Explore topic-wise InterviewSolutions in Current Affairs.

A committee of $5$ men and $3$ women is to be formed out of $7$ men and $6$ women. If two particular women are not to be included together in the committee, then the number of committees formed is

If $z=a+ab$ lies in third quadrant, then $\frac{\overline{z}}{z}$ also lies in the third quadrant if

In the expansion of ${(1-x-x^2+x^3)}^6,$ the coefficient of $x^7$ is

Which of the following are equal matrixes.

$A=\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$
$B=\left[\begin{array}{ccc}1& 2& 4\\ 3& 5& 6\\ 7& 8& 9\end{array}\right]$
$C=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$
$D=\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$
$E=\left[\begin{array}{cc}1& 3\\ 2& 4\end{array}\right]$

Value of Maxima of ${\left(\frac{1}{x}\right)}^x$ is

If $z_1,z_2,z_3$ and $z_4$ are the roots of the equation $z^4+z^3+z^2+z+1=0$, then


$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \text{(A)}& \left|\sum _{i=1}^4(z_i{)}^4\right|\text{is equal to}& \text{(p)}& 0\\ \text{(B)}& \sum _{i=1}^4(z_i{)}^5\text{is equal to}& \text{(q)}& 4\\ \text{(C)}& \prod _{i=1}^4(z_i+2)\text{is equal to}& \text{(r)}& 1\\ \text{(D)}& \text{Least value of}[|z_1+z_2|]\text{is}& \text{(s)}& 11\end{array}$

$\text{where}\left[\right]$ represents greatest integer function

Which of the following is the correct combination

The equation of the hyperbola whose foci are (6,4) and (-4,4) and eccentricity 2. is

If a line makes angles ${90}^{\circ },{135}^{\circ },{45}^{\circ }$ with the positive X,Y and Z-axes respectively, find its direction cosines.

A toy company manufactures two types of dolls, A and B. Market tests and available resources have indicated that the combined production level should not exceed 1200 dolls per week and the demand for dolls of type B is at most half of that for dolls of type A. Further, the production level of dolls of type A can exceed three times the production of dolls of other type by at most 600 units. If the company makes profit of Rs 12 and Rs 16 per doll respectively on dolls A and B, how many of each should be produced weekly in order to maximise the profit?

A swimming pool is to be drained for cleaning . If L represents the number of liters of water in the pool t seconds after the pool has been plugged off to drain and $L=200(10-t{)}^2$, how fast is the water running out at the end of 5s and what is the average rate at which the water flows out during the first 5s?

Let $a_1,a_2,a_3,\dots$ be a G.P. with $a_1=a$ and common ratio $r,$ where $a$ and $r$ positive integers, then the number of ordered pairs $(a,r)$ such that $\sum _{r=1}^{12}{\log }_8{a}_r=2010$ is
(correct answer + 1, wrong answer - 0.25)

Find the equation of the circle circumscribing the triangle formed by the lines $L_1=0,L_2=0$and $L_3=0$

Find the total number of selections of A + B + C + D objects where A are alike (of $1^{st}$kind), B are alike (of $2^{nd}$ kind), C are alike (of $3^{rd}$ kind) and D are alike (of $4^{th}$ kind).

There are $2n$ guests at a dinner party. Supposing that the master and mistress of the house have fixed seats opposite one another, and that there are two specified guests who must not be placed next to one another, the number of ways in which the company can be placed is

If $acos\theta +bsin\theta =m$ and $asin\theta -bcos\theta =n$, then $a^2+b^2$ = ____

Which of the following are antonyms of the word Cognizant?

1) Apprehensive

2) Ignorant

3) Unaware

4) Unfamiliar

Using quadratic formula solve the abx²+(b²-ac)xv- bc =o for x

Find the point on x²+ y² + 2x= 0 where normals parallel to x axis.

Given that - 4 is a root of the equation $2x^3+6x^2+7x+60=0$. Find the other roots.

If $\frac{cosx}{a}=\frac{sinx}{b}$ then |acos2x + bsin2x| is equal to

Let A be the set of all 25 students of Class X in a school. Let : A → N be
function defined by () = roll number of the student . Then is:

In a triangle ABC, angle A is greater than B. If the measures of angles A and B satisfy the equation $3sinx–4si{n}^{3}x=k,0<k<1$, then the value of angle C is

If a and b are the roots of equation $x^2$ + 4x + p = 0 where P= ${\sum }_{r=0}^n$ $n_{c_r}$ $\frac{1+rx}{(1+nx{)}^r}$$(-1{)}^r$
then the value of $|a-b|$ is

[IIT Screening 2001]

A circle passes through $(–2,4)$ and touches the y-axis at $(0,2).$ Which one of the following equations can represent a diameter of this circle?

If $y=\left(\frac{ax+b}{cx+d}\right)$ , then $2\frac{dy}{dx}.\frac{d^{3}y}{d{x}^3}$ is equal to

The value of $\int \frac{\cos x}{\sin (x-\frac{\pi }{6})\sin (x+\frac{\pi }{6})}dx$ is equal to
$(C$ is a constant of integration$)$

The coordinates of the point of contact of the tangent to the parabola $y^2=16x$, which is perpendicular to the line $2x-y+5=0$ are

cos130° cos40°+ sin130° sin40° is

If m is a natural such that $m\le 5,$ then the probability that the quadratic equation $x^2+mx+\frac{1}{2}+\frac{m}{2}=0$ has real roots is

Find the value of expression ${\sum }_{i=1}^n{\sum }_{j=1}^i$1

The value of x in the given parallelogram is

If $|z-1|\le 2$ and $|\omega z-1-{\omega }^2|=a$ (where $\omega$ is a cube root of unity) then complete set of values of $a$ is

The angle of intersection of the curves $y^2=\frac{2x}{\pi }andy=sinx$ is

Express
$(cos2\theta +isin2\theta {)}^{-5}$ $(cos3\theta -isin3\theta {)}^6$ $(sin\theta -icos\theta {)}^3$
in the form of A+iB is

If $cos\theta =\frac{1}{2}(a+\frac{1}{a}),andcos3\theta =\lambda (a^3+\frac{1}{a^3}),then\lambda =$

If $x,y,z$ are not equal and $\ne 0,\ne 1$ the value of $\left|\begin{array}{ccc}\log x& \log y& \log z\\ \log 2x& \log 2y& \log 2z\\ \log 3x& \log 3y& \log 3z\end{array}\right|$ is equal to

The area of the region bounded by the curve $y=x^{2}andy=se{c}^{-1}[-si{n}^{2}x],$ (where [.] denotes the greatest integer function), is

If $\int (2-3si{n}^{2}x)\sqrt{secx}dx=2f\left(x\right)\sqrt{g\left(x\right)}+c$ and f(x) is non constant function then

The eccentricity of the hyperbola $3x^2-4y^2=-12$ is