Explore topic-wise InterviewSolutions in .

The lines $(lx+my{)}^2-3(mx-ly{)}^2=0$ and lx + my + n = 0 form

The (m + n)th and the (m - n)th terms of a GP are p and q respectively. Show that the mth and the nth terms of the GP are $\sqrt{pq}$ and ${\left(\frac{q}{p}\right)}^{\left(\frac{m}{2n}\right)}$

Find the sign of the quadratic polynomial.

$f\left(x\right)=x^2+5|x|+6$

The domain of the function $f\left(x\right)=\sqrt{\frac{2^x+3^x}{2^x-3^x}}$ is

The solution set of $3^{x^2-4}\ge 243$ is

${\left[\frac{-1+\sqrt{(-3)}}{2}\right]}^{3n}$ + ${\left[\frac{-1-\sqrt{(-3)}}{2}\right]}^{3n}$

If both the roots of $x^2+2ax+a=0$ are less than $2$, then the set values of ${}^{\prime }{a}^{\prime }$ is

Find the perpendicular distance from the origin of the line joining the points $(cos\theta ,sin\theta )$ and $(cos\varphi ,sin\varphi )$.

If sin $\theta$ = $-\frac{1}{\sqrt{2}}$ and tan $\theta$ = 1, then $\theta$ lies in which quadrant.

The number of distinct real values of $\lambda$ for which the lines $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z+3}{{\lambda }^2}$ and $\frac{x-3}{1}=\frac{y-2}{{\lambda }^2}=\frac{z-1}{2}$ are coplanar is:

$\underset{x\to -1}{lim}\frac{(1+x)(1-x^2)(1+x^3)(1-x^4)....(1-x^{4n})}{{\left[\right(1+x\left)\right(1-x^2\left)\right(1+x^3\left)\right(1+x^4).......(1-x^{2n}\left)\right]}^2}\text{is equal to:}$

Consider any set of 201 observations $x_1,x_2,\cdots ,x_{200},x_{201}$. It is given that $x_1<x_2<\cdots <x_{200}<x_{201}$. Then, the mean deviation of this set of observations about a point k is minimum, when k equals

If $lo{g}_2(5\times 2^x+1)$$,lo{g}_4(2^{1-x}+1)$ and 1 are in A.P., then x equals

If the quadratic expression $a{x}^2+(a-2+3^{\sqrt{{\log }_{3}5}}-5^{\sqrt{{\log }_{5}3}})x+(5^{{\log }_{5}3}-3^{{\log }_{3}5})$ is negative for exactly two integral values of $x$, then the possible value(s) of $a$ is/are

If $\left|\frac{x+1}{x}\right|+|x+1|=\frac{(x+1{)}^2}{|x|},$ then $x\in$

If $f\left(x\right)=\left|\begin{array}{ccc}sinx& sina& sinb\\ cosx& cosa& cosb\\ tanx& tana& tanb\end{array}\right|,$

where $0<a<b<\frac{\pi }{2}$

then the equation

$f^{\prime }\left(x\right)=0$ has in the interval $(a,b)$

Evaluate ${\int }_0^{\pi /2}si{n}^{-1}\left(cosx\right)dx$

If $X=\{8^n-7n-1|nϵN\}$ and $Y=\{49n-49|nϵN\}$, then

If $\sin x\cos y=\frac{1}{2}$, then $\frac{d^{2}y}{d{x}^2}$ at $x=\frac{\pi }{4}$ is

The domain of the function $f\left(x\right)={\log }_e(x-[x\left]\right)$ is (where $[.]$ represents the greatest integer function)

Let $\omega$ be a complex cube root of unity with $\omega \ne 1$. A fair die is thrown three times. If $r_1,r_{2}and{r}_3$ are the numbers obtained on the die, then the probability that ${\omega }^{r_1}+{\omega }^{r_2}+{\omega }^{r_3}=0,$ is ?

Let $\tan A=\frac{p}{(p–1)}$ and $\tan B=\frac{1}{(2p–1)},$ if $A,B\in (0,\pi /2)$ then $A–B$ can be

The set of values of $x$ satisfying $1\le |x-1|\le 3$ is

Assume that $P\left(A\right)=P\left(B\right).$ Show that $A=B.$

The solution set of the equation, x $ϵ$ R, ${\left(\frac{4}{5}\right)}^x=2x-x^2$ - 10 is :

If the coefficient of the middle term in the

expansion of $(1+x{)}^{2n+2}$ is p and the coefficients of

middle terms in the expansion of $(1+x{)}^{2n+1}$ are q and r, then

If $x_1,x_2,\cdots ,x_n$ and $\frac{1}{h_1},\frac{1}{h_2},\cdots ,\frac{1}{h_n}$ are two $A.P.$s such that $x_3=h_2=8$ and $x_8=h_7=20,$ then $x_5\cdot h_{10}$ equals

Two dices are rolled one after the other. The probability that the number on the first is smaller than the number on the second is

Solution set of the inequality ${\log }_3(x+2)(x+4)+{\log }_{\frac{1}{3}}(x+2)<\frac{1}{2}{\log }_{\sqrt{3}}7$ is -

Which one of the following is NOT logically equivalent to$\neg \exists x\left(\forall y\right(\alpha )\wedge \forall z(\beta \left)\right)$

The eccentricity of the hyperbola $4x^2-y^2-8x-8y-28$ is equal to ___ .

Find the coordinates the foci, the vertices, the eccentricity and the length of the latus rectum of the hyperbola,

$16x^2-9y^2=576$

What is the condition for a line $y=mx+c$ to be tangent to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1.$

The term independent of x in the expansion of $\frac{(x+1{)}^{2m}}{x^m}$:

The sum of three numbers in G.P is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an arithmetic progression. Find the numbers.

If $(10{)}^9+2(11{)}^1(10{)}^8+3(11{)}^2(10{)}^7+\dots \dots +10(11{)}^9=k(10{)}^9$, then k is equal to

The conjugate of complex number $\frac{2-3i}{4-i}$ is .

Negation of the statement 'if it rains, I shall go to school' is

( z + a ) ( $\overline{z}+a)$ , where a is real , is equivalent to :

If ${\log }_{12}27=a$, then $\frac{3-a}{3+a}=$

Pick the correct plot for the function $y=x^2-2x+6$

A committee of 5 students is selected at random from a group consisting 10 boys and 5 girls. Given that there is at least one girl in the committee, calculate the probability that there are exactly 2 girls in the committee.

$\frac{1+ta{n}^{2}A}{1+co{t}^{2}A}$ =

Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is :

The coefficient of x in the equation $x^2$ + p$x$ + q = 0 was taken as 17 in place of 13, its roots were found to be -2 and -15, the roots of the original equation are

Two equal sides of an isosceles triangle are given by the equations $7x-y+3=0$ and $x+y-3=0$ and its third side passes through the point (1,10), Determine the equation of the third side.