Explore topic-wise InterviewSolutions in Current Affairs.

If $\underset{-1}{\overset{1}{\int }}\frac{x^3+|x|+1}{x^2+2|x|+1}dx=\ln \left(k\right),$ then which of the following is/are true?

Number of value(s) of $x$ which disobey(s) the condition ${\log }_3(2x^2+6x-5)>1,x\in N$ is

In $△ABC$ with altitude $AD,\angle BAC=\frac{\pi }{4}$, $BD=\frac{3}{2}$ and $DC=1$, then the length of side $AB$ is

If A and B are two matrices of 3 X 3 order, then

This section contains four questions, each having two matching lists. Choices for the correct combination of elements from List – I and List – II are given as options (A), (B), (C) and (D), out of which one is correct.

$\begin{array}{cccc}& \text{List - I}& & \text{List - II}\\ P.& If\alpha =\frac{\pi }{7}then\frac{1}{cos\alpha }+\frac{2cos\alpha }{cos2\alpha }& 1.& 2\\ Q.& \underset{x\to \infty }{Lt}\left[\right(x-1\left)\right(x-2\left)\right(x+3\left)\right(x+5\left)\right(x+10){]}^{\frac{1}{5}}-x=& 2.& 3\\ R.& {\int }_{-2}^2\frac{3x^{2}dx}{1+e^x}=& 3.& 4\\ S.& \text{Let f(x)}=x^3+x^2+2x-1.\text{The minimum integral value of x}& 4.& 8\\ & \text{if x satisfies f(f(x)) > f(2x + 1) is}& & \end{array}$

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The feasible region of an LPP is shown in the figure. If $Z=8x+3y,$ then the minimum value of $Z$ occurs at

What was the day of the week on 2${}^{nd}$ October, 2014?

If $P$ and $Q$ are two points on the hyperbola $\frac{x^2}{5}-\frac{y^2}{8}=1$ whose centre is $C$ such that $CP$ is perpendicular to $CQ,$ then the value of $\frac{1}{(CP{)}^2}+\frac{1}{(CQ{)}^2}$ is equal to

Equation of common tangent of $y=x^2,y=-x^2+4x-4$ is

If $\cos \theta =-\frac{7}{25}$ and $\pi <\theta <\frac{3\pi }{2}$, then $\tan \theta$ is equal to

An article manufactured by a company consists of two parts X and Y. In the process of manufacture of part X, 9 out of 104 parts may be defective. Similartly, 5 out of 100 are likely to be defective in the manufacture of the part Y. Calculate the probability that the assembled product will not be defective.

Find the value of $ta{n}^{-1}\left(tan\frac{2\pi }{3}\right).$

If the range of discrete data of n observations is zero, then

The angle between the lines $\left(si{n}^2\alpha \right)y^2–2xyco{s}^2\alpha +(co{s}^2\alpha -1)x^2=0$ is

Find the number of ways in which 10 doctor and 90 engineers can sit in a row having 100 chairs such that no doctor sit at either end of the row and between any two doctors, at least five engineers sit.

If each of the points $(x_1,4),(-2,y_1)$ lies on the line joining the points $(2,-1)$ and $(5,-3)$, then find $x_1+y_1$

If f(x) = 2x + 1, what is f(-3)?

The image of $x+y+z+1=0$, through the plane $2x–4y+2z+4=0,$ is

If $x_1,x_2,x_3,x_4$ are roots of the equation $x^4-x^{3}sin2\beta +x^{2}cos2\beta -xcos\beta -sin\beta =0$ then $ta{n}^{-1}{x}_1+ta{n}^{-1}{x}_2+ta{n}^{-1}{x}_3+ta{n}^{-1}{x}_4=$

The area enclosed between the parabola $y=x^2$ and the sraight line $y=x$ is

Let $a,b\in R^{+}$ such that ${\log }_{27}a+{\log }_{9}b=\frac{7}{2}$ and ${\log }_{27}b+{\log }_{9}a=\frac{2}{3}.$ Then the value of $ab$ is

If $A=\left[\begin{array}{ccc}0& 0& x\\ 0& x& 0\\ x& 0& 0\end{array}\right]$, then $A^{100}=$

If $(n+1)!=12(n-1)!$, then the value of $n$ is

If $\sin \theta =-\frac{3}{5}$ and θ lies in IV quadrant, then cosθ + cotθ equals



यदि $\sin \theta =-\frac{3}{5}$ तथा θ, IV चतुर्थांश में स्थित है, तब cosθ + cotθ का मान बराबर है

If a normal to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ meets the axes at $M\&N$ and the lines $MP\&NP$ are drawn perpendicular to the axes meeting at $P$, then locus of $P$ is

Find the
value of x for whichis
a unit vector.

Let $\overrightarrow{a}=\hat{i}-\hat{j},\overrightarrow{b}=\hat{i}+\hat{j}+\hat{k}$ and $\overrightarrow{c}$ be a vector such that $\overrightarrow{a}\times \overrightarrow{c}+\overrightarrow{b}=\overrightarrow{0}$ and $\overrightarrow{a}\cdot \overrightarrow{c}=4$, then $|\overrightarrow{c}{|}^2$ is equal to:

$\frac{d}{dx}\left[(x+1)(x^2+1)(x^4+1)(x^8+1)\right]=(15x^p-16x^q+1){(x-1)}^{-2}$

$\Rightarrow (p,q)=$

A rectangle $ABCD$ has its side $AB$ parallel to line $y=x$ and vertices $A,B$ and $D$ lie on $y=1,x=2$ and $x=-2$, respectively. Locus of vertex ${}^{\prime }{C}^{\prime }$ is