Explore topic-wise InterviewSolutions in Current Affairs.

The set of value(s) of $b$ for which function $f\left(x\right)=\{\begin{array}{cc}{x}^2+b^2-5b+6,& x<0\\ x,& x\ge 0\end{array}$ has a point of minima at $x=0,$ is

Let $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ be three vectors and are such that $\overrightarrow{a}\times \overrightarrow{b}=3(\overrightarrow{a}\times \overrightarrow{c}),|\overrightarrow{a}|=|\overrightarrow{c}|=2,|\overrightarrow{b}|=5,|\overrightarrow{b}\times \overrightarrow{c}|=5\text{and if}\overrightarrow{b}-3\overrightarrow{c}=\lambda \overrightarrow{a},$ then a value of ${\lambda }^2$ is

A natural number x is chosen at random from the first one hundred natural numbers. The probability that $\frac{(x-20)(x-40)}{x-30}<0$ is

6 girls and 5 boys sit together randomly in a row, the probability that no two boys sit together, is

Let $F_1(x_1,0)$ and $F_2(x_2,0),$ for $x_1<0$ and $x_2>0,$ be the foci of the ellipse $\frac{x^2}{9}+\frac{y^2}{8}=1.$ Suppose a parabola having vertex at the origin and focus at $F_2$ intersects the ellipse at point $M$ in the first quadrant and at point $N$ in the fourth quadrant.



The orthocentre of the triangle $F_{1}MN$ is

Using the method of completion of squares find one of the roots of the equation $2x^2-7x+3=0$. Also, find the equation obtained after completion of the square.

Tangents are drawn to the hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$

parallel to the straight line $2x-y=1$ The points of contacts of the tangents on the hyperbola are

$x=1+a+a^2+...\infty (a<1)$

$y=1+b+b^2+...\infty (b<1)$

Then the value of $1+ab+a^2{b}^2+.....\infty$ is

[MNR 1980; MP PET 1985]

If $y=\sec \left({\tan }^{-1}x\right)$, then $\frac{dy}{dx}$ at $x=1$ is equal to :

A ray of light along $x+\sqrt{3}y=\sqrt{3}$ gets reflected upon reaching X-axis, the equation of the reflected ray is

Let $\omega =\frac{\sqrt{3}+i}{2}\text{and}P=\{{\omega }^n:n=1,2,3,...\}.$ Further $H_1=\{zϵC;Rez>\frac{1}{2}\}\text{and}{H}_2=\{zϵC:Rez<\frac{-1}{2}\},$ where  is the set of all complex numbers. If $z_1ϵp\cap H_1,z_2ϵP\cap H_2$ and O represents the origin, then $\angle z_{1}O{z}_2=$

The common difference of the $A.P$. $b_1,b_2,.....b_m$ is $2$ more than the common difference of $A.P$. $a_1,a_2,.....a_n$. If $a_{40}=-159$, $a_{100}=-399$ and $b_{100}=a_{70}$, then $b_1$ is eqaul to

The ellipse $E_1:\frac{x^2}{9}+\frac{y^2}{4}=1$ is inscribed in a rectangle $R$ whose sides are parallel to the coordinate axes. Another ellipse $E_2$ passing through the point $(0,4)$ circumscribes the rectangle $R.$ The Eccentricity of the ellipse $E_2$ is

A (5,3),B(3,-2) are two fixed points; find the equation to the equation to the locus of a point P which moves so that the area of the triangle PAB is 9 uints.

The value of $\int \frac{3x^{13}+2x^{11}}{(2x^4+3x^2+1{)}^4}dx$ is equal to

(where $C$ is constant of integration )

Three collinear vectors $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$ are such that $x\cdot \overrightarrow{a}-\overrightarrow{b}+(x^2-1)\overrightarrow{c}=\overrightarrow{0},$ then the value(s) of $x$ is(are)

The set of points in $C$ satisfying the inequality $\left|\arg \right(z)-\frac{\pi }{2}|<\frac{\pi }{2}$ is

Find the missing term.

Find the sum of the series whose nth term is :

(i) $2n^3+3n^{3-1}$

(ii) $n^3-3^n$

(iii) $n^{(}n+1\left)\right(n+4)$

(iv)$(2n-1{)}^2$

A commitee of six persons is chosen from ten men and seven women so as to contain at least three men and two women. If two particular women refuse to serve on the same committee, the number of ways of forming the committee is

If $\left|\frac{|x|+2}{|x^2|+2|x|}\right|>\frac{1}{2}$, then $x\in$

If the volume of the tetrahedron with edges $\hat{i}+\hat{j}+\hat{k},\hat{i}+a\hat{j}+\hat{k}$ and $\hat{i}+2\hat{j}-\hat{k}$ is $6$ cubic units, then $a$ is