Explore topic-wise InterviewSolutions in Current Affairs.

Let $p\left(x\right)$ be a polynomial such that $p\left(x\right)–p^{\prime }\left(x\right)=x^n$, where $n$ is a positive integer. Then $p\left(0\right)$ equals

For what value of $\lambda$ the equation of the line $\lambda$x + (1+$\lambda$)y + (2+$\lambda$)x +$\lambda$y +3=0 represents a line parallel to x-axis is

Negate each of the following statements :

(i) All the students completed their homework.

(ii) There exists a number which is equal to its square.

A variable straight line of slope $4$ intersects the hyperbola $xy=1$ at two points. The locus of the point which divides the line segment between these two points in the $1:2$ is

The total revenue received from the sale of x units of a product is given by $R\left(x\right)=3x^2+36x+5$ .The marginal revenue, when x = 15

The equation $x^n=1,n>1,n\in N$ has roots $1,a_1,a_2,...,a_{n-1}$. Then which of the following are correct?

Tangent to the circle $x^2+y^2$ = 4 at any point on it in the first quadrant makes intercepts OA and OB on x and y axes respectively, O being the centre of circle. Find the minimum value of (OA + OB).

Evaluate: ${\int }_0^{\pi }\frac{4xsinx}{1+co{s}^{2}x}dx$.

OR

Evaluate: $\int \frac{x+2}{\sqrt{x^2+5x+6}}dx$.

Let f(x) and g(x) be two functions having finite non-zero third order derivatives f'''(x) and g'''(x) for all $xϵR$ . If $f\left(x\right)g\left(x\right)=1$ for all $xϵR$ then $\frac{f^{\prime \prime \prime }}{f^{\prime }}-\frac{g^{\prime \prime \prime }}{g^{\prime }}$ is equal to :

If the origin is the centriod of the triangle PQR with vertices $P(2a,2,6),Q(-4,3b,-10)$ and $R(8,14,2c),$ then find the values of a, b, and c.

If $xϵ[-1,1],\text{then range of}ta{n}^{-1}(-x)$ is

The numbers 1, 2, 3, ….., n are arrange in a random order. The probability that the digits 1, 2, 3, …., k(k< n) appear as neighbors in that order is

If $a+b+c=0,$ then the family of lines $3ax+by+2c=0$ pass through fixed point

${lim}_{x\to \frac{\pi }{2}}\frac{\sqrt{2}-\sqrt{1+sinx}}{co{s}^{2}x}$

If A = $\left[\begin{array}{cc}-1& 0\\ 0& 2\end{array}\right]$ , then $A^3–A^2$ =

$\frac{si{n}^{3}A+co{s}^{3}A}{sinA+cosA}+\frac{si{n}^{3}A-co{s}^{3}A}{sinA-cosA}=2$

A relation R is defined from {2, 3, 4, 5} to {3, 6, 7, 10} by : $xRy\iff x$ is relatively prime to y. Then, domain of R is

Following is the receipts and payments account of Modern Club, New Delhi for the year ending 31st March, 2014 :

$\begin{array}{cccc}\text{Receipts}& \text{Rs}& \text{Payments}& \text{Rs}\\ \text{Balance b/d on 1-4-2013}& 2,300& \text{Match Expenses}& 6,800\\ \text{Subscriptions}& 56,400& \text{Rent}& 9,600\\ \text{Interest}& 300& \text{Salaries}& 24,000\\ \text{Donation}& 6,000& \text{Sundry Expenses}& 3,600\\ \text{Donations for Building Fund}& 50,000& \text{Investments Purchased}& 30,000\\ \text{Match Fund}& 10,000& \text{Newspapers}& 750\\ \text{Miscellaneous receipts}& 430& \text{Sports Equipments}& 32,000\\ \text{Sale of Grass}& 100& \text{Balance c/d on 31-3-2014}& 18,780\\ & \underset{–}{\overline{1,25,530}}& & \underset{–}{\overline{1,25,530}}\end{array}$

Subscriptions outstanding on 31st March, 2013 were Rs 4,000 and on 31st March, 2014 were Rs 6,000. Salaries outstanding on 31st March, 2013 and on 31st March, 2014 were Rs 2,000 and Rs 2,500 respectively.

On 31st March, 2013, the Club had Investments worth Rs 12,000; Furniture Rs 10,000 and sports equipments valued at Rs 20,000.

Prepare Income & Expenditure A/c for the year ended 31st March, 2014 and a Balance Sheet as at that date after depreciating furniture by 20% and sports equipments by 25%.

The length of the perpendicular from the origin to the plane passing through three non-collinear points $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ is

If a b and c are in GP and $a^{1/x}=b^{1/y}=c^{1/z}$, prove that x, y and z are in AP.

Find $\frac{dy}{dx}$in the following questions:

$xy+y^2=tanx+y$

The length of the latus rectum of the hyperbola $3y^2-x^2=27$ is

Draw a rough sketch of the curve $y=\sqrt{x-1}$ in the interval [1, 5]. Find the area under the curve and batween the lines x = 1 and x = 5.

The point on $y-$ axis which is equidistant from the points $(12,3)$ and $(-5,10)$ is

The set of solutions satisfying both $x^2+5x+6\ge 0and{x}^2+3x-4<0is$

Let $a=min\{x^2+2x+3,xϵR\}andb=\underset{\theta \to 0}{lim}\frac{1-cos\theta }{{\theta }^2}$. The value of ${\Sigma }_{r=0}^n{a}^r.b^{n-r}$ is

If $0<\theta <2\pi$ and $2\cos \theta =\sqrt{3}\cos {10}^{\circ }-\sin {10}^{\circ }$, then the value of $\theta$ is

The rational term(s) in the expansion of ${(\sqrt{2}+(3{)}^{\frac{1}{5}})}^{10}$ is/are

An ellipse is rotated through a right angle in its own plane about its centre, which is fixed. If at a point tangents are drawn before and after rotation then locus of point of intersection of such tangents is

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning prize is $\frac{1}{100}$. What is the probability that he will win a prize.
atleast twice ?

If a variable line, $3x+4y-\lambda =0$ is such that the two circles $x^2+y^2-2x-2y+1=0$ and $x^2+y^2-18x-2y+78=0$ are on its opposite sides, then the set of all values of $\lambda$ will lie in the interval:

Let D be the domain of the real valued function f defined by $f\left(x\right)=\sqrt{25-x^2}$. Then, write D.

In inequality log _1/2(x^{​​​​​​2}​​​​​-6x+12) ≥ -2 there is one step which says (x-2)(x-4) ≤ 0,. then how can we conclude that x<2 and x>4 ?

For x $\in (-\pi ,\pi )$ then the number of values of x for which the given

equation ($\sqrt{3}sinx+cosx{)}^{\sqrt{(\sqrt{3}sin2x-cos2x+2)}}$ = 4 is

The length of the intercept made by the normal at (1,6) of the circle $x^2+y^2-4x-6y+3$ = 0 between the Coordinate axis is

The value of ${lim}_{x\to \infty }\frac{(x+1{)}^{10}+(x+2{)}^{10}+\cdots +(x+100{)}^{10}}{x^{10}+{10}^{10}}$ is

Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = {(a, b): |a − b| is even}, is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other. But no element of {1, 3, 5} is related to any element of {2, 4}.

Prove that cos/1-tan +sin/1- cot= cos + sin