Explore topic-wise InterviewSolutions in .

The length of normal chord of parabola $y^2=4x$, which subtends an angle of ${90}^{\circ }$ at the vertex is

If $b+ic=(1+a)z$ and $a^2+b^2+c^2=1,$ where $a,b,c\in R,$ then $\frac{1+iz}{1-iz}=\frac{a+ib}{k}$ where $k$ is equal to

The range of the function y=cotx is

$\underset{n\to 0}{lim}\frac{n!}{(n+1)!-n!}\text{is equal to:}$

In a group of tourists, $40\%$ liked Goa, $30\%$ liked Kerala and $30\%$ liked Bangalore. $7\%$ liked both Goa and Kerala, $5\%$ liked both Kerala and Bangalore, $10\%$ liked both Bangalore and Goa. If $86\%$ of these liked at least one of the places, then what percentage of people liked all three?

The Derivative of $e^x$

Which of the following is an empty set

The value of $cot(\frac{\pi }{4}-2co{t}^{-1}3)$ is equal to

An A.P., a G.P., and a H.P. have a and b for their first two terms their $(n+2{)}^{th}$ terms will be in G.P. if $\frac{b^{2n+2}-a^{2n+2}}{ab(b^{2n}-a^{2n})}$

If the coordinates of the points A, B, C, be (4,4), (3,-2) and (3,-16) respectively, then the area of the triangle ABC is [MP PET 1982]

Find the number of selections taking at least one out of 5 similar white balls, 6 similar green balls, 7 similar red balls and 8 distinct blue balls.

The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Then the sides of the triangle are

Let $E=\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+....$ then,

The lines represented by the equation $x^2+2\sqrt{3}xy+3y^2-3x-3\sqrt{3}y-4=0$, are

If $y=x^{(\log x{)}^{\log \left(\log x\right)}}$, then $\frac{dy}{dx}$ is

If the line x=a+m, y=-2 and y=mx are concurrent , then least value of |a| is

What is the range for 10, 25, -8, 43 and 27?

Match the following: $$\begin{array}{cc}\text{Column A}& \text{Column B}\\ 1.\{1,2,4,8\}& A.\{x:x\text{is a natural even number less than 10}}\\ 2.\left\{2\right\}& B.\{x:x\text{is a prime number and a divisor of 8}}\\ 3.\{2,4,6,8\}& C.\{x:x\text{is a divisor of 8}}\\ 4.\{4,6,8,9\}& D.\{x:x\text{is a composite number less than 10}\}\end{array}$$

If $p:x$ is odd ; $q:x^2$ is odd, then "$x$ is odd and $x^2$ is not odd" is represented as

A second order determinant is written down at random using the numbers 1, - 1 as elements. The probability that the value of the determinant is non zero is

The mean and S.D. of $1,2,3,4,5,6$is

The ratio of the A.M and G.M of two positive numbers a and b, is m : n. Show that $a:b=(m+\sqrt{m^2-n^2}):(m-\sqrt{m^2-n^2})$.

The digit at unit's place in the number $(13{)}^{1225}+(11{)}^{1915}-(23{)}^{1225}$ is equal to

Let $f\left(x\right)=\frac{x}{(1+x^7{)}^{\frac{1}{7}}}$ and $g\left(x\right)=\left(fofofofofofof\right)\left(x\right),\text{then}\int x^{5}g\left(x\right)dx$ is

Let C be the circle with centre at (1, 1) and radius 1. If T is the circle centred at (0, y) passing through origin and touching the circle C externally, then the radius of T is equal to

If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are $A\pm \sqrt{(A+G)(A-G)}.$

If $R=(6\sqrt{6}+14{)}^{2n+1}$ and f=R-[R], where [.] denotes the greatest integer function, then Rf equals:

Let A = {1, 2, 3, 4} and R be a relation in A given by R = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1), (3, 1), (1, 3)}. Then R is

If $0<\theta <2\pi$ and $2\cos \theta =\sqrt{3}\cos {10}^{\circ }-\sin {10}^{\circ }$, then the value of $\theta$ is

Which of the following functions are differentiable throughout $(-\pi ,\pi )$

Find the integral of the given function w.r.t - x

$y=x-\frac{1}{x}+\frac{1}{x^2}$

If the line $y=mx+c$ touches $x^2-y^2=1$ and $y^2=4x,$ then $m^2$ is equal to

If x is real, find the range of y from the equation $x^2(y-1)-2x+(2y-1)$ = 0

If the function $f\left(x\right)=\lambda |\sin x|+{\lambda }^2|\cos x|+g\left(\lambda \right),\lambda \in R,$ where $g$ is a function of $\lambda ,$ is periodic with fundamental period $\frac{\pi }{2},$ then

The value of $(\cos {75}^{\circ }-\cos {15}^{\circ }{)}^2+(\sin {75}^{\circ }-\sin {15}^{\circ }{)}^2$ is

Find the value of $\underset{x\to 0}{lim}\frac{\sqrt{a+x}-\sqrt{a}}{x}$

The coefficient of $x^m$ in $(1+x{)}^m+(1+x{)}^{m+1}+\cdots +(1+x{)}^n,$ where $m,n\in N$ and $m<n$, is

The minimum and maximum value of $y=\frac{x^2-x+4}{x^2+x+4}$ will be and respectively.

A player tosses a coin and scores one point for every head and two point for every tail that truns up. He plays on until his scores reaches or psses $n$. $P_n$ denotes the probability of getting a scores of exactly $n$

$$\begin{array}{cc}\text{List I}& \text{List II}\\ \begin{array}{cc}\text{(a)}& \text{the value of}{P}_n\text{is}\end{array}& \text{(p)}1\\ \begin{array}{c}\text{(b) the value of}{P}_n+\frac{1}{2}{P}_{n-1}\end{array}& \text{(q)}\frac{5}{4}\\ \begin{array}{c}\text{(c)}2P_{101}+P_{100}\end{array}& \text{(r)}2\\ \begin{array}{c}\text{(d)}{P}_1+P_2\end{array}& \text{(s)}\frac{1}{2}[P_{n-1}+P_{n-2}]\end{array}$$

$\text{Which of the following is the only}\text{correct option?}$

The equation $a{x}^2+bx+c=0$, where a,b,c are the sides of a $△ABC$, and the equation $x^2+\sqrt{2}x+1=0$ have a common root, the measure of $\angle C$ is

If ∝ and β are roots of $x^2$ + ax - b = 0 and γ, δ​ arethe roots of $x^2$ + ax + b = 0, then (α-γ) (β-δ) (α-δ) (β-γ)