Explore topic-wise InterviewSolutions in Current Affairs.

Area of the quadrilateral with its vertices at foci of the conics $9x^2-16y^2-18x+32y-23=0$ and $25x^2+9y^2-50x-18y+33=0$ is

Find the minors and cofactors of elements$a_{23},a_{32}\mathrm{and}{a}_{13}$of matrix $A=\left(a_{\mathrm{ij}}\right]=\left(\begin{array}{ccc}5& 6& 7\\ 5& 2& 3\\ 4& 8& 9\end{array}\right].$

In triangle ABC, right angled at B, if one angle is ${45}^{\circ }$, find the value of sin A, cosC, cot A and tan C respectively.

Which of the following function is a Periodic function -

The value of $\left(\frac{50}{6}\right)-\left(\frac{5}{1}\right)\left(\frac{40}{6}\right)+\left(\frac{5}{2}\right)\left(\frac{30}{6}\right)-\left(\frac{5}{3}\right)\left(\frac{20}{6}\right)+\left(\frac{5}{4}\right)\left(\frac{10}{6}\right)where\left(\frac{n}{r}\right)denotes{}^n{C}_r$ is

FInd the $n^{th}$ term of the series $(1{)}^3$ + ($1^3$ + $2^3$) + ($1^3$ + $2^3$ + $3^3$) + ------------------- n terms

For what value of $\lambda$, the vectors $\overrightarrow{a}=2\hat{i}+\lambda \hat{j}+\hat{k}\text{and}\overrightarrow{b}=\hat{i}+2\hat{j}+3\hat{k}\text{are orthogonal.}$

A point is moves on xy plane.If the sum of the distance from two mutual perpendicular lines is 5 then area under it is

The ratio in which $y-$ axis divides the line segment joining $(-3,5)$ and $(7,2)$ is

If $f\left(x\right)=si{n}^{2}x,g\left(x\right)=\sqrt{x}$ and $h\left(x\right)=co{s}^{-1}x,0\le x\le 1,$ then

4x^2+1>4x.find range of x

Which of the following are true:
(i) (2+3)!= 2!+3! (ii) (2 $\times$ 3)! = $2!\times 3!$

If the tangents on the ellipse $4x^2+y^2=8$ at the point $(1,2)$ and $(a,b)$ are perpendicular to each other, then $a^2$ is equal to:

$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+.....+\frac{1}{2^n}=1-\frac{1}{2^n}$

Foot of perpendicular drawn from the origin to the plane $2x–3y+4z=29$ is ____

If two circles with centres at $(a,0)$ and $(-a,0)$ having radii $b$ and $c$ units respectively such that $a>b>c$. Then the point of contacts of common tangents to these two circles will always lie on

For any positive integers $a,b,c\in \{1,2,3,\cdots ,9\}$, the minimum number of positive factors of the number $abcabc$ is

Find the equations of the medians of a triangle, the equations of whose sides are:

$3x+2y+6=0,2x-5y+4=0andx-3y-6=0$

Equation of the circle having centre at $(3,-1)$ and making an intercept of length $6$ units on the line $2x-5y+18=0$, is

If the maximum value of $(x+y{)}^2\text{is}\lambda$ and $P(x,y)$ satisfies $x^2+y^2=1$, then the number of tangents that can drawn from $(\lambda ,0)$ to the hyperbola $(x-2{)}^2-y^2=1$ is

Find the equations of the straight lines which cut off an intercept 5 from the y-axis and are equally inclined to the axes.

If $\text{cosec}\theta -\cot \theta =\frac{1}{2},$ then the value of ${\sec }^2\theta -{\cos }^2\theta$ is equal to

Find the value of $\frac{dy}{dx}$ at $\theta =\frac{\pi }{4},ifx=a{e}^{\theta }(sin\theta -cos\theta )$ and $y=ae\theta (sin\theta +cos\theta )$.

Find the principal values of the following questions:

$si{n}^{-1}(-\frac{1}{2})$

Given A = $\left[\begin{array}{cc}2& -3\\ -4& 7\end{array}\right]$, compute $A^{-1}$ and show that $2A^{-1}=9I-A$.

Solve

$x^2-x+2=0$

How to calculate angle theta when it is given like this

theta = sin^{​​​​-1}(1/3)

If the sum of twin primes is $84,$ then the smallest prime number among them is

If two circles of radii $5$ units touches each other at $(1,2)$ and the equation of the common tangent is $4x+3y=10$, then the equation of the circle is/are

If $g\left(x\right)=(x^2+2x+3)f\left(x\right),f\left(0\right)=5$ and $\underset{x\to 0}{lim}\frac{f\left(x\right)-f\left(0\right)}{x-0}=4,$ then $g^{\prime }\left(0\right)$ is equal to

A number is chosen at random from the numbers $10$ to $99$. By seeing the number a man will laugh if the product of the digits is $12$. If he chooses three numbers with replacement, then the probability that he will laugh at least once is

${lim}_{x\to 1}\frac{\sqrt{5x-4}--\sqrt{x}}{x^3-1}$

There are four boxes $A_1,A_2,A_3$ and $A_4$. Box $A_i$ has i cards and on each card a number is printed, the numbers are from 1 to i. A box is selected randomly, the probability of selection of box $A_i$ is $\frac{i}{\sum i}$ and then a card is drawn. Let $E_i$ represents the event that a card with number 'i' is drawn.

$P\left(\frac{A_3}{E_2}\right)$ is equal to

The value of $tan\theta +tan({60}^{\circ }+\theta )+tan({120}^{\circ }+\theta )$ is

Sum of all the values of x satisfying the equation $lo{g}_{17}lo{g}_{11}(\sqrt{x+11}+\sqrt{x})=0$ is

If $\overrightarrow{a}=\hat{i}+\hat{j}-\hat{k},\overrightarrow{b}=\hat{i}-\hat{j}+\hat{k}$, and $\overrightarrow{c}$ is unit vector perpendicular to the vector $\overrightarrow{a}$ and coplanar with $\overrightarrow{a}$ and $\overrightarrow{b}$then a unit vector $\overrightarrow{d}$ perpendicular to both $\overrightarrow{a}$ and $\overrightarrow{c}$, is

A line passing through the point A with position vector a= 4i+ 2j+2k is parallel to the vector b = 2i+3j+6k . Find the length of the perpendicular drawn on this line from a point P with position vector r= i + 2 j+ 3k

The vertices of a quadrilateral are A (-2, 6), B (1, 2), C (10, 4) and D (7, 8). Find the equations of its diagonals.

A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability that one is red, one is white and one is blue.

A point moves in such a way that the sum of its distance from $xy$-plane and $yz$-plane remains equal to its distance from $zx$-plane. The locus of the point is

There is a certain sequence of positive real numbers. Beginning from the third term, each term of the sequence is the sum of all the previous terms. The seventh term is equal to 1000 and the first term is equal to 1. The second term of this sequence is equal to

If $5x+9=0$ is the directrix of the hyperbola $16x^2-9y^2=144,$ then its corresponding focus is :

$Thelengthofthestraightlinex-3y=1interceptedbythehyperbola{x}^2-4y^2=1is$

The orthocenter of the triangle formed by the lines $xy=0$ and $x+y=1$ is

If $A(-4,3)$, $B(5,7)$, then the point on the line segment $AB$ which is two thirds away from $A$ to $B$ is