Explore topic-wise InterviewSolutions in Current Affairs.

Find the equation of the right bisector of the line segment joining the points $(a,b)$ and $(a_1,b_1)$.

Lines are drawn parallel to the line $4x-3y+2=0,$ at a distance $\frac{3}{5}$ units from the origin. Then which of the following points lies on any of these lines ?

For each of the following statements, determine whether an inclusive "OR" or exclusive "OR" is used. Give reasons for your answer.

(i) Students can take Hindi or sanskrit as their third language.

(ii) To entry a country, you need a passport or a voter registration card.

(iii) A lady gives birth to a baby boy or a baby girl.

(iv) To apply for a driving licence, you should have a ration card or a passport.

If f is a real valued function given by $f\left(x\right)=27x^3+\frac{1}{x^3}$ and $\alpha ,\beta$ are roots of $3x+\frac{1}{x}=2$. Then,

$\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+.....+\frac{1}{(3n-2)(3n+1)}=\frac{n}{3n+1}$

Solve the following system of equations in R.
|4-x|+1<3

For $x\in R,x\ne 0$ if $y\left(x\right)$ is a differentiable function such that $x\underset{1}{\overset{x}{\int }}y\left(t\right)dt=(x+1)\underset{1}{\overset{x}{\int }}ty\left(t\right)dt,$ then $y\left(x\right)$ equals:

Let $a,b\in N$ with $2\le a\le 2020$ and $2\le b\le 2020$.
$P,Q,R$ are three sets defined as
$P=\left\{\right(a,b):{\log }_{a}b+6{\log }_{b}a=5\}$
$Q=\left\{\right(a,b):b=a^2\}$
$R=\left\{\right(a,b):b=a^3\}.$
Then which of the following is (are) correct?

The number of ordered triplets$(x,y,z)$ where $x,y$ and $z$ are positive integers which satisfy the equation $xyz=24$ is

Question 1 (i)
For which value (s) $\lambda$, do the pair of linear equations $\lambda x+y={\lambda }^{2}andx+\lambda y=1$ have no solution.

Match the following
$\begin{array}{cc}Functions& Derivatives\\ \left(a\right)x^n& 1\left)\frac{1}{x}\right(lo{g}_{a}e)\\ \left(b\right)e^x& 2)\frac{1}{x},x>0\\ \left(c\right)a^x& 3)n{x}^{n-1},nisaconstant\\ \left(d\right)lo{g}_{e}x& 4)a^{x}lo{g}_{e}a,a>0\\ \left(e\right)lo{g}_{a}x& 5)e^x\end{array}$

If $f\left(x\right)=max\{1+\sin x,1,1-\cos x\},\forall x\in [0,2\pi ]$ and $g\left(x\right)=max\{1,x-1\}\forall x\in R$, then

If $\sin x=\frac{1}{3}$ and $\cos x<0$, then the value of $\tan 3x$ is

If the normal of the plane makes angles of $\frac{\pi }{4},\frac{\pi }{4}$ and $\frac{\pi }{2}$ with positive x-axis, y-axis and z-axis respectively and the length of the perpendicular line segment from origin to the plane is $\sqrt{2}$, then the equation of the plane is

The half-life of radon is 4 days. 10 gram of radon after 16 days will reduce to

Let $3600=x\cdot y$, where $x$ and $y$ are natural numbers, then the possible pairs $(x,y)$ is

A closed cylindrical tank of radius 7 m and a height 4 m is made from a sheet of metal. How much sheet of metal is required?

The value of the expression ${\cos }^4\frac{\pi }{8}+{\cos }^4\frac{3\pi }{8}+{\cos }^4\frac{5\pi }{8}+{\cos }^4\frac{7\pi }{8}$ is

If $A$ and $B$ are mutually exclusive events, given that $P\left(A\right)=\frac{3}{5},P\left(B\right)=\frac{1}{5}$, then $P\left(A\text{or}B\right)$ is

The tangents to the curve $y=x^3-6x^2+9x+4,0\le x\le 5$ has maximum slope at $x$ which is equal to

The number of solution(s) of $y=x^2+10x+22$ and $y=\log x,$ is

Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two non-collinear unit vectors. If $\overrightarrow{u}=\overrightarrow{a}-(\overrightarrow{a}.\overrightarrow{b})\overrightarrow{b}$ and $\overrightarrow{v}=\overrightarrow{a}\times \overrightarrow{b},$ then $|\overrightarrow{v}|$ is

Find the sum of ${}^n{C}_0$ - $\frac{{}^n{C}_1}{2}$ + $\frac{{}^n{C}_2}{3}$ ...............

How many integers satisfy the relation |x - 1|$\le$ 2

Integrate the following functions.
$\int \frac{1}{x-\sqrt{x}}dx.$

A trust fund has Rs 30000 that must be invested in two different types of bonds. The first bond pays 5% interest per year and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide R 30000 amoung the two types of bonds, if the trust fund must obtain an annual total interest of
(a) Rs 1800

(b) Rs 2000

Find the equation of normal to the parabola $y^2=4ax$ at point (h,k) on the parabola

If three complex numbers are in AP then they lie on

Please provide the answer with explanation for how the concept of AP is used here.

If one end point of the focal chord of the parabola $y^2=4ax$ is $(1,2)$, then the other end point lies on

if a,b,c $ϵ$ R,a,b,c $\ne$ 0, $\sum$ $a^2$ = $\sum$ab, then a,b,c are in

On Sunday, 845 people went to a Zoo. On Monday, only 169 people went. What is the percent decrease in the people visiting the Zoo on Monday?

If ∝,β are the roots of the equation 2$x^2$ - 3x - 5 = 0, then the equation whose roots are $\frac{5}{\propto }$ , $\frac{5}{\beta }$ is :

In an increasing geometric series, the sum of the second and the sixth term is $\frac{25}{2}$ and the product of the third and fifth term is $25.$ Then, the sum of $4^{\text{th}},6^{\text{th}}$ and $8^{\text{th}}$ terms is equal to :

If $x_n$ = cos( $\frac{\pi }{4^n}$) + i sin( $\frac{\pi }{4^n}$) then $x_1{x}_2{x}_3.........\infty =$

The number of non-negative integral solutions of the equation $x+y+z+5t=15$ is

Find the length of subtangent on the curve $y=\frac{x}{1+x}$, where the slope of the tangent is $\frac{1}{9}$

[ The point where the tangent is drawn is in first quadrant ]

Find the equation to the circle which passes through the origin and has its center on the line $x+y+4=0$ and cuts the circle $x^2+y^2-4x+2y+4=0$ orthogonally.

At what point in the interval $[0,2\pi ]$, does the function sin 2x attain its maximum value?

Find the maximum and minimum values, if any, of the following function given by,

$f\left(x\right)=|sin4x+3|$

Find the value of $\underset{x\to 5}{lim}(x^2-5x+10)$