I is an integr

If $2ta{n}^{-1}x=si{n}^{-1}\frac{2x}{1+x^2}$, then:

The mean and variance of a random variable $X$ having a binomial distribution are $6$ and $3$ respectively. The probability of variable $X$ less than $2$ is

O is the centre, AB and AC are two diagonals of the adjacent faces of a rectangular box. If angles AOB, BOC and COA are $\theta ,\varphi ,\Psi$ respectively then cos $\theta +cos\varphi +cos\Psi$ is equal to

In a school, 40% of the students draw and paint. 40% of those who draw do not paint. If the students do one of the two, then what % of students paint?

If A and B are two events such that $P\left(A\right)=\frac{2}{5}$ and $P(A\cap B)=\frac{3}{20}$, then $P\left(A|\right(A^{\prime }\cup B^{\prime }\left)\right)$ is equal to

$\alpha$, $\beta$, $\gamma$ are the roots of $x^3-3x^2$ + 3x + 7 = 0(w is cube root of unity) then $(\frac{\alpha -1}{\beta -1}+\frac{\beta -1}{\gamma -1}+\frac{\gamma -1}{\alpha -1})$ is

What the eccentricity of the hyperbola with its principal axes along the

coordinate axes and which passes through (3,0) and $(3\sqrt{2},2)$

If $-3\le x^2+4x+4\le 9$, then $x\in$

Let $x$ be the length of one of the equal sides of an isosceles triangle, and let $\theta$ be the angle between them. If $x$ is increasing at the rate $\left(\frac{1}{12}\right)m/hr,$ and $\theta$ is increasing at the rate of $\frac{\pi }{180}rad/hr,$ then the rate in$\frac{m^2}{hr}$ at which the area of the triangle is increasing when $x=12m$ and $\theta =\frac{\pi }{4},$ is

Evaluate $\underset{0}{\overset{1/2}{\int }}\frac{dx}{\sqrt{1-x^2}}+\underset{1}{\overset{2/\sqrt{3}}{\int }}\frac{\sqrt{x^2-1}}{x}dx$

If from any point on the asymptote a straight line be drawn perpendicular to the transverse axis, the product of the segments of this line, intercepted between the point & the curve is always equal to _____

The solution set of $\frac{2x}{x^2-9}\le \frac{1}{x+2}$ is

If $f\left(x\right)=\frac{1}{x-2}$ and $g\left(x\right)=\frac{3}{x-5}$, then the domain of $f\left(g\right(x\left)\right)$ is

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (x + a)

Find the number of terms in the expansion of $(a+b+c{)}^n.$

The circle $x^2+y^2-4x-4y+4=0$ is inscribed in a triangle which has two of its sides along the coordinate axes. If the locus of the circumcentre of the triangle is $x+y-xy+k\sqrt{x^2+y^2}=0$, then the value of $k$ is equal to

Find the angle between planes 2x +7y +11z - 3 = 0 & 5x +3y +9z +1 = 0

The number of solutions of $\sqrt{4-x}+\sqrt{x+9}=5$ is

The range of the function ${\sin }^{2n}x+{\cos }^{2n}x;x\in R,n\in N$ is

If for $z$ as real or complex, $(1+z^2+z^4{)}^8=C_0+C_1{z}^2+C_2{z}^4+\cdots +C_{16}{z}^{32}$, then

If $A$ is a square matrix such that $A\left(\text{adj}A\right)=\left(\begin{array}{ccc}4& 0& 0\\ 0& 4& 0\\ 0& 0& 4\end{array}\right),$ then value of $\text{det(adj}A)$ equals to

Let $P=\left[a_{ij}\right]$ be a $3\times 3$ matrix and let $Q=\left[b_{ij}\right]$, where $b_{ij}=2^{i+j}{a}_{ij}$ for $1\le i,j\le 3$. If the determinant of $P$ is $2$, then the determinant of the matrix $Q$ is

If $H_1,H_2,\dots ,H_{20}$ be $20$ harmonic means between $2$ and $3$, then the value of $\frac{H_1+2}{H_1-2}+\frac{H_{20}+3}{H_{20}-3}$ is