Explore topic-wise InterviewSolutions in Current Affairs.

Find the domain and the range of the real function, $f\left(x\right)=\frac{x^2+1}{x^2-1}$

A fair coin is tossed four times, and a person win Re 1 for each head and lose Rs 1.50 for each tail that turns up. From the sample space calculate how many different amounts of money you can have after four tosses and the probability of having each of these amounts.

The x coordinate of a point on the line joining the points P(2,2,1) and Q(5,1,-2) is 4.Find its z-coordinate.

Find the graph of the function $f\left(x\right)=a^x$ where $0<a<1.$

Solution set of $lo{g}_3(x^2-2)<lo{g}_3(\frac{3}{2}\left|x\right|-1)$ is

A block comes down a stationary inclined plane of angle of inclination $\theta$ with a constant velocity. The acceleration with which the incline should be moved towards right horizontally so that the block now moves upwards with constant velocity is

A matrix $A$ is such that $A^2=2A-I$, where $I$ is unity matrix, then for $n\ge 2$, $A^n$ is equal to

The locus of the foot of perpendicular from the origin on each member of the family (4a+3)x-(a+1)y-(2a+1)=0 is

$sin{50}^0$ - $sin{70}^0$ + $sin{10}^0$ =

[MNR 1979]

State the converse and contrapositive of each of the following statements :

(i) If it is hot outside, then you feel thirsty.

(ii) I go to a beach whenever it is a sunny day.

(iii) A spositive integer is prime only if it has no divisors other than 1 and itself.

(iv) If you live in Delhi, then you have winter clothes.

(v) If a quadrilateral is a parallelogram, then its diagonals bisect each other.

A die marked 1,2,3 in red and 4,5,6 in green is tossed. Let A be the event, 'number is even' and B be the event, 'number is red'. Are A and B independent ?

What is the condition for a line $y=mx+c$ to be a tangent to the parabola$(y-k{)}^2=4a(x-h)$.

The value of $\int \frac{e^{6\log x}-e^{5\log x}}{e^{4\log x}-e^{3\log x}}dx$ is equal to

The value of $2{\sin }^2\frac{\pi }{6}+{\text{cosec}}^2\frac{7\pi }{6}\cdot {\cos }^2\frac{\pi }{3}$ is

What type of function is the exponential function e^x function on R ?

The coefficient of x⁴ in the expansion of (x^1/2 - x^2/3)⁷ is:

$\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+\frac{1}{16.21}+...+\frac{1}{(5n-4)(5n+1)}$

If f(x+2y, x-2y)=xy, then f(x, y) equals

If $\sum _{r=0}^n{\left(\frac{{}^n{C}_{r-1}}{{}^n{C}_r+{}^n{C}_{r-1}}\right)}^3=\frac{25}{24},$ then the value of $n$ is

If the circles $x^2+y^2+2ax+c=0and{x}^2+y^2+2by+c=0$ touch each other, then c is _________.where $a\&bϵR$.

A point P lying inside the curve $y=\sqrt{2ax-x^2}$ is moving such that its shortest distance from the curve at any position is greater than its distance from x-axis. The point P enclose a region whose area is equal to

If $z$ = $x+iy$, $|z+1|$ = $|z-1|$ and arg $⟮\frac{z-1}{z+1}⟯$ = $\frac{\pi }{4}$, then z =

Show that if A is a subset of B then C-B is a subset of C-A

If $y=\left|\begin{array}{ccc}f\left(x\right)& g\left(x\right)& h\left(x\right)\\ 1& m& n\\ a& b& c\end{array}\right|$
Then $\frac{dy}{dx}$ is equal to

Number of functions from a set $A$ containing $6$ elements to a set $B$ containing $3$ elements such that every element in $B$ has atleast one preimage is

The third term from the end in the expansion of ${(\frac{3x}{5}-\frac{5}{2x})}^8$ is

Using elementary transformations, find the inverse of the followng matrix.

$\left[\begin{array}{cc}2& 3\\ 5& 7\end{array}\right]$

In the expansion of ${(x^2-\frac{1}{3x})}^9$, the term without x is equal to

A unit vector $\overrightarrow{a}$ makes an angle of $45°$ with positive $z-$axis and if $\overrightarrow{a}+\hat{i}+\hat{j}$ is a unit vector, then $\overrightarrow{a}=$

Find the equation of the circle which circumscribes the triangle formed by the lines:
(i) $x+y+3=0,x-y+1=0$ and $x=3$
(ii) $2x+y-3=0,x+y-1=0$ and $3x+2y-5=0$
(iii) $x+y=2,3x-4y=6$ and $x-y=0.$
(iv) $y=x+2,3y=4x$ and $2y=3x$.

Sum the following series to n terms : 3+5+9+15+23+....

If ${\overline{x}}_1$ and ${\overline{x}}_2$ are the means of two distributions such that ${\overline{x}}_1<{\overline{x}}_2$ and $\overline{x}$ is the mean of the combined
distribution, then

Find the square root of the following complex numbers :

(i) -5 + 12 i

(ii) -7 - 24i

(iii) 1 - i

(iv) - 8 - 6i

(v) 8 - 15i

(vi) -11 - 64 $\sqrt{-1}$

(vii) 1 + 4 $\sqrt{-3}$

(viii) 4i

(ix) - i

The value of is $si{n}^{-1}\left(\frac{\sqrt{3}}{2}\right)-si{n}^{-1}\left(\frac{1}{2}\right)$ is

If $\theta$ lies in the first quadrant and cos $\theta =\frac{8}{17}$, then the value of $cos({30}^{\circ }+\theta )+cos({45}^{\circ }-\theta )+cos({120}^{\circ }-\theta )$ is

If the equation $\frac{x^2-bx}{ax-c}=\frac{m-1}{m+1}$ has roots equal in magnitude but opposite in sign, then m =

The sum of $20$ terms of the progression $\frac{1}{4},-\frac{1}{2},1,-2,4,\dots \dots$ is

A committee of $5$ members is to be formed from $6$ boys and $5$ girls. The number of ways in which the committee can be formed so that the committee must contain atleast one boy and one girl having majority of boys is

Consider an 'n' sided regular polygon with the origin as its centre. If $z_1$ be the complex number representing a vertex $a_1$ of the polygon, then the number associated with the vertex that is adjacent to $a_1$ is

The equation of the normal at the point (6,4) on the hyperbola $\frac{x^2}{9}-\frac{y^2}{16}=3$ is

Which of the following represents the condition for a matrix A to be hermitian Matrix. Given that the general element of the matrix is aij.

Which of the following points lie on XZ plane?

The figure shows a portion of the graph $y=2x-4x^3$. The line y = c is such that the areas of the regions marked I and II are equal. If a,b are the x-coordinates of A,B respectively, then a + b equals