Explore topic-wise InterviewSolutions in Current Affairs.

Show that the solution set of the following linear in equations is an unbounded set :

$x+y\ge 9,3x+y\ge 12,x\ge 0,y\ge 0$

$\text{If}f\left(z\right)=\frac{7-z}{1-z^2},\text{wehre}z=1+2i,\text{then}|f\left(z\right)|\text{is}$

A black and a red die are rolled.
Find the conditional probability of obtaining the sum 8 given that the red die resulted in a number less than 4.

${\int }_0^{\pi }xsinxco{s}^{2}xdx$

Show that $2^{4n+4}-15n-16,$ where $nϵN$ is divisible by 225.

If for non-zero x, $af\left(x\right)+bf\left(\frac{1}{x}\right)=\frac{1}{x}-5$, where $a\ne b$, find f(x).

Tan inverse minus x =-tan inverse x

Oct inverse minus x =π-cot inverse x

Sec inverse minus x =π-sec inverse x

Costco inverse minus x =-cosec inverse x

Prove that $\frac{\text{cos}x}{(1-sinx)}=tan(\frac{\pi }{4}+\frac{x}{2})$

Probability that given two digit number is divisible by 2,3 and 5 is,

In how many ways five different balls be arranged so that two particular balls are never together ?

If $\sqrt{3}\cot x-\text{cosec}x=1$, then $x$ can be
(where $n\in Z$)

Study the following information carefully and answer the questions below.

A team of five is to be selected from amongst five boys A, B, C, D and E and four girls P, Q, R and S. Some criteria for selection are—

Unless otherwise stated, these criteria are applicable to all questions below.

Q66. If two of the members are girls and D is one of the members, the members of the team other than D are:

Find the maximum and minimum values, if any, of the following function given by,

$h\left(x\right)=sin\left(2x\right)+5$

Assume X,Y,Z, W and P are matrices of orders $2\times n,3\times k,2\times p,n\times 3andp\times k$ respectivley.

The restrictions on n,k and p so that PY+WY will be defined are
(a)k=3, p=n
(b)k is arbirary, p=2
(c)p is arbitary
(d)k =2, p =3

Let A be an invertible 2 x 2 real matrix. If A^-1 =then det(12A) equals:

A black and a red die are rolled.
Find the conditional probability of obtaining a sum greater 9 than given that the black die resulted in a 5.

Find the conditional probability of obtaining the sum 8 given that the red die resulted in a number less than 4.

$ta{n}^{-1}\frac{1}{5}+ta{n}^{-1}\frac{1}{7}+ta{n}^{-1}\frac{1}{3}+ta{n}^{-1}\frac{1}{8}=\frac{\pi }{4}$

1. How many times must a man toss a fair coin so that the probability of having atleast one one head is more than 90%

If $\frac{si{n}^{4}x}{2}+\frac{co{s}^{4}x}{3}=\frac{1}{5}$ , prove that $ta{n}^{2}x=\frac{2}{3}$

How many times must a man toss a fair coin so that the probability of having atleast one head is more than $90\%$?

A tangent to the parabola $y^2=4ax$ meets x axis at a point T. This tangent meets the tangent at the vertex at point P. If rectangle TAPQ is completed then the locus of Q is.

5 countries president and prime minister went for a summit. If all 5 prime ministers shake hand to president at random, in how many ways they can shake hand if all 5 PMs shake hand only to their country president only.

A line segment $AB$ of length $2$ units, where $A=(1,0)$ is rotated in anticlockwise direction through an angle ${15}^{\circ }$ about $A$. If initially $AB$ is making an angle ${45}^{\circ }$ with the positive direction of $X$- axis in anticlockwise direction, then the distance between origin and the new position of $B$ is

F is

The general solution(s) of $\theta$ satisfying the equation ${\tan }^2\theta +\sec 2\theta =1$ can be (where $n\in Z$)

If $z$ is a complex number satisfying $|z{|}^2–|z|-2<0$, then the value of $|z^2+zsin\theta |$, for all values of $\theta$, is

In a polygon no three diagonals are concurrent .if the total no of point of intersection of diagonal s is 70..no of diagonals of polygon

Ans 20

Pls explain in detail without giving just formula

If $xϵ[-1,1],$ then the range of ${\tan }^{-1}(-x)$ is

The value of $\left\{\frac{3^{2003}}{28}\right\}$ , where {.} denotes the fractional part, is equal to :

If $R=\left\{\right(x,y):x,y\in W,x^2+y^2=25\}$,
then the number of elements in $R$ is

If $\sqrt{\sqrt{2x}+\sqrt{-x^4-1}}=a+ib$, Find the value of $a^2-b^{2}and4a^2{b}^2$

Shape of the feasible region formed by the following constraints is

X + y ≤ 2, x + y ≥ 5, x ≥ 0, y ≥ 0

p $\to$ (q $\vee$ r) is false, then the true values of p, q, r respectively are

The volume of cube is increasing at the constant rate of 3 cm³/s. Find the rate of change of edge of the cube when its edge is 5 cm.

If the coefficient of $x^7$ in $(a{x}^2+\frac{1}{bx}{)}^{11}$ is equal to the coefficient of $x^{-7}$ in $(ax-\frac{1}{b{x}^2}{)}^{11}$, then ab =

If |x| < 1 and $y=x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+........thenx=$

The value of $\underset{x\to \infty }{lim}{\left(\frac{p^{1/x}+q^{1/x}+r^{1/x}+s^{1/x}}{4}\right)}^{3x},$ where $p,q,r,s>0$ is equal to

Prove that the area of the parallelogram formed by the lines.

$a_{1}x+b_{1}y+c_1=0,a_{1}x+b_{1}y+d_1=0,a_{2}x+b_{2}y+c_2=0,a_{2}x+b_{2}y+d_2=0$ is $\left|\frac{(d_1-c_1)(d_2-c_2)}{a_1{b}_2-a_2{b}_1}\right|$ sq. units.

Deduce the condition for these lines to form a rhombus.

If $P=[a_{ij}{]}_{n\times n}$ be any matrix and it is non singular matrix. If |P| = |Q| = 1 and adj B = A, then $adj\left(Q^{-1}B{P}^{-1}\right)$ is

The value of ${lim}_{x\to 0}\frac{\sqrt{a^2-ax+x^2}-\sqrt{a^2+ax+x^2}}{\sqrt{a+x}-\sqrt{a-x}}$ is