Explore topic-wise InterviewSolutions in Current Affairs.

For the question given below verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.

$x^2=2y^{2}logy:(x^2+y^2)\frac{dy}{dx}-xy=0.$

f(x) $\{\begin{array}{c}{x}^3-3,ifx\le 2\\ x^2+1,ifx>2\end{array}$

Number of planes possible satisfying the condition that it should be parallel to 2 given vectors.

Let $O$ be the origin, and $\overrightarrow{OX},\overrightarrow{OY},\overrightarrow{OZ}$ be three unit vectors in the directions of the sides $\overrightarrow{QR},\overrightarrow{RP},\overrightarrow{PQ},$ respectively, of a triangle $PQR.$

$|\overrightarrow{OX}\times \overrightarrow{OY}|=$

${lim}_{x\to 2}\frac{x^3-3x^2-9x-2}{x^3-x-6}$

The length L (in centimeters) of a copper rod is a linear function of its Celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L interms of C.

Prove that:

$1+co{s}^{2}2\theta =2(co{s}^4\theta +si{n}^4\theta )$

Consider the following population and year graph:

Find the slope of the line AB and using it, find what will be the population in the year 2010.

If $P$ is a point on the rectangular hyperbola $x^2-y^2=a^2$, $C$ is its centre and $S,$ and $S^{\prime }$ are the two foci, then $SP.S^{\prime }P=$

Following is the Receipts and Payments Account of the Sumit Club and Resorts for the year ending 31st March, 2018.

$\begin{array}{cccc}\text{Receipts}& \text{Amount}& \text{Payments}& \text{Amount}\\ & \left(\text{Rs}\right)& & \left(\text{Rs}\right)\\ \text{To Balance b/d}& 44,000& \text{By Salaries}& 4,40,000\\ \text{To Subscription}& 9,80,000& \text{By Furniture puchased on}& \\ \text{To Entrance Fees}& 80,000& \text{1st October, 2017}& 1,00,000\\ \text{To Sports Fund}& 80,000& \text{By Sports Expenses}& 60,000\\ \text{To Sale of Drama Tickets}& 2,70,000& \text{By Drama Expenses}& 1,84,000\\ \text{To Sale of Waste Paper}& 2,500& \text{By Newspapers}& 2,500\\ \text{To Interest on Investment}& 20,000& \text{By Refreshments}& 32,000\\ (10\%on2,00,000)& & \text{By Lighting and Heating}& 60,000\\ & & \text{By Medicines Purchased}& 40,000\\ & & \text{By Balance c/d}& 5,58,000\\ \text{Total}& 14,76,500& \text{Total}& 14,76,500\end{array}$

Prepar Income and Expenditure Account for the year ending 31-03-2018, after taking into account the following adjustments :

(i) The Club has 2,000 members each paying an annual subscription of Rs 500 and the subscription of eighty members are still in arrears.

(ii) Stock of medicines as on 31st March, 2018 was Rs 10,000.

(iii) Salaries are paid Rs 40,000 per month.

(iv) Entrance fees is to be capitalised.

(v) Depreciate Furniture 10$\%$ p.a. ( taking into account Furniture on 1st April, 2017 was Rs 4,00,000).

The direction cosines of a line are l, m and n, and the direction ratios of the same line are a, b & c. Then, the expression is always correct.

The power factor of an R-L circuit is $\frac{1}{\sqrt{2}}$. If the frequency of AC is doubled, then what will be the power factor?

If the operation $\oplus$ is defined by $a\oplus b=a^2+b^2$ for all real numbers ‘a’ and ‘b’, then $(2\oplus 3)\oplus 4=$

The solution set of the inequality $\frac{(3^x-4^x)\cdot \ln (x+2)}{x^2-3x-4}\le 0$ is

${\int }_0^{\pi /4}\frac{si{n}^{2}xco{s}^{2}xdx}{(si{n}^{3}x+co{s}^{3}x{)}^2}=$

Let A = {3,6,12,15,18,21},

B= {4,8,12,16,20},

C = {2,4,6,8,10,12,14,16} and

D = {5,10,15,20}. Find :

(i) A - B (ii) A - C

(iii) A - D (iv) B - A

(v) C - A (vi) D - A

(vii) B - C (viii) B - D

Let $a_1,a_2,a_3,a_4$ …….. be an arithmetic progression and $g_1,g_2,g_3,g_4$ …… be a geometric progression. If $a_1+g_1=1,a_2+g_2=4,a_3+g_3=15and{a}_4+g_4=2$, then

If $c$ is a point at which Rolle's theorem holds for the function, $f\left(x\right)={\log }_e\left(\frac{x^2+\alpha }{7x}\right)$ in the interval $[3,4]$, where $a\in R$, then $f"\left(c\right)$ is equal to:

The distance between the lines $3x-4y+9=0$ and $6x-8y-15=0$ is ___ units

If the equation $p{x}^2+(2-q)xy+3y^2-6qx+30y+6q=0$ represents a circle, then which of the following is/are correct?

The value of $k$ for which the equation $|x-2|+|x-6|-|x+1|=k$ has atleast one solution

The number of distinct primes dividing 12! + 13! + 14! is

In $△ABC,A\left(z_1\right),B\left(z_2\right)$ and $C\left(z_3\right)$ are inscribed in the circle $|z|=5$. If $H\left(z_H\right)$ be the orthocentre of $△ABC$, then $z_H=$

Let A be the non-singular square matrix of order $3\times 3$ then |adj A| is equal to

a) $|A|$
b) $|A{|}^2$
c) $|A{|}^3$
d) $3|A|$

Two men A and B start with velocities V at the same time from the junction of two roads inclined at ${45}^{\circ }$ to each other. If they travel by different roads, then find the rate at which they are being separated.

6 3/5=x/100=y/1000 find the value of x and y?

The number of integral points (integrals poems mean both coordinate should should be integers ) exactly with the interiors of triangle with vertices (0,0),(4,3)and(21,0)

The total number of ways in which a couple can sit around a table with $6$ guests if the couple takes consecutive seats is

Let $A,B$ and $C$ represents the angles of $△ABC$. If $\tan \frac{A}{2},\tan \frac{B}{2},\tan \frac{C}{2}$ are in H.P., then the minimum value of $\cot \frac{B}{2}$ is

Find the maximum value and the minimum value of $3x^4-8x^3+12x^2-48x+25$ on the interval [0,3].

Integrate the following functions.
$\int (4x+2)\sqrt{x^2+x+1}dx.$

The value(s) of $x,$ which satisfy the equation $|x-2{|}^2+|x-2|-2=0$ is/are

The value of $\left|\begin{array}{ccc}y+z& x& x\\ y& z+x& y\\ z& z& x+y\end{array}\right|$ is equal to

For a positive integer n, let
$f_n\left(\theta \right)=\left(tan\frac{\theta }{2}\right)(1+sec\theta )(1+sec2\theta )(1+sec4\theta )\dots (1+sec{2}^n\theta )$.
Then

$\text{Derivative of}lo{g}_{10}^x.w..r.to{x}^{2}is$

Sum of the series $\frac{3}{1^2}+\frac{5}{1^2+2^2}+\frac{7}{1^2+2^2+3^2}+......$ upto 100 terms is

There are $5$ people and $5$ different pairs of shoes. If each person chooses at random one right shoe and one left shoe how many combinations can be made in which no one gets a correct pair.

The equation(s) of the circle passing through the points of intersection of the circles $x^2+y^2-2x-4y-4=0,$ $x^2+y^2-10x-12y+40=0$ and having radius $4$ units is/are

In $△ABC,\angle A={\tan }^{-1}2$ and $\angle B={\tan }^{-1}3$ and the length of side opposite to the smallest angle is $2\sqrt{5}.$ If perimeter of the triangle is $\sqrt{l}+\sqrt{m}+\sqrt{n}$ and circumradius is $\sqrt{k},$ then