Explore topic-wise InterviewSolutions in Current Affairs.

Given that $a.b=0$ and $a\times b=0$. What can you conclude about the vectors a and b?

${lim}_{n\to \infty }\left[\frac{1-2+3-4+5-6+\cdots (2n-1)-2n}{\sqrt{n^2+1}+\sqrt{n^2-1}}\right]$ is equal to

If z₁ and z₂ are two non-zero complex such that $\mid z_1+z_2\mid =\mid z_1\mid +\mid z_2\mid ,$ then arg $\left(z_1\right)-$ arg $\left(z_2\right)$ is equal to

The interval in which the function $f\left(x\right)=2x^3–3x^2–36x+7$ is strictly increasing is

If${\int }_0^{\pi }xf\left(sinx\right)dx=A{\int }_0^{\frac{\pi }{2}}f\left(sinx\right)dx,$ then A=

The mean and the variance of five observations are $4$ and $5.20$, respectively. If three of the observations are $3,4$ and $4$ ; then the absolute value of the difference of the other two observations, is :

Let $k$ be the non-zero real number such that the quadratic equations $k{x}^2+2x+k=0$ has two distinct real roots $\alpha and\beta (\alpha <\beta ).$

If $\beta <\sqrt{2}+\alpha$, then

If $xϵ[-1,1],thenrangeofta{n}^{-1}(-x)$ is

There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is

The number of solutions of the equation $1+{\sin }^{4}x={\cos }^{2}3x,x\in [-\frac{5\pi }{2},\frac{5\pi }{2}]$ is :

Show that the statement

p : " if x is a real number such that $x^3+x=0$ then x is 0 " is true by

(i) direct method

(ii) method of contrapositive

(iii) method of contradition.

Find the coordinates of the vertices of a triangle, the equations of whose sides are :

$\left(i\right)x+y-4=0,2x-y+3=0andx-3y+2=0$ $\left(ii\right)y(t_1+t_2)=2x+2a{t}_1{t}_2,y(t_2+t_3)=2x+2a{t}_2{t}_{3}and,y(t_3+t_1)=2x+2a{t}_1{t}_3.$

If ${}^{15}{C}_r{:}^{15}{C}_{r-1}=11:5$, find r.

Let $f$ and $g$ be continuous function on $[0,a]$ such that $f\left(x\right)=f(a-x)$ and $g\left(x\right)+g(a-x)=4,$ then $\underset{0}{\overset{a}{\int }}f\left(x\right)g\left(x\right)dx$ is equal to :

The two equations $x^3+1=0$ and $a{x}^2+bx+c=0,a,b,c\in R$ have two roots in common. Then $a+b$ is equal to

(a) If A and B be mutualy exclusive events associated with a random experiment such that P(A) = 0.4 and P(B) = 0.5, then find :
(i) $P(A\cup B)$ (ii) $P(\overline{A}\cup \overline{B})$

(iii) $P(\overline{A}\cup B)$ (iv) $P(A\cup \overline{B})$

(b) A and B are two events such that P(A)= 0.54, P(B) = 0.69 and $P(A\cup B)$ = 0.35. Find:

(i) $P(A\cup B)$ (ii) $P(\overline{A}\cup \overline{B})$

(iii) $P(A\cup \overline{B})$ (iv) $P(B\cup \overline{A})$

(c) Fill in the blanks in the following table :

P(A) P(B)

$P(A\cap B)$ $P(A\cup B)$

(i) $\frac{1}{3}$ $\frac{1}{5}$ $\frac{1}{15}$___

(ii) 0.35 ___ 0.25 0.6

(iii) 0.5 0.35 ___ 0.7

Which among the following is\are function(s)

If $p:x$ is odd; $q:x^2$ is odd. Then "$x$ is odd and $x^2$ is not odd", is represented as

If $A=\left[\begin{array}{cc}-8& 5\\ 2& 4\end{array}\right]$ satisfies the equation $x^2+4x-p=0,thenp=$

If $B_0=\left[\begin{array}{ccc}-4& -3& -3\\ 1& 0& 1\\ 4& 4& 3\end{array}\right],B_n=\text{adj}\left(B_{n-1}\right),\forall n\in N$ and $I$ is identity matrix of order $3.$ Then $B_1+B_3+B_5+B_7+B_9$ is equal to

Let $S$ be the set of all column matrices $\left[\begin{array}{c}{b}_1\\ b_2\\ b_3\end{array}\right]$

such that $b_1,b_2,b_3\in R$ and the system of equations (in real variables)

$$\begin{array}{c}-x+2y+5z=b_1\\ 2x-4y+3z=b_2\\ x-2y+2z=b_3\end{array}$$

has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for each $\left[\begin{array}{c}{b}_1\\ b_2\\ b_3\end{array}\right]\in S$?

The product of slope of tangents from point $(0,1)$ to the circle $x^2+y^2-2x+4y=0$ is

If the domain of the function $f\left(x\right)={\log }_e\left({\log }_{|\cos x|}\right(x^2-7x+26)-\frac{4}{{\log }_2|\cos x|})$ is set $A$, then $A$ contain(s) the interval(s)

Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find E(X).

Find the value of $\underset{x\to 0}{lim}{x}^{2}sin\left(\frac{1}{x}\right)$ using sandwich theorem.

If R = {$(x,y):x,yϵZ,x^2+y^2\le 4$} is a relation on Z, then domain of R is

If $\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]A\left[\begin{array}{cc}-3& 5\\ 2& -4\end{array}\right]=\left[\begin{array}{cc}1& -5\\ 11& -27\end{array}\right]$, then the matrix $A$ is equal to

Find $\frac{1}{2}$${}^n{C}_1$ - $\frac{2}{3}$${}^n{C}_2$ + $\frac{3}{4}$${}^n{C}_3$.................$\frac{(-1{)}^{n+1}n}{n+1}$×${}^n{C}_n$

Find a unit vector perpendicular to each of the vectors a + b and a - b, where $a=3\hat{i}+2\hat{j}+2\hat{k}$ and $b=\hat{i}+2\hat{j}-2\hat{k}$

Which of the following functions are Monotonically increasing functions throughout the domain?

The negation of the statement $(p\vee q)\wedge r$ is

A line meets the coordinate axes in A and B. If a circle is circumscribed about the $\Delta$ AOB . If m, n are the distances of the tangent to the circle at the origin from the points A and B respectively,The diameter of the circle is

If $\int f\left(x\right)dx=\psi \left(x\right)\text{, then}\int x^{5}f\left(x^3\right)dx$ is equal to

The area inside the parabola $5x^2–y=0$ but outside the parabola $2x^2–y+9=0$ is

$\left|\begin{array}{ccc}x+y+2z& x& y\\ z& y+z+2x& y\\ z& x& z+x+2y\end{array}\right|=2(x+y+z{)}^3$

If circle $x^2+y^2-6x-10y+c=0$ does not touch (or) intersect the coordinates axes and the point $(1,4)$ is inside the circle, then the range of $c$ is

What is the locus of the point for which y = 0, z = 0?

Two straight line intersect at a point $O.$ Points $A_1,A_2,...A_n$ are taken on a line and points $B_1,B_2,...B_n$are taken on the other line. If the point $O$ is not to be used, then number of triangles that can be drawn using these points as vertices, is

${\int }_0^{\frac{\pi }{4}}ta{n}^{2}xdx=$ [Roorkee 1983, Pb. CET 2000]

A stone is dropped into a quiet lake and waves moves in circles at a speed of $3cm/s$. At the instant, when the radius of the circular wave is $10cm$, then the rate at which its perimeter is increasing is

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are non-coplanar vectors and $\overrightarrow{d}=\lambda \overrightarrow{a}+\mu \overrightarrow{b}+\nu \overrightarrow{c},$ then $\lambda$ equal to

In a G.P., $T_2$ + $T_5$ = 216 and $T_4$ :$T_6$ = 1:4 and all terms are integers, then its first term is