Explore topic-wise InterviewSolutions in .

If $A=\left[\begin{array}{ccc}0& \alpha & \alpha \\ 2\beta & \beta & -\beta \\ \gamma & -\gamma & \gamma \end{array}\right]$ is an orthogonal matrix, then the number of possible triplets $\alpha ,\beta ,\gamma$

Find $\frac{dy}{dx}$in the following questions:

2x+3y=sin y.

The value of $\int ({\sin }^{3}x+{\cos }^{3}x)dx$ is

(where $C$ is constant of integration)

The general solution of the differential equation, $x\left(\frac{dy}{dx}\right)=y\ln \left(\frac{y}{x}\right),$ where $c$ is an arbitrary constant, is :

What will be the next number in the given sequence?

1000, 900, 800, 700, 600, ____

Write the first five
terms of the sequences whose n^th term is

Show that $\varphi ,\left\{0\right\}$ and 0 are all different.

Let $A$ denote the event that a $6$-digit integer formed by $0,1,2,3,4,5,6$ without repetitions, be divisible by $3.$ Then probability of event $A$ is equal to :

Let $z_1$ and $z_2$ be roots of the equation $z^2+pz+q$ = 0,p,q$\in$c,Let A and B represents $z_1$ and $z_2$ in the complex plane. If $\angle AoB$ = $\alpha$ $\ne$ 0, AND OA = OB;O is the origin, then $\frac{p^2}{4q}$ =

Describe the following sets in Roster form :

(i) {x : x is a letter before e in the English alphabet}.

(ii) {$xϵN:x^2<25$}

(iii) {$xϵN$: x is a prime number, 10 < x < 20}.

The value of ${\int }_0^a\frac{1}{\sqrt{\mathrm{ax}-x^2}}\mathrm{dx}$ is

If p and q are order and degree of differential equation $y^2(\frac{d^{2}y}{d{x}^2}{)}^2+3x(\frac{dy}{dx}{)}^{\frac{1}{3}}+x^2{y}^2=sinx$, then

Find the equation for the ellipse that satisfies the given conditions: Ends of major axis, ends of minor axis (±1, 0)

Let $H:\frac{x^2}{a^2}-\frac{y^2}{b^2}=1,\text{where}a>b>0,$be a hyperbola in the $xy-$plane whose conjugate axis $LM$ subtends an angle of ${60}^{\circ }$ at one of its vertices $N.$ Let the area of the triangle $LMN$ be $4\sqrt{3}.$



$\begin{array}{cccc}& LIST-I& & LIST-II\\ P.& \text{The length of the conjugate axis of}H\text{is}& 1.& 8\\ Q.& \text{The eccentricity of}H\text{is}& 2.& \frac{4}{\sqrt{3}}\\ R.& \text{The distance between the foci of}H\text{is}& 3.& \frac{2}{\sqrt{3}}\\ S.& \text{The length of the latus rectum of}H\text{is}& 4.& 4\end{array}$



The correct option is:

If the roots of the equation $x^2-4x+4-a^2=0$ lie between the roots of the equation $x^2-2(a+2)x+a(a-2)=0$ such that $a$ is real then ${}^{\prime }{a}^{\prime }$ belongs to the interval

Let $X=1,2,3$ and $Y=4,5$. Find whether the following subsets of $X\times Y$ are functions from X to Y or not.

(i) $f=\left\{\right(1,4),(1,5),(2,4),(3,5\left)\right\}$

(ii)$g=\left\{\right(1,4),(2,4),(3,4\left)\right\}$

(iii) $h=\left\{\right(1,4),(2,5),(3,5\left)\right\}$

(iv) $k=\left\{\right(1,4),(2,5\left)\right\}$

1. 864

The equation ${\sin }^{-1}x=|x-a|$ will have atleast one solution if

${lim}_{x\to \infty }\frac{3x^3-4x^2+6x-1}{2x^3+x^2-5x+7}$

Two coins are tossed simultaneously 360 times. The number of times ‘2 Tails’ appeared was three times ‘No Tail’ appeared and the number of times ‘1 tail’ appeared is double the number of times ‘No Tail’ appeared. What is the probability of getting ‘Two tails’?

Common tangent equations to $9x^2-16y^2=144$ and $x^2+y^2=9$ are

The value of $\underset{0}{\overset{2000\pi }{\int }}\frac{dx}{1+e^{\sin x}}$ is equal to

If (2 + √5) ÷ (2 - √5) = x and (2 - √5) ÷ (2 + √5) = y; find the value of x^{​​​​​​2} - y^{​​​​​​2}

The value of the integral $I=\underset{1/2014}{\overset{2014}{\int }}\frac{{\tan }^{-1}x}{x}dx$ is

Differentiate
in
three ways mentioned below

(i) By using product
rule.

(ii) By expanding the
product to obtain a single polynomial.

(iii By logarithmic
differentiation.

Do they all give the
same answer?

A bag contains 6 white, 7 red and 5 blue balls. Three balls are drawn at random. Find the probability of the event 'balls drawn are one of each color'.

Which of the following definite integral(s) vanishes?

If $I=\int ({\sin }^{3}x+{\cos }^{2}x\cdot \sin x)dx,$ then the value of $I$ is

(where $C$ is constant of integration)