Explore topic-wise InterviewSolutions in Current Affairs.

If x^2+2ax+a<0

for all x belongs to [1,2] then find set of all possible value of a.

A survey shows that 63% of the Americans like cheese whereas 76% like apples. If x% of the Americans like both cheese and apples then find the value of x.

Let $f:R\to R$ be any function and $g\left(x\right)=\frac{1}{f\left(x\right)}$. Then which of the following is/are not true?

If $A$ is any square matrix of order $3\times 3$ then $|3A|$ is equal to

If $Z_1,Z_2,Z_3$ are complex numbers such that $|Z_1|=|Z_2|=|Z_3|=1and{Z}_1+Z_2+Z_3=0$, then area of triangle whose vertices $Z_1,Z_2$ and $Z_3$ is

$Ifa=cos\alpha cos\beta +sin\alpha sin\beta cos\gamma ,b=cos\alpha sin\beta -sin\alpha cos\beta cos\gamma andc=sin\alpha sin\gamma then{a}^2+b^2+c^{2}isequalto$

$\begin{array}{cccccc}& \text{Column - I}& & \text{Column - II}& & \text{Column - III}\\ \left(I\right)& y.(y^{\prime }{)}^2-x{y}^{\prime }(1+y)+x^2=& \left(i\right)& \left[y\right]=1,\text{where [.] is greatest}& \left(p\right)& \text{Curve is bounded with area},\pi \\ & 0,y\left(\sqrt{3}\right)=2& & \text{integer function}& & \\ \left(II\right)& y^{\prime }=\frac{y^2-x^2}{2xy},y\left(1\right)=1& \left(ii\right)& \text{Maximum value of y is 3}& \left(Q\right)& \text{Area bounded by curve in first quadrant with}\\ & & & & & \text{co-ordinate axes is}\frac{3\pi }{4}\\ \left(III\right)& y^{\prime }=\frac{-9x}{y},y\left(1\right)=0& \left(iii\right)& \text{Maximum value of y is not defined}& \left(R\right)& \text{Curve is conic with eccentricty},\frac{1}{2}\\ \left(IV\right)& y^{\prime }=\frac{x}{y},y\left(2\right)=0& \left(iv\right)& \text{Maximum value of y is 1}& \left(S\right)& \text{Curve is conic with eccentricity},\sqrt{2}\end{array}$

The correct combination is

If $\int x^{26}(x-1{)}^{17}(5x-3)dx=\frac{x^{27}.(x-1{)}^{18}}{k}+c,$ where c is the constant of integration, then the value of k is

PM and PN are the perpendiculars from any point P on the rectangular hyperbola $xy=c^2$ to the asymptotes.

If the locus of the mid point of MN is a conic, then its eccentricity is

If $f:(0,\infty )\to R$ and $F\left(x\right)={\int }_0^{x}f\left(t\right)$ dt. If $F\left(x^2\right)=x^2(1+x)$ then f(1) =

Calculate the open economy multiplier with proportion of taxes, T = tY, instead of lump-sum taxes as assumed in the text.

If ${lim}_{x\to a}\frac{x^9-a^9}{x-a}={lim}_{x\to 5}(4+x)$, find all possible values of a.

${lim}_{x\to 2}\frac{\sqrt{1+4x}-\sqrt{5x+2x}}{x-2}$

The value of $\sum _{n=0}^{100}{i}^{n!}$ equals (where $i=\sqrt{-1})$

Let f: R $\to$ R such that f(x + 2y) = f(x) + f(2y) + 4xy, $\forall$ x, y $ϵ$ R and f(0) = 0.

If $I_1={\int }_0^{1}f\left(dx\right),I_2={\int }_{-1}^{0}f\left(x\right)dx,and{I}_3={\int }_{-1}^{1}f\left(x\right)dx,then$

A spherical iron ball of $10\text{cm}$ radius is coated with a layer of ice of uniform thickness that melts at the rate of $50{\text{cm}}^3/\text{min}$. When the thickness of ice is $5\text{cm}$, then the rate (in $\text{cm/min}$) at which the thickness of ice decreases, is :

Find the value of p so that three lines 3x + y - 2 = 0, px + 2y - 3 = 0 and 2x - y - 3 = 0 may intersect at one point.

If P (n,4) = 12. P (n,2), find n.

How many words (with or without dictionary meaning) can be made from the letters in the word MONDAY, assuming that no letter is repeated, if
(i) 4 letters are used at a time?
(ii) all letters are used at a time?
(iii) all letters are used but first is vowel?

If $\int e^{\sec x}\left(\sec x\tan xf\right(x)+(\sec x\tan x+{\sec }^{2}x\left)\right)dx=e^{\sec x}f\left(x\right)+C$, then a possible choice of $f\left(x\right)$ is :

For any three sets A, B and C

The number of functions $f$ from $\{1,2,3,....,20\}$ onto $\{1,2,3,...,20\}$ such that $f\left(k\right)$ is a multiple of $3$, whenever $k$ is a multiple of $4$, is :

If $z=\frac{(\sqrt{3}+i{)}^3(3i+4{)}^2}{(8+6i{)}^2}$, then |$z$| is equal to

A unit vector coplanar with $\overrightarrow{i}+\overrightarrow{j}+3\overrightarrow{k}\text{and}\overrightarrow{i}+3\overrightarrow{j}+\overrightarrow{k}$ and perpendicular to $\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}$ is

The inverse of the proposition $(p\wedge \sim q)\to r$ is

Let $f\left(x\right)=\sum _{r=0}^{20}{a}_r{x}^r$ and $g\left(x\right)=\sum _{r=0}^9{b}_r{x}^r+\sum _{r=10}^{20}{x}^r.$ If $f\left(x\right)=g(x+1)$, then the value of $a_{10}$ is

The number of terms in the expansion of $(a+b+c{)}^{20}$ is

The value of $\sin {40}^{\circ }{35}^{\prime }\cos {19}^{\circ }{25}^{\prime }+\cos {40}^{\circ }{35}^{\prime }\sin {19}^{\circ }{25}^{\prime }$ is

The area of the region bounded by the curve $y=x^2$ and the line $y=16$ is

3sinA + 4cosA = 5 then what is the value of 4sinA - 3cosA

The possible value of ‘k’ if the equation $2cosx+cos2kx=3$ has only one solution

Why do we take log in frendulich isotherm?

Solve the differential equation $\frac{dy}{dx}+1=e^{x+y}$.

$\text{If A}=\left(\begin{array}{cc}cos\alpha sin\alpha & \\ -sin\alpha cos\alpha & \end{array}\right),\text{find}\alpha \text{satisfying}0<\alpha <\frac{\pi }{2}\text{when}A+A^T=\sqrt{2}{I}_2;\text{where}{A}^T\text{is the transpose of A}.$

Find two positive numbers x and y such that x+y = 60 and $x{y}^3$ is maximum.

A fair coin and an unbiased die are tossed. LEt A be he event 'head appears on the coin' and B be the events '3 be the events '3 on the die', Cheek whether A and B are independent events or not.

If f(x)=$x^{\frac{1}{2}},g\left(x\right)=x^{\frac{1}{3}}andh\left(x\right)=x^{\frac{2}{3}}$. Find $\frac{f\left(x\right)+g\left(x\right)}{f\left(x\right)+h\left(x\right)}$

How many of the permutations of 10 different things taken 4 at a time with one particular thing : (a) Never occur (b) Always occur.

If $tan\theta =\sqrt{n}$ for some non-square natural number n, then sec2$\theta$ is

If A = {1, 4, 9}, B = {1, 2, 3} and C = {1, 3, 5}, find A $\cap$ (B $\cap$ C).

A solution curve of the differential equation given by $(x^2+xy+4x+2y+4)\frac{dy}{dx}-y^2=0$ passes through (1, 3)

The equation of the tangent to the curve at (1, 3) is