Explore topic-wise InterviewSolutions in Current Affairs.

Let $A=\left[a_{ij}\right]$ is a diagonal matrix of order $4$ and $k$ is the possible number of zeros in $A.$ Then $k$ can be

Tangents are drawn to $x^2+y^2=1$ from any arbitrary point $P$ on the line $2x+y-4=0$. The corresponding chord of contact passes through a fixed point whose coordinates are

In a $\Delta$ ABC , 2s = perimeter and R = circumradius. Then,S/Ris equal to

Match $\text{List I}$ with the $\text{List II}$ and select the correct answer using the code given below the lists :



$\begin{array}{cccc}& \text{List I}& & \text{List II}\\ \text{(A)}& \text{Let}f\text{be a real-valued differentiable function on}R\text{such that}{f}^{\prime }\left(1\right)=6\text{and}{f}^{\prime }\left(2\right)=2.& \text{(P)}& 4\\ & \text{Then}\underset{h\to 0}{lim}\frac{f(3\cos h+4\sin h-2)-f\left(1\right)}{f(3e^h-5\sec h+4)-f\left(2\right)}\text{is equal to}& & \\ \text{(B)}& \text{For}a>0,\text{let}f:[-4a,4a]\to R\text{be an even function such that}f\left(x\right)=f(4a-x)\text{for all}& \text{(Q)}& 5\\ & x\in [2a,4a]\text{and}\underset{h\to 0}{lim}\frac{f(2a+h)-f\left(2a\right)}{h}=4.\text{Then}\underset{h\to 0}{lim}\frac{f(h-2a)-f(-2a)}{2h}\text{is equal to}& & \\ \text{(C)}& \text{Suppopse}f\text{is a differentiable function on}R.\text{Let}F\left(x\right)=f\left(e^x\right)\text{and}G\left(x\right)=e^{f\left(x\right)}.& \text{(R)}& 3\\ & \text{If}{f}^{\prime }\left(1\right)=e^3\text{and}f\left(0\right)=f^{\prime }\left(0\right)=3,\text{then}\frac{G^{\prime }\left(0\right)}{F^{\prime }\left(0\right)}\text{is equal to}& & \\ \text{(D)}& \text{Let}f\left(x\right)=max\{\cos x,x,2x-1\}\text{where}x\ge 0.\text{Then number of points of}& \text{(S)}& 2\\ & \text{non-differentiability of}f\left(x\right),\text{is equal to}& & \\ & & \text{(T)}& 1\end{array}$



Which of the following is a CORRECT combination?

A circle is tangent to the x and y axes in the first quadrant at the points $P$ and $Q$ respectively. $BC$ and $AD$ are parallel tangents to the circle with slope $-1$. If the points $A$ and $B$ are on the y- axis while $C$ and $D$ are on the x-axis and the area of the quadrilateral $ABCD$ is $900\sqrt{2}$ sq. units, then the radius of the circle is

If three consecutive coefficients in the expansion of $(1+x{)}^n$ be 165, 330 and 462, then ${}^n{C}_2$ =

In an objective paper, there are two sections of $10$ questions each. For "section $1$", each question has $5$ options and only one option is correct and "section $2$" has $4$ options with multiple answers and marks for a question in this section is awarded only if he ticks all correct answers. Marks for each question in "section $1$" is $1$ and in "section $2$" is $3.$

(There is no negative marking)

If a canidate attempts only two questions by guessing, one from "section $1$" and one from "section $2$", the probability that he scores in both questions is

If in a certain language, MOSERLW is the code for WLRESOM, which word would be coded as ELKCAHS?

$\frac{{}^{11}{C}_0}{1}$ + $\frac{{}^{11}{C}_1}{2}$ + $\frac{{}^{11}{C}_2}{3}$+.............. $\frac{{}^{11}{C}_{10}}{11}$ =

${lim}_{x\to 0}\frac{sin3\theta }{tan2\theta }$

Find the 20^th term in the following sequence whose n^th term is

The general solution of the differential equation $\frac{dy}{dx}=\frac{x(2\ln x+1)}{\sin y+y\cos y},x>0$ is

(where $c$ is constant of integration)

ABC is an isosceles triangle inscribed in a circle of radius r. If AB = AC and h is the altitude from A to BC.The triangle ABC has perimeter $P=2[\sqrt{(2hr-h^2)}+\sqrt{2hr}]$ and A be the area of the triangle .Find $\underset{h\to 0}{lim}\frac{A}{P^3}$

If the line $x-1=0$ is the directrix of the parabola $y^2-kx+8=0$, then one of the values of $k$ is

If the value of $\underset{0}{\overset{\pi /4}{\int }}{e}^x\left[\frac{2+\sin 2x}{1+\cos 2x}\right]dx=p{e}^{\pi /q}+r,$ then which of the following statements is/are correct $?$

(where $p,q,r\in R$ )

The domain of f(x) is (0, 1). Then the domain of $f\left(e^x\right)+f\left(ln|x|\right)$ is

Integrate the following functions.
$\int \frac{5x+3}{x^2+4x+10}dx.$

Find the sum to n terms of the series 3 × 8 + 6 × 11 + 9 × 14 +…

If $\sin \alpha$ is a root of the equation $25x^2+5x-12=0$ and $x$ belongs to the range of the function $f\left(x\right)=-|\cos x|,$ then the value of $|\sin 2\alpha |$ is

If the product of three numbers in GP is 216 and the sum of their products in pairs is 156, find the numbers.

1.2 + 2.2²
+ 3.2² + … + n.2ⁿ = (n
– 1) 2ⁿ⁺¹ + 2

Prove that
sin² 6x – sin² 4x = sin 2x
sin 10x

From the following information calculate the amount of subscriptions to be credited to the Income & Expenditure Account for the year 2016-17:

$\begin{array}{cc}& \text{Rs}\\ \text{Subscriptions received during the year}& 80,000\\ \text{Subscriptions outstanding on 31st March, 2016}& 26,000\\ \text{Subscriptions outstanding on 31st March, 2017}& 6,000\\ \text{Subscriptions received in Advance on 31-3-2016}& 15,000\\ \text{Subscriptions received in Advance on 31-3-2017}& 10,000\\ \text{Subscriptions of Rs 2,000 are still in arrears for the year 2015-16}& \end{array}$

The
value of the integral

is

A. 6

B. 0

C. 3

D. 4

Find the eccentric angle of a point on the ellipse $\frac{x^2}{6}+\frac{y^2}{2}=1$ whose distance from centre is 2.

In a race between Achilles and tortoise, people assigned probability to Achilles winning and tortoise winning. These probability pairs are listed below. How many of these pairs satisfy the axiomatic approach, assuming only two possible results are tortoise wins and Achilles wins.

Choose the correct option and justify your choice.

(i)

(A). sin60°

(B). cos60°

(C). tan60°

(D). sin30°

(ii)

(A). tan90°

(B). 1

(C). sin45°

(D). 0

(iii) sin2A = 2sinA is true when A =

(A). 0°

(B). 30°

(C). 45°

(D). 60°

(iv)

(A). cos60°

(B). sin60°

(C). tan60°

(D). sin30°

The area of an acute triangle $ABC$ is $\Delta$, the area of its pedal triangle is '$p$', where $\cos B=\frac{2p}{\Delta }$ and $\sin B=\frac{2\sqrt{3}p}{\Delta }$. The value of $8({\cos }^{2}A\cos B+{\cos }^{2}C)$ is