Explore topic-wise InterviewSolutions in Current Affairs.

The value of x for which $co{s}^{-1}\left(cos4\right)>3x^2-4x$ is

If a, b, c are in A.P., prove that the straight lines $ax+2y+1=0,bx+3y+1=0$ and $cx+4y+1=0$ are concurrent.

Which one of the following has a square planar geometry?

Using all the letters of the word PROBLEM how many words can be formed such that the consonants occupy the middle place ?

Football teams $T_1$ and $T_2$ have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of $T_1$ winning, drawing and losing a game against $T_2$ are $\frac{1}{2},\frac{1}{6}$ and $\frac{1}{3}$, respectively. Each team gets 3 points for a win, 1 point for a draw and 0 points for a loss in a game. Let $X$ and $Y$ denote the total points scored by teams $T_1$ and $T_2$, respectively, after two games.

$P(X=Y)$ is

If(1+x)^n =C0+C1x+C2x^2+......Cnx^n, prove that

1) 3C0-8C1+13C2-18C3+.....upto (n+1) terms

In Triangle ABC. Line joining the Circum-centre and Ortho-centre is Parallel to side AC, then value of tan A tan C is equal to

The $\text{cosine}$ of the angle between any two diagonals of a cube is

If A and B are two independent events such that $P(\overline{A}\cap B)=\frac{2}{15}$ and $P(A\cap \overline{B})=\frac{1}{6}$, then P(B) is

Consider lines

$L_1:\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k}$

$L_2:\frac{x-1}{2}=\frac{y-4}{2}=\frac{z-5}{1}$

Equation of plane containing these lines is

Statements: U + V, W - Y, Y $\times$ U

Conclusions:

I. W + U

II. W $÷$ V

The lie $x-b+\lambda y=0$ cuts the parabola $y^2=4ax$ at $P\left(t_1\right)$ and $Q\left(t_2\right)$. If $b\in [2a,4a]$ and $\lambda \in R$, then the value(s) $\left[t_1{t}_2\right]$ is/are
(where $[.]$ repreasents the greatest integer function and $t_1,t_2$ are parametic points)

If $\frac{x(4^x-1)(3^x-9)}{({\log }_{2}x-1)(|x|-2)}\ge 0$, then $x\in$

Time taken by the projectile to reach $B$ from $A$ is $t$. Then the distance $AB$ is equal to

The direction cosines of the z-axis is equal to

If the point $(\alpha ,{\alpha }^2)$ lies between $x+y-2=0$ and $4x+4y=3,$ then the range of $\alpha$ is

Which of the following is/are not an identity relation on the set $A=\{a,b,c\}$

${\int }_0^{\frac{\pi }{2}}\frac{\sqrt{cotx}}{\sqrt{cotx}+\sqrt{tanx}}dx=$ [MP PET 1990, 95; IIT 1983; MNR 1990]

Find the probability that a randomly chosen three-digit number has exactly three factors.

From $P(–4,0)$, tangents $PA$ and $P{A}^{\prime }$ are drawn to a circle, $x^2+y^2=4$. Where $A$ and $A^{\prime }$ is point of contact and $A$ lies above x-axis. Rhombus $PA{P}^{\prime }{A}^{\prime }$ is completed.

$\begin{array}{cccccc}& \text{Column-I}& & \text{Column-II}& & \text{Column-III}\\ \left(I\right)& A\equiv (-1,\sqrt{3})& \left(i\right)& PA=2\sqrt{3}& \left(P\right)& P^{\prime }\text{lies on the circle},x^2+y^2=4\\ \left(II\right)& A^{\prime }\equiv (-1,-\sqrt{3})& \left(ii\right)& \text{Area of}\Delta PA{A}^{\prime }=3\sqrt{3}\text{sq.units}& \left(Q\right)& \Delta PA{A}^{\prime }\text{is equilateral}\\ \left(III\right)& P^{\prime }=(4,0)& \left(iii\right)& P{P}^{\prime }=6& \left(R\right)& P^{\prime }\text{lies outside the circle},x^2+y^2=4\\ \left(IV\right)& P^{\prime }=(2,0)& \left(iv\right)& \text{Area of}\Delta PA{A}^{\prime }=4\sqrt{3}\text{sq.units}& \left(S\right)& P^{\prime }\text{lies inside circle},x^2+y^2=4\end{array}$

Which one of the following is correct?

Ttwo lines whose d.c's are related by al+bm+cn=0, fmn +gnl +hlm =0 are perpendicular, if

If the sum of an infinite decreasing G.P. is 3 and the sum of the squares of its term is $\frac{9}{2}$, then write its firstterm and common difference.

The equation of the plane through $(1,2,-3)$ and $(2,-2,1)$ and parallel to $X-$ axis is

Write the area of the triangle having vertices at(a,b+c),(b,c+a),(c,a+b).

Suppose $S_1$ and $S_2$ are two unequal circles; AB and CD are the direct common tangents to these circles. A transverse common tangent PQ cuts AB at R and CD at S. If AB = 10, then RS is

Concentric circles of radius $1,2,3,\dots ,100$ units are drawn such that the interior of the smallest circle is coloured red and the angular regions are coloured alternatively green and red, so that no two adjacent regions are of the same colour. Then the area of green region (in sq. units) is

There are $5$ multiple choice questions (only one correct option) in test. If the first three questions have $4$ choices each and the next two have $5$ choices each, then number of possible ways in which a student can answers all the question is

If the ratio of the $5^{\text{th}}$ term from the beginning to the $5^{\text{th}}$ term from the end in the expansion of ${(\sqrt[4]{42}+\frac{1}{\sqrt[4]{43}})}^n$ is $\sqrt{6}:1,$ then the value of $n$ is

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

Let three points $A(2,3,4),B(3,4,2)$ and $C(4,2,3)$ in space are given. A point $D$ in space is such that it is at a distance of $\sqrt{6}$ units from the three given points. The volume of tetrahedron $ABCD$ is -

Let $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,a>b$, be an ellipse with foci $F_1$ and $F_2$. Let $AO$ be its semi-minor axis, where $O$ is the centre of the ellipse. The lines $A{F}_1$ and $A{F}_2$, when extended, cut the ellipse again at points $B$ and $C$ respectively. Suppose that the triangle $ABC$ is equilateral. Then the eccentricity of the ellipse is

The number of points of intersection of the two curves y=2sin x and $y=5x^2+2x+3$ is

Write the following relations as sets of ordered pairs and find which of them are functions :
(i) $\left\{\right(x,y):y=3x,xϵ(1,2,3),yϵ(3,6,9,12\left)\right\}$
(ii) $\left\{\right(x,y):y>x+1,x=1,2\}$ and y = 2, 4, 6
(iii) $\left\{\right(x,y):x+y=3,x,yϵ\{0,1,2,3\left\}\right\}$