Explore topic-wise InterviewSolutions in Current Affairs.

The solution set of the equation $\sin 3x+\cos 2x=-2$ is
(where $n\in Z$)

In Hydrogen - like atoms, ratio of $E_{4n}-E_{2n}$ and $E_{2}n-E_n$ is proportional to

If $\frac{\log a}{b-c}=\frac{\log b}{c-a}=\frac{\log c}{a-b},a,b,c>0$, then

Which of the following functions are bijections?

The range of f(x) = $\frac{x^2+x+1}{x^2+x-1}$

Integrate the following functions.
$\int \frac{se{c}^{2}x}{\sqrt{ta{n}^{2}x+4}}dx.$

Discuss the continuity of the following functions :

(a) f(x) = sin x + cos x

(b) f(x) = sin x + cos x

(c) f(x) = sin x cos x

Solve the inequalities in Exercieses 7 to 10 and represent the solution graphically on number line:

$5(2x-7)-3(2x+3)\le 0,2x+19\le 6x+47$

if the roots of the equation x² -2mx +m² - 1 =0 lie in the interval (-2,4) then,

a) m ~ (-1,3) b) m~(1,5)

c) m~(-3,1) d) m~(-1.5)

where ~ stand for "belongs to".

Write the domain and range of $f\left(x\right)=\sqrt{x-\left[x\right]}$

Column - 1 contains definitions of various functions f(x) in terms of real parameter 'a'

Column - 2 contains information about the coefficient of $x^2$ in the binomial expansion of f(x) for small numerical values of x

Column - 3 contains the corresponding value of 'a'

$\begin{array}{cccccc}& \text{Column 1}& & \text{Column 2}& & \text{Column 3}\\ \text{(I)}& f\left(x\right)=\frac{a(2-3x)}{(1-2x)(2+x)},|x|<\frac{1}{2}& \text{(i)}& \frac{1}{4}& \text{(P)}& 10\\ \text{(II)}& f\left(x\right)=\sqrt{\frac{1+2x}{4-x}},|x|<1& \text{(ii)}& \frac{1}{64}& \text{(Q)}& 4\\ \text{(III)}& f\left(x\right)=\frac{1}{\sqrt{1-ax}}-\sqrt{1+ax},|x|<\frac{1}{a}& \text{(iii)}& 10& \text{(R)}& \frac{1}{4}\\ \text{(IV)}& f\left(x\right)=\frac{a(1-x)}{1+x+x^2+x^3},|x|<1& \text{(iv)}& 4& \text{(S)}& \sqrt{8}\end{array}$

Which of the following options is the only CORRECT combination ?

Let $f\left(x\right)$ be defined in $[–2,2]$ by $f\left(x\right)=\{\begin{array}{cc}max\{\sqrt{4-x^2},\sqrt{1+x^2}\}& -2\le x\le 0\\ min\{\sqrt{4-x^2},\sqrt{1+x^2}\}& 0<x\le 2\end{array}$ . Then $f\left(x\right)$ is

Let $f\left(x\right)=\sqrt{x^2+1}$. Then, which of the following is correct?

The equation of common tangent to the parabolas $y^2=4x$ and $x^2=4y$ is

Sir,

Tommorow is my math exam what points would you suggest me to score good marks in my SA1 exams.i will be highly grateful to you for your efforts.!

The quadratic equation whose roots are $\tan 22{\frac{1}{2}}^{\circ }$ and $\cot 22{\frac{1}{2}}^{\circ }$ is

The sum of the infinite terms of the series ${\cot }^{-1}(1^2+\frac{3}{4})+{\cot }^{-1}(2^2+\frac{3}{4})+{\cot }^{-1}(3^2+\frac{3}{4})+\cdots$ is equal to

The inverse of function $y=\frac{2^x}{1+2^x}$ is :

Let $A,B$ be two distinct points on the parabola $y^2=4x$. If the axis of the parabola touches a circle of radius $r$ having $AB$ as diameter, the slope of the line $AB$ is

Find the equation to the director circle of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

A class consists of 80 students, 25 of them are girls 55boys 10of them are rich and remaining poor 20 of them are fair complexioned. The probability of selecting a fair complexioned rich girl is

Write minors and cofactors of elements of following determinants

$\left|\begin{array}{ccc}1& 0& 4\\ 3& 5& -1\\ 0& 1& 2\end{array}\right|$

If the lines $ax+12y+1=0,bx+13y+1=0$ and $cx+14y+1=0$ are concurrent, then a, b, c are in

The extremities of latus rectum of a parabola are $(1,1)$ and $(1,-1)$. Then the equation(s) of the parabola is/are

The coordinates of a point which divide the line joining the points $P(2,3,1)$ and $Q(5,0,4)$ in the ratio $1:2$ are

Using integration, find the area of the triangular region whose sides have the equations y = 2x + 1, y = 3x + 1 and x = 4.

Every point of feasible region is called a ……… to the problem.

Find $\frac{dy}{dx}$, if x and y are connected parametrically by the equations given in questions without eliminating the parameter.

$x=2a{t}^2,y=a{t}^4.$

Let $A=\left[\begin{array}{ccc}1& -2& 1\\ -2& 3& 1\\ 1& 1& 5\end{array}\right]$

$(A^{-1}{)}^{-1}=A$

From a point perpendicular tangents are drawn to ellipse $x^2+2y^2=2$. The chord of contact touches a circle which is concentric with given ellipse. Then find the ratio of maximum and minimum area of circle ___

If the system of equation $ax+y=3,x+2y=3,3x+4y=7$ is
consistent, then value of $a$ is given by

Prove that the points (2, -1), (0, 2), (2, 3) and (4, 0) are the coordinatesof the vertices of a parallelogram and find the angle between its diagonals.

The order and degree of the differential equation

[DCE 2002]

1+cot²θ=?

Prove that cot $(\frac{\pi }{4}-2co{t}^{-1}3)=7$

If A, B and C are angles of a triangle, then the determinant
$\left|\begin{array}{ccc}-1& cosC& cosB\\ cosC& -1& cosA\\ cosB& cosA& -1\end{array}\right|$ is equal to

(a) 0
(b) -1
(c) 1
(d) None of these

The tangent to the hyperbola, $xy=c^2$ at a point $P$ intersects the x-axis at $T$ and the y-axis at $T^{\prime }.$ The normal to the hyperbola at $P$ intersects x-axis at $N$ and y-axis at $N^{\prime }.$ The areas of the triangles $PNT$ and $P{N}^{\prime }{T}^{\prime }$ are $\Delta$ and ${\Delta }^{\prime }$ respectively, then $\frac{1}{\Delta }+\frac{1}{{\Delta }^{\prime }}$ is