Explore topic-wise InterviewSolutions in Current Affairs.

If $\alpha ,\beta$ be the roots of the equation $a{x}^2+bx+c=0$. Let $S_n={\alpha }^n+{\beta }^n,$ for $n\ge 1$
If $\Delta =\left|\begin{array}{ccc}3& 1+S_1& 1+S_2\\ 1+S_1& 1+S_2& 1+S_3\\ 1+S_2& 1+S_3& 1+S_4\end{array}\right|$, then $\Delta$ is equal to

For a first order reaction, the plot of against log C gives a straight line with a slope equal to:

Let , $f\left(x\right)=a{x}^2+bx+c,g\left(x\right)=a{x}^2+px+qwherea,b,c,q,p,ϵRandb\ne p$. If their discriminants are equal and f(x) = g(x) has a root , $\alpha$ then

The equation of the normal to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ at the positive end of latus rectum in the first quadrant

Sketch the following graphs :
(i) y=2 sin 2x
(ii) y= 3 sin x
(iii) $y=2sin(x-\frac{\pi }{4})$
(iv) y=2 sin (2x-1)
(v) y=3 sin(3x+1)
(vi) $y=3sin(2x-\frac{\pi }{4})$

The integer k for which the inequality $x^2-2(4k-1)x+15k^2-2k-7>0$ is valid for any x, is

Express the following complex numbers in the standard form a + i b :

$\left(i\right)(1+i)(1+2i)\left(ii\right)\frac{3+2i}{-2+i}\left(iii\right)\frac{1}{(2+i{)}^2}\left(iv\right)\frac{1-i}{1+i}\left(v\right)\frac{(2+i{)}^3}{2+3i}\left(vi\right)\frac{(1+i)(1+\sqrt{3i})}{1-i}\left(vii\right)\frac{2+3i}{4+5i}\left(viii\right)\frac{(1-i{)}^3}{1-i^3}\left(ix\right)(1+2i{)}^{-3}(x\left)\frac{3-4i}{(4-2i)(1+i)}\right(xi\left)(\frac{1}{1-4i}-\frac{2}{1+i})\left(\frac{3-4i}{5+i}\right)\right(xii)\frac{5+\sqrt{2i}}{1-\sqrt{2i}}$

The value of ‘a’ for which one root of the quadratic equation $(a^2-5a+3)x^2+(3a-1)x+2=0$ is twice as large as the other, is

If $p\Rightarrow (q\vee r)$ is false, then the truth values of $p,q,r$ are respectively :

The CFSE for $\left[Fe\right(CN{)}_6{]}^{3-}$ is

In a triangle ABC, if $\frac{cosA}{a}=\frac{cosB}{b}=\frac{cosC}{c}$ and a = 2, then its area is

For the following probability distribution: $\begin{array}{cccccc}X& -4& -3& -2& -1& 0\\ P\left(x\right)& 0.1& 0.2& 0.3& 0.2& 0.2\end{array}$ E(X) is equal to

Equation of the parabola, if coordinates of vertex and focus are $(0,0)$ and $(2,3)$ respectively, is

If $S_n$ denotes the sum of first n terms of an A.P. $<a_n>$ such that $\frac{S_m}{S_n}=\frac{m^2}{n^2}$, then $\frac{a_m}{a_n}=$

The equation of straight line which is equidistant from the points $A(2,–2)$, $B(6,1)$ and $C(–3,4)$ can be

If the difference between the roots of the equation

$x^2+ax+8=0is2,$ write the values of a.

Find the equations to the sides of the triangles the coordinates of whose angular points are respectively : (i) (1, 4), (2, -3) and (-1, -2) (ii) (0, 1), (2, 0) and (-1, -2).

Define optimal (feasible) solution of a linear programming problem.

The Receipts and Payments Account of Harimohan charitable institution is given

Receipts and Payments Account

for the year ending March 31, 2007

$\begin{array}{cccc}\text{Receipts}& \text{Amt. (Rs)}& \text{Payment}& \text{Amt (Rs)}\\ \text{Balance b/d}& & \text{Furniture}& 3,000\\ \text{Cash at Bank}& 22,000& \text{Investments}& 55,000\\ \text{Cash in Hand}& 8,800& \text{Advance for Building}& 20,000\\ \text{Donations}& 32,000& \text{Charities}& 60,000\\ \text{Subscriptions}& 50,200& \text{Salaries}& 10,400\\ \text{Endowment Fund}& 60,000& \text{Rent and Taxes}& 4,000\\ \text{Legacies}& 24,000& \text{Printing}& 1,000\\ \text{Interest on Investment}& 3,8000& \text{Postage}& 300\\ \text{Interset on Deposits}& 800& \text{Advertisements}& 1,100\\ \text{Sale of Old Newspapers}& 500& \text{Insurance}& 4,800\\ & & \text{Balance c/d}& \\ & & \text{Cash at Bank}& 32,000\\ & & \text{Cash in Hand}& 10,500\\ & \underset{–}{\overline{2,02,100}}& & \underset{–}{\overline{2,02,100}}\end{array}$

Prepare the Income and Expenditure Account for the year ended on March 31, 2007 after considering the following

(i) It was decided to treat Fifty percent of the amount received on account of Legacies and Donations as income.

(ii) Liabilities to be provided for are

Rent Rs 800; Salaries Rs 1,200; Advertisement Rs 200.

(iii) Rs 2,000 due for interest on investment was not actually received.

The value of the expression $({\tan }^{4}x+2{\tan }^{2}x+1){\cos }^{2}x$, when $x=\frac{\pi }{12}$ is equal to

The value of $\left|\begin{array}{ccc}(a+1)(a+2)& a+2& 1\\ (a+2)(a+3)& a+3& 1\\ (a+3)(a+4)& a+4& 1\end{array}\right|$ is :

If $x\in (-\frac{\pi }{2},\frac{3\pi }{2}),$ then ${\tan }^{-1}\left(\frac{\cos x}{1+\sin x}\right)$ is equal to

The number of real solution(s) of $||x-2|-2|-2|x|=|x-3|$ is

If a tangent to the circle $x^2+y^2=1$ intersects the coordinate axes at distinct points $P$ and $Q$, then the locus of the mid-point of $PQ$ is:

Show that area of the prallelogram whose diagonals are given by $\overrightarrow{a}and\overrightarrow{b}is\frac{\overrightarrow{a}\times \overrightarrow{b}}{2}$. Also, find the area of the parallelogram, whose diagonals are $2\hat{i}-\hat{j}+kand\hat{i}+3\hat{j}-\hat{k}.$

Evaluate the following limit:

$\underset{x\to 3}{\text{lim}}\frac{x^4-81}{2x^2-5x-3}$

Let $A_1{A}_2{A}_3{A}_4{A}_5{A}_6{A}_1$ be regular hexagon. Write the x-components of the vectors represented by the six sides taken in order. Use the fact that the resultant of these six vectors is zero, to prove that $cos0+cos\frac{\pi }{3}+cos\frac{2\pi }{3}+cos\frac{3\pi }{3}+cos\frac{4\pi }{3}+cos\frac{5\pi }{3}=0$.

Use the known cosine values to verify the result.

Solve the irrational inequality:
$\frac{3}{\sqrt{2-x}}-\sqrt{2-x}\le 2$

If A be one A.M. and p, q be two G.M.'s between two numbers, then 2A is equal to

If f(x) , g(x) and h(x) are three differentiable functions throughout their domains and given that their first derivatives are -

$f^{\prime }\left(x\right)<0$

$g^{\prime }\left(x\right)=0$

$h^{\prime }\left(x\right)\le 0$

throughout their domains. Then choose the correct option of monotonically decreasing functions -

Find the value of the following:

$ta{n}^{-1}\left(tan\frac{7\pi }{6}\right)$

Is the function defined by $x^2$ - sin x+5 continuous at $x=\pi$ ?

If $\alpha ={30}^{\circ }$ and $\beta ={60}^{\circ }$, then the value of $\frac{\sin \alpha +\sec 2\alpha +\tan (\alpha +{15}^{\circ })}{\tan \beta +\cot (\frac{\beta }{2}+{15}^{\circ })+\tan \alpha }$ is

If the length of the tangents from $(a,b)$ to the circles $x^2+y^2-4x-5=0$ and $x^2+y^2+6x-2y+6=0$ are equal, then the value of $10a-2b$ is

Let $L$ be an end of the latus rectum of $y^2=4x$. If the normal at $L$ meets the curve again at $M$ and the normal at $M$ meets the curve again at $N,$ then area of $△LMN$ (in sq. units) is

The value of$x+y+x$ is $15,$if $a,x,y,z$ and bare in AP while the value of $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$ is $\frac{5}{3}$,If,$\frac{1}{a},\frac{1}{x},\frac{1}{y},\frac{1}{z}$ and $\frac{1}{b}$ are in AP . Find the values of a and b.

Study the following information and answer the questions given below

1. A, B, C, D, E, and F are six members of a family.

2. One is a student, one housewife, one doctor, one teacher, one lawyer and one engineer.

3. There are two married couples in the family

4. B is a teacher and the mother of C.

5. D is the grandmother of C and is a housewife.

6. F is a lawyer and is the father of A.

7. C is the brother of A.

8. E is the father of F and is a doctor.

Q66. How is A related to D?

Write the following in the simplest form.

$ta{n}^{-1}\frac{1}{\sqrt{x^2-1}},|x|>1$

Find $\frac{dy}{dx}$in the following questions:

$x^2+x^{2}y+x{y}^2+y^3=81.$