Explore topic-wise InterviewSolutions in Current Affairs.

If $|x{|}^2-6|x|+9\le 4$, then $x\in$

If from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn, then the probability that 2 white and 1 black ball will be drawn is

Find the equation of a line which passes through the point (22, - 6) and is such that the intercept on x-axis exceeds the intercept on y-axis by 5.

If x < 0, then find the value of
$2\left({\tan }^{-1}\frac{1}{x}+{\tan }^{-1}x\right)$

${lim}_{x\to 8}\frac{\sqrt{1+\sqrt{1+x}}-2}{x-8}=$

If $p=2$ and $q=-5,$ then the distance between $p$ and $q$ along the number line is

If $y={\sin }^{-1}\left(x\sqrt{1-x}-\sqrt{x}\sqrt{1-x^2}\right\}\mathrm{and}0<x<1,\mathrm{then}\frac{\mathrm{dy}}{\mathrm{dx}}$is

Derivative of the function, $f\left(x\right)=2\ln {\left(x\right)}^5+2\ln {\left(x\right)}^3+\ln {\left(x\right)}^2-\ln \left(x\right)+2x$ is

Let $A$ be a $3\times 3$ matrix with $\text{det}\left(A\right)=4.$ Let $R_i$ denote the $i^{th}$ row of $A.$ If a matrix $B$ is obtained by performing the operation $R_2\to 2R_2+5R_3$ on $2A,$ then $\text{det}\left(B\right)$ is equal to:

If a line makes an angle of ${30}^{\circ }$ with the positive direction of $y-$ axis measured in anticlockwise direction, then the slope of the line is

A student has to answer 10 questions, choosing at least 4 from each of part A and part B. If there are 6 questions in part A and 7 in part B, in how many ways can the student choose 10 questions ?

What is the total number of proper subsets of a set consisting of n elements ?

Show that the given differential equation is homogeneous and then solve it.

$(1+e^{\frac{x}{y}})dx+e^{\frac{x}{y}}(1-\frac{x}{y})dy=0$

If $l_1,m_1,n_{1}and{l}_2,m_2,n_2$ are the direction cosines of two mutually perpendicular lines, show that the direction consines of the line perpendicular to both of these are $m_1{n}_2-m_2{n}_1,n_1{l}_2-n_2{l}_1,l_1{m}_2-l_2{m}_1$

Equation(s) of the tangents drawn from $(4,10)$ to the parabola $y^2=9x$ is/are

An electronic assembly consists of two subsystems say A and B. From previous testing procedures, the following probabilities are assumed to be known

P(A fails)=0.2, P(B fails alone)=0.15, P(A and B fails)=0.15

Evaluate the following probabilities

P(A fails alone)

$If(x-1{)}^2+(y-b{)}^2=c^2,forsomec>0,provethat\frac{[1+{\left(\frac{dy}{dx}\right)}^2{]}^{\frac{3}{2}}}{\frac{d^{2}y}{d{x}^2}}isaconstantindependentofaandb.$

Write the negation of the following compound statement. 'There is a real number which is not a complex number'.

Evaluate the determinants..

$\left|\begin{array}{ccc}3& -1& -2\\ 0& 0& -1\\ 3& -5& 0\end{array}\right|$

$\left|\begin{array}{ccc}3& -4& 5\\ 1& 1& -2\\ 2& 3& 1\end{array}\right|$

$\left|\begin{array}{ccc}0& 1& 2\\ -1& 0& -3\\ -2& 3& 0\end{array}\right|$

$\left|\begin{array}{ccc}2& -1& -2\\ 0& 2& -1\\ 3& -5& 0\end{array}\right|$

A solid AB has zns structure if the radius of cation a is 100 pm what is the radius of a anion B

Differentiate the function with respect to x,

x inverse x cos x+x square +1/x square -1

Find the 4th term from the end in the expansion of ${(\frac{x^3}{2}-\frac{2}{x^2})}^9$

Find the number of $5$ digit numbers using digits $0,1,2,3,4,5$ (without repetition) such that they are divisible by $5$ :

If [.] denotes the greatest integer function, then which of the following is/are ture?

In a certain town , $60$% of the families own a car, $30$% own a house and $20$% own both a car and a house. If a family is randomly chosen, what is the probability that this family owns a car or a house but not both?

If from a point $P$, $3$ normals are drawn to parabola $y^2=4ax$, then the locus of $P$ such that one of the normal is angular bisector of other two normals is

Find the roots of the equation $x^2-2xcos\theta$ + 1 = 0.

Suppose $a,b,c$ are positive integers such that $2^a+4^b+8^c=328.$ Then $\frac{a+2b+3c}{abc}$ is equal to

The chord of the contact of tangents from a point $P$ to a circle passes through $Q$ ($Q$ lies outside the circle). If $a_1$ and $a_2$ are the lengths of the tangents from $P$ and $Q$ to the circle respectively, then $PQ$ is equal to

The multiplicative inverse of 7+5i is:

Solution of differential equation
$(x\frac{dy}{dx}+y)=e^{xy-1n{x}^2}(x\frac{dy}{dx}-y)$

The function f(x) = 3x + 1 is

The distance of the point (1, -5, 9) from the plane x - y + z = 5 measured along the line x = y = z is

A man running round a race course notes that the sum of the distances of two flag posts from him is 8 meters.The area of the path he encloses in square meters if the distance between flag posts is 4 is

The mean marks of $100$ students were found to be $40$. Later on it was discovered that a score of $53$ was misread as $83$. The corrected mean corresponding to the corrected score is

The number of points at which the function $f\left(x\right)=\{\begin{array}{cc}\left[\cos \pi x\right],& 0\le x\le 1\\ |x-1|[x-2],& 1<x\le 2\end{array}$
is discontinuous, is
$\left(\right[.]$ denotes the greatest integral function $)$