Explore topic-wise InterviewSolutions in Current Affairs.

Solve $2{\cos }^2\theta +\cos \theta -1=0$

If $(1+i)(1+2i)(1+3i).....(1+ni)=a+bi$, then2.5.10.... $1+n^2$ is equal to

If the lines represented by the equation $a{x}^2-bxy-y^2=0$ make angles $\alpha$ and $\beta$ with the x - axis, then $\tan (\alpha +\beta )$ =

If $I_1={\int }_0^{\frac{\pi }{2}}xsinxdx\&I_2={\int }_0^{\frac{\pi }{2}}xcosxdx$, then which of the following is true?

Find the rth term of an A.P, the sum of whose first n terms is $3n^2+2n$

Let A = { $x:xϵN,$ x is a multiple of 3\)} and

B = {$x:xϵN$ and x is a multiple of 5}. Write $A\cap B$.

Value(s) of $x$ for $\frac{|x^2-2|x|+1|}{|x|+1}=2$ is/are

The diagram below shows a sinusoidal curve. The equation of the curve will be

O is the circumcenter of $\Delta \mathrm{ABC}\mathrm{and}{R}_1,R_2\mathrm{and}{R}_3$are the radii of the circumcircles of the triangles OBC, OCA and OAB. Then $\frac{a}{R_1}+\frac{b}{R_2}+\frac{c}{R_3}=$ .

How many ways are there to arrange the letters of the word EDUCATION so that all the following three conditions hold?

– the vowels occur in the same order (EUAIO);

– the consonants occur in the same order(DCTN);

– no two consonants are next to each other.

Let $p,qandr$ be real numbers $(p\ne q,r\ne 0)$, such that the roots of the equation $\frac{1}{x+p}+\frac{1}{x+q}=\frac{1}{r}$ are equal in magnitude but opposite in sign, then the sum of squares of these roots is equal to :

If $\frac{x^2}{3-\alpha }+\frac{y^2}{2}=1$ represents an ellipse whose major axis is along the $x-$axis, then the range of $\alpha$ is

Represent to solution set of each of the following in equations graphically in two dimensional plane :

$3x-2y\le x+y-8$

$\text{If}x+iy=\frac{3+5i}{7-6i},\text{then y=}$

If one of the lines of $m{y}^2+(1-m^2)xy-m{x}^2=0$ is a bisector of the angle between the lines $xy=0$, then $m$ can be

The average of $5$ distinct positive integers is $33$. If the average of the three largest numbers within this set is $39$ then the difference of the maximum and minimum possible values of the median of the $5$ numbers is

If $\overrightarrow{a}=i+2j+2k,|\overrightarrow{b}|=5$ and the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is $\frac{\pi }{6}$, then the area of the triangle formed by these two vectors as two sides is

Sum of the series $\sum _{r=1}^n\frac{1}{(ar+b)(ar+a+b)}$, (where $a\ne 0$) is

The range of $\alpha$ for which the points $(\alpha ,\alpha +2)$ and $(\frac{3\alpha }{2},{\alpha }^2)$ lie on opposite sides of the line $2x+3y-6=0$ is

If $\cos \left(2{\tan }^{-1}x\right)=\frac{1}{2}$, then the value of $x$ is _______

Let A = {$x:xϵN$}, B = {$x:x=2n,nϵN$}, C = {$x:x=2n-1,nϵN$} and , D = {x: x is a prime natural number}. Find :

(i) $A\cap B$ (ii) $A\cap C$

(iii) $A\cap D$ (iv) $B\cap C$

(v) $B\cap D$ (vi) $C\cap D$

The number of ordered pair(s) of $(x,y)$satisfying $3y=[\sin x+[\sin x+\left[\sin x\right]\left]\right]$ and $[y+[y\left]\right]=2\cos x$ is
​​​​​​​(correct answer + 1, wrong answer - 0.25)

sinA/ 1+ cosA + 1+ cosA/ sinA=

Which of the relations is not a function?

If $a,b,c,d,e,f$ are A.M.'s between $2$ and $12$, then the value of $a+b+c+d+e+f$ is

Let any circle $S$ passes through the point of intersection of lines $\sqrt{3}(y-1)=x-1$ and $y-1=\sqrt{3}(x-1)$ and having its centre on the acute angle bisector of the given lines. If the common chord of $S$ and the circle $x^2+y^2+4x-6y+5=0$ passes through a fixed point, then the fixed point is

If $a_1$ < $a_2$< $a_3$ < $a_4$ < $a_5$ < $a_6$, then the equation $(x-a_1)(x-a_3)(x-a_5)+2(x-a_2)(x-a_4)(x-a_6)$ = 0 has

Find the vector and Cartesian equations of the planes.

that passes through the point (1,0,-2) and the normal to the plane is $\hat{i}+\hat{j}-\hat{k}.$

that passes through the point (1,4,6) and the normal to the plane is $\hat{i}-2\hat{j}+\hat{k}.$

$\int \frac{\sqrt{1+x^2}}{x^4}dx$

Evaluate the integrals using substitution.
${\int }_0^2\frac{1}{x+4-x^2}dx.$

If $\int {\cos }^{4}xdx=Ax+B\sin 2x+C\sin 4x+D$, then $\{A,B\}$ equals

Find the integrals of the functions.
$\int \frac{1}{cos(x-a)cos(x-b)}dx.$

The line $AB$ cuts off equal intercepts $2a$ from the axes. From any point $P$ on the line $AB$ perpendiculars $PR$ and $PS$ are drawn on the axes. Locus of mid-point of $RS$ is

In a hyperbola the distance between the foci is 2 and the distance between directrices is 1 Its eccentricity is

If the product of power of point (1, 1) and (–1, –1) with respect to circle $x^2+y^2+2px+2qy+4=0$ is negative and the circle neither touches nor intersects co-ordinate axes, then the area of region formed by the set of ordered pair (p, q) on pq plane is

The value of x${}^{1/2}$ .y${}^{-1}$ . z${}^{2/3}$, when x = 9 , y = 3 and z = 8 is

The approximate value of $(1.0002{)}^{3000}$ is

If cos A - 3 sinA = -1 and A is an acute angle; then the value of sin A is?

${\int }_0^a$ ln(cot a +tan x)dx, where a $ϵ(0,\frac{\pi }{2})$ is