Explore topic-wise InterviewSolutions in .

The number of ways in which one or more balls can be selected out of $10$ white, $9$ green and $7$ black balls is

For real $x$, let $f\left(x\right)=x^3+5x+1$, then

Let ${\cos }^{-1}\left(x\right)+{\cos }^{-1}\left(2x\right)+{\cos }^{-1}\left(3x\right)=\pi ,$ where $x>0.$ If $x$ satisfies the cubic equation $a{x}^3+b{x}^2+cx-1=0,$ then $a+b+c$ has the value equal to

A variable line $L$ is drawn through $O(0,0)$ to meet the lines $L_1:x+2y-3=0$ and $L_2:x+2y+4=0$ at points $M$ and $N$ respectively. A point $P$ is taken on line $L$ such that $\frac{1}{O{P}^2}=\frac{1}{O{M}^2}+\frac{1}{O{N}^2}$. Then the locus of $P$ is

If the angles of a triangle ABC be in A.P., then

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

A rectangle is inscribed in a circle with a diameter lying along the line $3y=x+7$. If the two adjacent vertices of the rectangle are $(-8,5)$ and $(6,5)$, then the area of the rectangle (in sq. units) is :

Angle between line

$\frac{x-5}{1}=\frac{y-2}{2}=\frac{z-8}{2}$ and plane $2x+y+2z+5=0$ is

Which of the following has most number of divisors?

If a triangle has its orthocenter at (1, 1) and circumcenter at $(\frac{3}{2},\frac{3}{4})$ , then the coordinates of the centroid of the triangle are

A natural number x is chosen at random from the first 100 natural numbers. Then the probability that, $x+\frac{100}{x}>50$ is:

The arcs of the same length in two circles subtend angles of ${28}^{\circ }$ and ${35}^{\circ }$ at their centres. Then the ratio of their respective radii is

Find the equation of the straight line that has y - intercept 5 and is parallel to the straight line x - 3y = 3

Which of the following line(s) is nearest to origin

The term independent of $x$ in the expansion of $(1+x+2x^3){(\frac{3x^2}{2}-\frac{1}{3x})}^9$ is

Let line $L$ passes through the point of intersection of $2x+y-1=0$ and $x+2y-2=0$. If $L$ makes a triangle with the coordinate axes of area $\frac{5}{8}\text{sq. units}$, then the equation of $L$ can be

If $P_1$ and $P_2$ are the lengths of the perpendiculars from the points (2,3,4) and (1,1,4) respectively from the plane 3x-6y+2z+11 =0, then $P_1$ and $P_2$ are the roots of the equation

Which among the following are triangular matrices?

Which of the following is roster form of $\{x:x$ is even prime number greater than $2\}$?

Let $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ be 2 sets of solution satisfying the following equations:

${\log }_{10}\left(2xy\right)=4+({\log }_{10}x-1)({\log }_{10}y-2)$

${\log }_{10}\left(2yz\right)=4+({\log }_{10}y-2)({\log }_{10}z-1)$

${\log }_{10}\left(zx\right)=2+({\log }_{10}z-1)({\log }_{10}x-1)$

such that $(x_1>x_2)$,

then match the elements of List - I with the correct answer in List -II.



$\begin{array}{cc}\text{List -I}& \text{List -II}\\ \left(I\right)\frac{y_1}{x_1}& \left(P\right)2\\ \left(II\right)\frac{z_1}{x_2}& \left(Q\right)100\\ \left(III\right)\frac{z_1{x}_2}{z_2}& \left(R\right)1000\\ \left(IV\right)\frac{y_2+z_1}{x_2}& \left(S\right)150\end{array}$



Which of the following is the only 'INCORRECT' combination?

The solution set of $\frac{x^2-4}{x^2-16}\le 0$ is

If $(7,5)$ are the new coordinates of $P$ when origin is shifted to $(1,1)$, then the original coordinates of $P$ are

The range of $f\left(x\right)=x^3+x$ is

If $A=\{1,2,3,4,5\}$ then which of the following is correct?

If the sides of a triangle are in the ratio $2:\sqrt{6}:(\sqrt{3}+1)$, then the largest angle of the triangle will be

If the centre, vertex and focus of a hyperbola are $(4,3),(8,3),(10,3)$ respectively, then the equation of the hyperbola is

If $(h,k)$ is the centre of a circle touching $x-$axis at a distance $3$ units from the origin and makes an intercept of $8$ units on the $y-$axis, then the equation of circle when $(h+k)$ is maximum, is

In how many ways can $15$ identical blankets be distributed among $6$ persons such that everyone gets atleast one blanket and two particular persons get equal blankets and another three particular persons get equal blankets.

If $\frac{x+4}{x-2}>0,$ then

The general solution of $\sin x+\cos x=1$ is

A dice is rolled and two events P and Q are given as

P = {1, 4, 3, 5}, Q = {2, 6}

Which of the following describes the relation between P and Q?

In any triangle ABC, $\frac{tan\frac{A}{2}-tan\frac{B}{2}}{tan\frac{A}{2}+tan\frac{B}{2}}$

The first negetive term in the sequence of $56,55\frac{1}{5},54\frac{2}{5},\cdots$

Solve: $\sqrt{x-2}$ ≥ -1

The equation to the circle with centre (2, 1) and touching the line 3x + 4y = 5 is

The tangent to the curve $x^2+y^2=25$ parallel to the line 3x-4y=7 exist at the point

The point on the $Y-$axis equidistant from the point $(9,3)$ and $(-5,2),$ is

The equation of the curve passing through the origin and satisfying the differential equation ${\left(\frac{dy}{dx}\right)}^2=(x-y{)}^2$, is

What is the maximum and minimum distance of the point (9, 12) from the circle $x^2+y^2-6x-8y-24=0$

If $k_1,k_2,k_3$ are real numbers and the equation $k_1{x}^2+k_{2}x+k_3=0$ have three roots, then value of $k_1+k_2+k_3$ is

The value of the expression $\tan \frac{\pi }{7}+2\tan \frac{2\pi }{7}+4\tan \frac{4\pi }{7}+8\cot \frac{8\pi }{7}$ is equal to

Three six-faced fair dice are thrown together. The probability that the sum of the numbers appearing on the dice is k $(3\le k\le 8)$ is

If three unequal positive real numbers a,b,c are in G.P. and a-b,c-a, a-b are in H.P., then the values of a+b+c is independent of