Explore topic-wise InterviewSolutions in Current Affairs.

Find the mean , and standard deviation for the following data :

(i) $\begin{array}{ccccccc}Yearrender:& 10& 20& 30& 40& 50& 60\\ Noofperson\left(cumulative\right):& 15& 32& 51& 78& 97& 109\end{array}$

(ii) $\begin{array}{cccccccccccccccc}Marks:& 2& 3& 4& 5& 6& 7& 8& 9& 10& 11& 12& 13& 14& 15& 16\\ Frequency:& 1& 6& 6& 8& 8& 2& 2& 3& 0& 2& 1& 0& 0& 0& 1\end{array}$

(a) Can a truck be an intermediate good? Give reasons for your answer.

(b) Calculate GDP at factor cost by Income and Expenditure method.

$\begin{array}{ccc}\text{S. No.}& \text{Items}& \text{Rs. in crores}\\ \left(i\right)& \text{Personal consumption expenditure}& 730\\ \left(ii\right)& \text{Wages and salaries}& 700\\ \left(iii\right)& \text{Employer's contribution to social security schemes}& 100\\ \left(iv\right)& \text{Gross business fixed investment}& 60\\ \left(v\right)& \text{Profit}& 100\\ \left(vi\right)& \text{Gross residential construction investment}& 60\\ \left(vii\right)& \text{Government purchases of goods and services}& 200\\ \left(viii\right)& \text{Gross public investment}& 90\\ \left(ix\right)& \text{Rent}& 50\\ \left(x\right)& \text{Inventory investment}& 20\\ \left(xi\right)& \text{Exports}& 40\\ \left(xii\right)& \text{Interest}& 50\\ \left(xiii\right)& \text{Imports}& 20\\ \left(xiv\right)& \text{Net factor income from abroad}& (-)10\\ \left(xv\right)& \text{Mixed income}& 100\\ \left(xvi\right)& \text{Depreciation}& 20\\ \left(xvii\right)& \text{Subsidies}& 10\\ \left(xviii\right)& \text{Indirect taxes}& 20\end{array}$

OR

Give reasons, on the treatment assigned to the following while estimating national income:

(a) Expenditure on medicines by a government hospital

(b) Expenditure on medicines by Fortis Hospital

(c) Salaries paid to the residents of USA working in Indian Embassy in USA

(d) Rent received by Indian residents for their buildings rented out to foreigners in India

The sum of the distinct real values of $\mu ,$ for which the vectors, $\mu \hat{i}+\hat{j}+\hat{k},\hat{i}+\mu \hat{j}+\hat{k},\hat{i}+\hat{j}+\mu \hat{k}$ are co-planar, is:

If the circle $x^2+y^2+4x+22y+c=0$ bisects the circumference of the circle $x^2+y^2-2x+8y-d=0(c,d>0),$ then the maximum possible value of $cd$ is

1. undefined
2. undefined
3. undefined
4. undefined

Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers ?

The line $2x-y+6=0$ meets the circle $x^2+y^2-2y-9=0$ at A and B. Find the equation of the circle on AB as diameter.

If $A\cap B=B$ , then

Let n be a positive integer. Then the number of common factors of n² + 3n + 1 and n² + 4n + 3 is

If AFB is a focal chord of the parabola $y^2=4ax$ and AF = 4, FB = 5, then the latus-rectum of the parabola is equal to

Let $S=\left\{\right(\lambda ,\mu )\in R\times R:f(t)=(|\lambda |e^{|t|}-\mu )\cdot \sin (2|t|),t\in R,\text{is a differentiable function}\}.$
Then $S$ is a subset of :

Find the smallest positive integer value of n for which $\frac{(1+i{)}^n}{(1-n{)}^{n-2}}$ is a real number.

If cot A = $\frac{12}{5}$, then the value of (sin A+cos A) $\times$ cosec A is:

The value of ${\int }_1^{16}ta{n}^{-1}\sqrt{\sqrt{x}-1}dx$ is

If $\alpha$ is one of the principal solutions which satisfies the equation $1+{\sin }^2\theta =3\sin \theta \cos \theta ,$ then which of the following is not possible?

Write the set of all positive integers whose cube is odd.

Write the coefficient of the middle term in the expansion of $(1+x{)}^{2n}.$

$2+5+8+11+...+(3n-1)=\frac{1}{2}n(3n+1)$

Consider a polynominal $p\left(x\right)=x^6+2x^2+1$. If $x_1,x_2,\dots ,x_6$ are the roots of $p\left(x\right)=0$ and $q\left(x\right)=x^3-1$, then the value of $\prod _{i-1}^{6}q\left(x_i\right)$ is
(where $\prod$ stands for product of terms)

If $2+i$ and $\sqrt{5}-2i$ are the roots of the equation $(x^2+ax+b)(x^2+cx+d)=0,$ where $a,b,c,d$ are real constants, then product of all roots of the equation is

A cricket club has $15$ members, of whom only $5$ can bowl. If the names of $15$ members are put into a box and $11$ are drawn at arandom, then the probability of getting an eleven containing at least $3$ bowlers is

Evaluate:
$\left|\begin{array}{ccc}a-b-c& 2a& 2a\\ 2b& b-c-a& 2b\\ 2c& 2c& c-a-b\end{array}\right|$

Which of the following statements are correct for oblique hyperbola $xy=8$
1. Equation of tangent at P(4, 2) is $x+2y=8$

2. Equation of normal at P(t) is $x{t}^3-yt=2\sqrt{2}(t4-1)$

If {x} denotes the fractional part of x, then $\left\{\frac{82\times k+2}{82}\right\}$ = $\{k+\frac{2}{82}\}$ is, where k is an integer greater than 1:

If the distance between the points $(2,1)$ and $(\alpha ,3)$ is equal to minimum value of the quadratic equation $y=x^2-4x+6$ i.e. $\beta$ and which is possible at $x=\gamma$, then $\alpha +\beta +\gamma$ is:

Prove that the following functions do not have maxima or minima:

$f\left(x\right)=e^x$

$g\left(x\right)=logx$

$h\left(x\right)=x^3+x^2+x+1$

$Iftan\theta +tan(\theta +\frac{\pi }{3})+tan\left(\theta \frac{2\pi }{3}\right)=3,\text{then which of the following is equal to 1}$

A manufacturer sells the products x,y,z in two markets, annual sales are indicated below.
$\begin{array}{cccc}Market& Products& & \\ I& 10000& 2000& 18000\\ II& 6000& 20000& 8000\end{array}$
(b)If the unit costs of the above three commodities are Rs 2.00m Rs 1.00 and 50 paise respectively. Find the gross profit.

The graph of $y=\frac{1}{x}-1$ is

A particle moves on x-axis according to the equation $x=x_{0}si{n}^{2}wt$, the motion is simple harmonic,

Differentiate sin2xcos²x

Arrange the given words in the sequence in which they occur in the dictionary and then choose the correct sequence from the options

(1) Cloth (2) Cinema (3) Chronic (4) Christmas (5) Create

Greatest negative integral value of n for which ${\left(\frac{1+i}{1-i}\right)}^n$ = 1 is

Let a square with side length ${}^{\prime }{p}^{\prime }$ and making an angle of $\theta$ with $x-$ axis, has one vertex at origin. If $0<\theta <\frac{\pi }{2}$, then the equation of the diagonals of the square is

Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue.
Then the value of $\frac{m}{n}$ is ___

Let $J={\int }_0^{\frac{1}{2}}(\frac{1}{4}-x^2{)}^{4}dxandK={\int }_0^{\frac{1}{2}}{x}^4(1-x{)}^{4}dx,$ then

Statements: U*V, X $ W, U**W

Conclusions:

I. W $ V

II. U ** X

$\begin{array}{c}AdjointofthematrixN\left[\begin{array}{ccc}-4& -3& -3\\ 1& 0& 1\\ 4& 4& 3\end{array}\right]\end{array}$ is [MP PET 1989]

The distance of the point (2, 1, – 2) from the line $\frac{x-1}{2}=\frac{y+1}{1}=\frac{z-3}{-3}$ measured parallel to the plane x + 2y + z = 4 is

The locus of the point of interaction of two tangents of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ which make an angle α with one another is