Explore topic-wise InterviewSolutions in Current Affairs.

Which of the following options look similar to the sum of the given 4 vectors ?

The number of natural numbers less than 1000 in which no two digits are repeated is

Determine f(0) so that the function f(x) defined by f(x) = (4x-1)³ / [sinx/4 log(1+x²/3) becomes continuous at x=0.

Let f: n⁺ to n⁺ be a function satisfying the relation f( x. f (y))= f (x .y) + X for all xy belonging to R then

Lim. [ ( f(x))^1/3-1]÷[(f(x))^1/2-1]=______

X----->0

Solve the following system of equations in R.

$-5<2x-3<5$

The ratio of the $5^{th}$ term from the beginning to the $5^{th}$ term from the end in the binomial expansion of ${(2^{\frac{1}{3}}+\frac{1}{2(2{)}^{\frac{1}{3}}})}^{10}$ is:

The angles of a quadrilateral are in A.P. whose common difference is ${10}^{\circ }$. Find the angles.

Solve the following system of equations in R.

$3x-1\ge 5,x+2>-1$

In a class of 175 students the following data shows the number of students one or more subjects. Mathematics 100 ; Physics 70; Chemistry 40; Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and Chemistry 23 ; Mathematics ,Physics and Chemistry 18. How many students have offered Mathematics alone ?

If $S_1,S_2,S_3,....S_m$ are the sums of n terms of m A.P.'s whose first terms are 1,2,3,.....,m\) and common differences are $1,3,5,....2m-1$ respectively, then $S_1+S_2+S_3+....S_m=$

If the function $f$ defined as $f\left(x\right)=\frac{1}{x}-\frac{k-1}{e^{2x}-1},x\ne 0,$ is continuous at $x=0$,then the ordered pair $(k,f\left(0\right))$ is equal to:

tan $9^{\circ }$ - tan ${27}^{\circ }$ - tan ${63}^{\circ }$ + tan ${81}^{\circ }$ =

6 boys and 6 girls sit in a row at random. The probability that all the girls sit together is

The minimum value of $x^2+y^2$, when $x+y=a$, where $a$ is a positive odd integer and $x,y$ are non negative integers is

Two balls are drawn at random from a bag containing 2 white, 3 red. 5 green and 4 black balls, one by one without, replacement. Find the probabilitythat both the balls are of different colours.

In class 11 math if we study chapter SETS,PERMUTATION AND COMBINATION AND PROBABLITY FIRST then their is also a need of another concept of any other chapter of class 11 for these all chapter?

Five numbers are in A.P., whose sum is $25$ and product is $2520$. If one of these five numbers is $-\frac{1}{2}$, then the greatest number amongst them is

A circle touching the $x$-axis at $(3,0)$ and making an intercept of length $8$ on the $y$-axis passes through the point :

The domain of the function $f\left(x\right)=\frac{\sin \left(\log \right(x^2-4x+4\left)\right)}{\left(\right[x]-1)}$, where $[.]$ denotes the greatest integer function, is

Two plane mirrors AB and BC are inclined at angle $\theta$ as shown in figure. If mirror AB is horizontal and emergent ray after two reflections is vertical, then $\theta$ is

If k is scalar $(k\ne 0)$, I is an identity matrix and A is a square matrix . Then which among the following will always be a scalar matrix.

The medians AD and BE of a triangle with vertices $A(0,b),B(0,0)$ and $C(a,0)$ are perpendicular to each other, if

Tangents are drawn from the origin to the curve y = sin x, then their point of contact lie on the curve

Find the position vector of point R which divides the line joining two points P(2a + b) and Q(a - 3b) externally in the ratio 1 : 2. Also, show that P is the middle point of the line segment RQ.

If a circle passes through the point (0, 0), (a, 0), (0, b), then find the coordinates of its centre.

If ${}^{16}{C}_{2r}{=}^{16}{C}_{r+2^{\prime }}$ find ${}^r{C}_4$

Find the area enclosed between the curve $y=5x-x^{2}andy=x$ .

The number $(101{)}^{100}–1$ is divisible by

Find the number of numbers, greater than a million, that can be formed with the digits 2,3,0,3,4,2,3.

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

Let $\alpha$ be the angle between the lines whose direction cosines satisfy the equations $l+m-n=0$ and $l^2+m^2-n^2=0$. Then the value of ${\sin }^4\alpha +{\cos }^4\alpha$ is :

State whether the following statements are true or false :

(i) 1 $ϵ$ {1, 2, 3} (ii) a $\subset$ {b, c, a}

(iii) {a} $\subset$ {a, b, c}

(iv) {a, b} = {a,a,b,b, a}

(v) The set {x : x +8=8} is the null set.

The equation $\frac{x^2}{2-\lambda }+\frac{y^2}{\lambda -5}+1=0$ represents an ellipse, if

The minimum distance between the curves $x^2=4y$ and $x^2+y^2+18x+12y+81=0$

Identify the function from the description given.

1. Its an irrational function

2. Its graph is mirror image of y =$x^{2n}$ about y = x, for some n $\ge$ 1, n $\in$ I and x $\ge$ 0

3. x $\le$ f(x) $\le$ $x^{1/6}$ if x $\in$ [0, 1]

4. Its domain and range are [0, $\infty$)

Let $f\left(x\right)=\{\begin{array}{cc}1+x,& 0\le x\le 2\\ 3-x,& 2<x\le 3\end{array}$ then $f\left\{f\right(x\left)\right\}=$

The value of ${\log }_y{x}^3{\log }_z{y}^4{\log }_x{z}^5$ is

What is the value of cos 105⁰+cos75⁰?

The distances of the point (1,2,3) from the coordinate area are A, B, and C respectively now consider the following equations
$\left(1\right)A^2=B^2+C^2\text{(2)}{B}^2=2C^2\text{(3)}2A^2{C}^2=13B^2$
Which of these holds true?

Write minors and cofactors of elements of following determinant. $\left|\begin{array}{cc}a& c\\ b& d\end{array}\right|$

In a single throw a three dice, find the probability of gettin the same number on all the three dice.

If the angle between the planes $2x-y+z=4$ and $x+\lambda y+2z=11$ is $\frac{\pi }{3}$, then the values of $\lambda$ are