Explore topic-wise InterviewSolutions in Current Affairs.

Evaluate:
${\{{\left(\frac{1}{3}\right)}^{-1}-{\left(\frac{1}{4}\right)}^{-1}\}}^{-1}$

Let a, b, c be complex such that $ab+bc+ca=\frac{1}{2},(a+b+c)=2,abc=4$ then the value of $\frac{1}{ab+c-1}+\frac{1}{bc+a-1}+\frac{1}{ac+b-1}$ is

How many integral values of $x$ disprove the existence of ${\log }_3(x^2-2x-3)$?

For $n>0,{\int }_0^{2\pi }\frac{xsi{n}^{2n}x}{si{n}^{2n}x+co{s}^{2n}x}dx=$

To $1.0L$ of $0.01M$ $N{H}_3$ solution, the following quantities of $1.0M$ $HCl$ is added. ($p{K}_b\left(N{H}_3\right)=4.74$)
List-I contains questions and List-II contains their answers.
$\begin{array}{cc}\text{List-I}& \text{List-II}\\ \text{Volume of HCl added}& \text{pOH}\\ \text{(I) 2.0 mL}& \text{(P) 11.0}\\ \text{(II) 5.0 mL}& \text{(Q) 4.14}\\ \text{(III) 10.0 mL}& \text{(R) 4.74}\\ \text{(IV) 11.0 mL}& \text{(S) 8.37}\\ & \text{(T) 8.20}\\ & \text{(U) 11.35}\end{array}$

If $f:Z\to Z$ be a linear function such that $f\left(2\right)+f\left(1\right)=4,f\left(2\right)-2f\left(1\right)=-1$, then $f\left(3\right)$ is

What is the inverse of the function { (1,2),(2,3), (3,1) } from the set A ={1,2,3} to itself?

If $2x=y^{1/5}+y^{-1/5}$ then $(x^2-1)\frac{d^{2}y}{d{x}^2}+x\frac{dy}{dx}=$

If a plane cuts off intercepts -6, 3, 4 from the co-ordinate axes, then the length of the perpendicular from the origin to the plane is

If two different tangents of $y^2=4ax$ are normals to $x^2=4y$, then

The chord of contact of the tangents drawn from a point on the circle, $x^2+y^2=a^2$ to the circle $x^2+y^2=b^2$ touches the circle $x^2+y^2=c^2$ then a, b, c are in:

${lim}_{x\to 1}(1-x)tan\left(\frac{\pi x}{2}\right)$

In a single throw of a die describe the following events :

(i) A = Getting a number less than 7

(ii) B = Getting a number greater than 7

(iii) C = Getting a multiple of 3

(iv) D = Getting a number less than 4

(v) E = Getting an even number greater 4

(vi) F = Getting a number not less than 3.

Which of the following is / are true

The shortest distance between the point $(\frac{3}{2},0)$ and the curve $y=\sqrt{x},(x>0),$ is :

${lim}_{x\to \frac{\pi }{4}}\frac{\sqrt{2}-cosx-sinx}{(4x-\pi {)}^2}$

Three sides AB, BC and CA of a triangle ABC are $5x-3y+2=0,x-3y-2=0$ and $x+y-6=0$ respectively. Find the equation of the altitude through the vertex A.

The sum of digits of every possible 8 digit number is noted. Which sum occurs most often?

If the line 5x + 12y - 9 = 0 is a tangent to the hyperbola $x^2-9y^2=9$ , then its point of contact is

For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate solve any problem is $\frac{4}{5}$, then the probability that he is unable to solve less than two problems is :

If $p\left(x\right)$ is a cubic polynomial with $p\left(1\right)=3,p\left(0\right)=2,p(-1)=4,$ then $\underset{-1}{\overset{1}{\int }}p\left(x\right)dx$ is

If sin 2x = 4 cos x, then x =

sin A + sin 3A/ cos A + cos 3A = tan 2A

Prove

cotAcosA/cotA+cosA = cot A-cosA/cotAcosA

An ellipse has OB as a semi-minor axis. F and F' are its foci and the angle FBF' is a right angle. Then, the eccentricity of the ellipse is ___

Find the equation for the ellpse that satisfies the given conditions
Vertices $(0,\pm 13),Foci(0,\pm 5)$

Insert 7 A.M.s between 2 and 17.

Three events A, B and C have probabilities $\frac{2}{5},\frac{1}{3}$ and $\frac{1}{2}$, respectively. If,

$P(A\cap C)=\frac{1}{5}andP(B\cap C)=\frac{1}{4}$, then find the values of $P\left(\frac{C}{B}\right)andP(A^{\prime }\cap C^{\prime }).$

The integral of the function $e^x$ is

Let $A=\left[\begin{array}{cc}0& 1\\ 0& 0\end{array}\right]$, show that (aI+bA)^n=a^nI+$n{a}^{n-1}$ bA, where, I is the identity matrix of order 2 and $n\in N.$

If $a_1,a_2,a_3,...,a_n$ is an arithmetic progression with common difference d, then evaluate the following expression.

$tan[ta{n}^{-1}\left(\frac{d}{1+a_1{a}_2}\right)+ta{n}^{-1}\left(\frac{d}{1+a_2{a}_3}\right)+ta{n}^{-1}\left(\frac{d}{1+a_3{a}_4}\right)+\cdots +ta{n}^{-1}\left(\frac{d}{1+a_{n-1}{a}_n}\right)]$

Prove that :
(i) $sin{38}^{\circ }+sin{22}^{\circ }=sin{82}^{\circ }$
(ii) $cos{100}^{\circ }+cos{20}^{\circ }=cos{40}^{\circ }$
(iii) $sin{50}^{\circ }+sin{10}^{\circ }=cos{20}^{\circ }$
(iv) $sin{23}^{\circ }+sin{37}^{\circ }=cos{7}^{\circ }$
(v) $sin{105}^{\circ }+cos{105}^{\circ }=cos{45}^{\circ }$
(vi) $sin{40}^{\circ }+sin{20}^{\circ }=cos{10}^{\circ }$

Write the number of all possible words that cna be formed using the letters of the word 'MATHEMATICS'.

In what ratio is the line joining the points (2, 3) and (4, -5) divided by the line passing through the points (6, 8) and (-3, -2).

Find the length of latusrectum of the ellipse $4x^2+9y^2=144$

Find the equation of the normal lines to the curve $3x^2-y^2=8$ which are parallel to the line $x+3y=4.$

A die is thrown twice, then the probability that 2 comes in first throw and 6 or 1 comes in second throw is,

Match the following.

$$\begin{array}{cc}ColumnA& ColumnB\\ 1.A=\{x:xisanoddnaturalnumber\}& a.\{\frac{1}{2},\frac{1}{3},\frac{2}{3},\frac{3}{4},\frac{3}{5},\frac{5}{7}\}\\ 2.B=\{x:x=(n^2)\},n\in Nandx<100& b.\{1,4,9,16,25,........10000\}\\ 3.C=\{x:x=\frac{n}{n+2},wherenisanaturalnumberand1\le n\le 6\}& c.\{1,4,9,16,25,36,49,64,81\}\\ 4.D=\{x:xisaletterofthewordTRIGONOMETRY\}& d.\{G,E,I,M,N,O,R,T,Y\}\\ & e.\{1,3,5,7,9,...............\}\\ & \end{array}$$

Let $x^3+ax+1=0and$ $x^4+a{x}^2+1=0$ have a common root. Then a =

The solution to the system of linear inequalities. That is, the set of all points that satisfy all the constraints is called

What is mean by closed bracket and open bracket in inverse trigonometric functions and function please elaborate deeply with examples

The perpendicular distance from the point $(2,-3)$ to a line which makes equal intercepts on the co-ordinate axis is $4$ units. Then the value of the intercept is

The shortest distance between the line $y-x=1$ and the curve $x=y^2$ is :