Explore topic-wise InterviewSolutions in Current Affairs.

The maximum value of the function $f\left(x\right)=3x^3-18x^2+27x-40$ on the set $S=\{x\in R:x^2+30\le 11x\}$ is :

Find the value of

Tangents are drawn from (4, 4) to the circle $x^2+y^2-2x-2y-7=0$ to meet the circle at A and B. The length of the chord AB is

The Z-parameter matrix for the two-port network shown is



$\left[\begin{array}{cc}2j\omega & j\omega \\ j\omega & 3+2j\omega \end{array}\right]$



Where the entries are in ${}^{\prime }{\Omega }^{\prime }$.



Suppose $Z_b\left(j\omega \right)=R_b+j\omega$



The value of $R_b$ (in $\Omega$) equals

1. 3

There are three copies each of four different books. The number of ways in which they can be arranged in a shelf is

If $a=\hat{i}+\hat{j}+\hat{k},b=2\hat{i}-\hat{j}+3\hat{k}andc=\hat{i}-2\hat{j}+\hat{k}$ find a unit vector parallel to the vector 2a - b + 3c.

If $1+3{\log }_{10}\sqrt{2+x}+4{\log }_{10}\sqrt{2-x}=3{\log }_{10}\sqrt{4-x^2}$, then the value of $x$ is

For non-negative real numbers $h_1,h_2,h_3,k_1,k_2,k_3,$ if the algebraic sum of the perpendiculars drawn from the points $(2,k_1),$ $(3,k_2),$ $(7,k_3),$ $(h_1,4),$ $(h_2,5),$ $(h_3,-3)$ on a variable line passing through $(2,1)$ is zero, then

If $A=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$ (where $bc\ne 0{)}^{10}$ satisfies the equation $x^2+k=0$ then ?

If the lines $\frac{x-1}{-3}=\frac{y-2}{2k}=\frac{z-3}{2}and\frac{x-1}{3k}=\frac{y-1}{1}=\frac{z-6}{-5}$ perpendicular, then find the value of k.

Let $A$ and $B$ are two matrices of same order $3\times 3$ given by $A=\left[\begin{array}{ccc}1& 3& \lambda +2\\ 2& 4& 6\\ 3& 5& 8\end{array}\right]$ and $B=\left[\begin{array}{ccc}3& 2& 4\\ 3& 2& 5\\ 2& 1& 4\end{array}\right].$

If $Tr(AB{)}^T+Tr(BA{)}^T=Tr\left(BA\right),$ then the value of $2\lambda$ equals to

$a>0,\underset{-\pi }{\overset{\pi }{\int }}\frac{si{n}^{2}x}{1+a^x}dx=$

If $f\left(x\right)=\left|\begin{array}{cc}4\sin x& 3\cos x\\ 2^x& x^2\end{array}\right|,$ then $f^{\prime }\left(0\right)$ is

A sequence $d_1,d_2,d_3,\cdots$ is defined by letting $d_1=2$ and $d_k=\frac{d_{k-1}}{k}$ for all natural number $k\ge 2.$ Then which of the following is/are correct?

(Solve using mathematical induction)

If function $f\left(x\right)=\{\begin{array}{cc}2x,& x\le 0\\ a-\left\{x\right\},& 0<x<1\end{array}$ has a local maximum at $x=0,$ then which of the following can be a possible value of ${}^{\prime }{a}^{\prime }$

Pair the subtraction statements with their answers.

Pick the odd pair out:

If the equations $x^2+3x+5=0$ and $a{x}^2+bx+c=0;a,b,c\in N$ have a common root, then the least possible value of $a+b+c$ is

The Receipts and Payments Account for the year ending 31-03-2018 of the Moses Club is as follows:

$\begin{array}{cccc}\text{Receipts}& \text{Amount}& \text{Payments}& \text{Amount}\\ & (Rs.)& & (Rs.)\\ \text{To Balance b/d}& 77,000& \text{By Salaries}& 30,000\\ \text{To Subscription (Outstanding of 2017}& 1,15,000& \text{By Rent}& 25,000\\ \text{Rs. 20,000 and advance of 2019 Rs 5,000)}& & \text{By Printing and Stationery}& \text{18,000}\\ \text{To Sale of Periodicals}& 2,000& \text{By Electricity}& 15,000\\ & & \text{By Periodicals}& 18,000\\ & & \text{By Sports Equipment}& 50,000\\ & & \text{By Advertisements}& 2,000\\ & & \text{By Refreshments}& 10,000\\ & & \text{By Balance c/d}& 26,000\\ & 1,94,000& & 1,94,000\end{array}$

(a) Annual subscription to be received every year is Rs. 1,00,000.

(b) Rent of the club for two months is pending.

(c) Electricity charges worth Rs. 3,000 are prepaid.

(d) Assets as on 01-04-2017 : Sports Equipment Rs. 80,000; 6% Fixed Deposit worth Rs. 50,000.

(e) Depreciation 10 % p.a on Sports Equipment.

Prepare Income and Expenditure Account for the year ending 31-03-2018.

1. 1

$\begin{array}{cc}Graphs& Functions\\ a& x^{\frac{1}{2}}\\ b& x^{\frac{1}{3}}\\ c& x^{\frac{1}{4}}\\ d& x^{\frac{1}{5}}\end{array}$

If $\overrightarrow{a}$ is a vector of magnitude 50 and is collinear with the vector $\overrightarrow{b}=6\hat{i}-8\hat{j}-\frac{15}{2}\hat{k}$ and makes an obtuse angle with the positive direction of z - axis, then $\overrightarrow{a}$ is equal to

Let four vectors $\overrightarrow{r}=3\hat{i}+2\hat{j}-5\hat{k},\overrightarrow{a}=2\hat{i}-\hat{j}+\hat{k},\overrightarrow{b}=\hat{i}+3\hat{j}-2\hat{k}$ and $\overrightarrow{c}=-2\hat{i}+\hat{j}-3\hat{k}$ are such that $\overrightarrow{r}=\lambda \overrightarrow{a}+\mu \overrightarrow{b}+v\overrightarrow{c},$ then $\lambda +\mu +v$ is

Write the maximum number of points of intersection of 8 straight lines in a plane.

Are the following pairs of sets equal ? Give reasons.

(i) A = {2,3}, B = {x : x is a solution of $x^2+5x+6=0$}

(ii) A = {x : x is a letter of the word "WOLF"}

B = {x : x is a letter of the word "FOLLOW"}

Find the range of values of l for which the variable line 3x+4y-l=0 lies between the circles x²+y²-2x-2y+1=0 and x²+y²-18x-2y+78=0 without intercepting a chord on either circle.

If $y=ln{\left(\frac{x}{a+bx}\right)}^x$,then $x^3\frac{d^{2}y}{d{x}^2}$ is equal to