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If y = mx be one of the bisectors of the angle between the lines $a{x}^2-2hxy+b{y}^2=0$, then

If the sum of three numbers in A.P. is 12 and sum of their cubes is 408, then sum of their squares is:

The equation of the circle passing through the foci of the ellipse $\frac{x^2}{9}+\frac{y^2}{16}=1$ and having the centre at (0, 3) is

(IIT JEE Main 2013)

Divide $4x^3+12x^2+11x+3byx+1$ and then find the quotient.

If $\cos \alpha =\frac{2}{3},$ then the range of values of $\varphi$ on the ellipse

$x^2+4y^2=4$ falls inside the circle $x^2+y^2+4x+3=0$ is

If $lo{g}_4$ 5 = a and $lo{g}_5$ 6 = b, then $lo{g}_3$ 2 is equal to

Consider the statement :

P:if x a real number such that $x^3+4x=0$, then x=0

Prove that p is a true statement , using: (i) direct method (ii) method of contradiction (iii) method of contrapositive

Two lines $L_1:x=5,\frac{y}{3-\alpha }=\frac{z}{-2}$ and $L_2:x=\alpha ,\frac{y}{-1}=\frac{z}{2-\alpha }$ are coplanar. Then, $\alpha$ can take value(s)

Matrices of order $3\times 3$ are formed using the elements of set $A=\{-3,-2,-1,0,1,2,3\}.$ Then the probability that matrices are either symmetric or skew-symmetric, is

The solution of 8x$\equiv$6(mod 14) is

$\text{The function}$ $f:R+\to (1,e)\text{defined by}f\left(x\right)=\frac{X^2+e}{X^2+1}$ is

Find the square root of $\sqrt{2x}+\sqrt{-x^4-1}$

If H is the orthocentre of $\Delta$ ABC, then AH is equal to

Let $A(0,1),B(1,1),C(1,-1)$ and $D(-1,0)$ be four points. If $P$ is any other point, then the minimum value of $PA+PB+PC+PD$ is equal to

If α and β are the roots of the equation $x^2-a(x+1)-b=0$, then $(\alpha +1)(\beta +1)=$

If a letter is chosen at random from the English alphabet, find probability that the letter chosen is

(i) a vowel, and

(ii) a consonant

An enquiry into the budgets of the middle class families in a certain city gave the following information

$\begin{array}{cccccc}\text{Expenses on items}& \text{Food}& \text{Fuel}& \text{Clothing}& \text{Rent}& \text{Miscellaneous}\\ & 35\%& 10\%& 20\%& 15\%& 20\%\\ \text{Price (in Rs ). in 2004}& 1500& 250& 750& 300& 400\\ \text{Price (in Rs ). in 1995}& 1400& 200& 500& 200& 250\end{array}$

What is the cost of living index of 2004 as compared with 1995?

If $x,y,z$ are non zero numbers in A.P. and ${\tan }^{-1}x,{\tan }^{-1}y,{\tan }^{-1}z$ are also in A.P., then

The value of ${\int }_{-1}^1(2\left|x\right|-{\left|x\right|}^3)dx$ is

Number of values of $k$ so that the equations $x^2+kx+(k+2)=0\text{and}{x}^2+(1-k)x+3-k=0$ have exactly one common root, is -

Let $x_1{x}_2{x}_3{x}_4{x}_5{x}_6$ be a six digit number.The number of such numbers if

$x_1<x_2<x_3<x_4<x_5<x_6$ is

The area (in sq. units) of the region $A=\left\{\right(x,y)\in R\times R|0\le x\le 3,0\le y\le 4,y\le x^2+3x\}$

is:

If a function $f:\{1,2,3,4\}\to \{1,2,3,4,5,6,7,8,9\}$ is defined, then the function $f$ can be

If ${\log }_{a}x>y$ and $a>1$. Then

$f\left(x\right)$ is a function defined on entire number line and is even and odd at the same time. Find the value of $f\left(10\right)\times f\left(5\right)$.

Evaluate the following limit:
$\underset{z\to 1}{\text{lim}}\frac{z^{\frac{1}{3}}-1}{z^{\frac{1}{6}}-1}$

The centre of the conic represented by the equation $x^2-6xy+y^2+6x+14y-2=0$ is

For any two independent events $E_1$ and $E_2$ in a space $S$, $P\left[\right(E_1\cup E_2)\cap (E_1\cap E_2\left)\right]$ is equal to

If $x,y,z$ are positive numbers, then the minimum value of $(x+y)(y+z)(z+x)(\frac{1}{x}+\frac{1}{y})(\frac{1}{y}+\frac{1}{z})(\frac{1}{z}+\frac{1}{x})$ is

If $f:R\to R$ is a differentiable function and $f\left(2\right)=6$, then $\underset{x\to 2}{lim}\underset{6}{\overset{f\left(x\right)}{\int }}\frac{2tdt}{(x-2)}$ is :

The value of $x$ satisfying ${\log }_{16}x+{\log }_{x}16={\log }_{512}x+{\log }_{x}512$ is/are

Find the result in the form a + ib.

Let set A = {1, 2, 3}, set B = {2, 3, 4}, set C = {4, 5}. Find (A ∩ B) $\times$ C.

Convert the complex number $\frac{-16}{1+i\sqrt{3}}$ into polar form.

Find tha locus of the mid-point of the chords of the hyperbola $\frac{x^2}{2}-\frac{y^2}{3}=1$ which subtends a right angle at the origin

If $A=\left[\begin{array}{cc}4& 2\\ -1& 1\end{array}\right]$ and I is the identity matrix of order 2, then (A - 2I)(A - 3I) =

Find the ratio in which the line joining A(2,1,5) and B(3,4,3) is divided by the plane 2x+2y-2z=1. Also, find the coordinates of the point of division.

A man throws a die until he gets a number bigger than 3. The probability that he gets 5 in the last throw

If n is positive integer and three consecutive

coefficients in the expansion of $(1+x{)}^n$ are in the

ratio 6 : 33 : 110, then n =

$1+2+3+...............+n$

If sum of $n$ of a series is given by $S_n=3n^2+3n$, then $n^{th}$ term of the series is

Consider $P$ is a point on $y^2=4ax,$ if the normal at $P,$ the axis and the focal radius of $P$ form an equilateral triangle. Then coordinates of $P$ are

Let $S\left(K\right)=1+3+5+.....+(2K-1)=3+K^2$. Then which of the following is true?

If $x^2+x+1=0$ and $x^2+ax+b=0$ have a common root, then the minimum value of $(x-a{)}^2+2b$ is