Explore topic-wise InterviewSolutions in Current Affairs.

Suppose that a bond promises Rs. 500 at the end of two years with no intermediate return. If the rate of interest is 5% per annum, what is the price of the bond?

If the locus of the circumcentre of of variable triangle having sides $y-$axis, $y=2$ and $lx+my=1$, where $(l,m)$ lies on the parabola $y^2=4ax$ is a curve $C$, then the curve $C$ is symmetric about the line

Verify: ${\mathrm{x}}^3+{\mathrm{y}}^3=(\mathrm{x}+\mathrm{y})({\mathrm{x}}^2–\mathrm{xy}+{\mathrm{y}}^2)$

The domain of $f\left(x\right)=\sqrt{{\log }_{2}x}-{\log }_2\sqrt{x}$ is

The value of $\underset{x\to 0}{lim}\frac{(1+x{)}^{1/x}-e}{x}$ is

Let $S$ be the circle in the $xy$-plane defined by the equation $x^2+y^2=4$.

Let $E_1{E}_2$ and $F_1{F}_2$ be the chords of $S$ passing through the point $P_0(1,1)$ and parallel to the $x$-axis and the $y$-axis, respectively. Let $G_1{G}_2$ be the chord of $S$ passing through $P_0$ and having slope $-1$. Let the tangents to $S$ at $E_1$ and $E_2$ meet at $E_3$, the tangents to $S$ at $F_1$ and $F_2$ meet at $F_3$, and the tangents to $S$ at $G_1$ and $G_2$ meet at $G_3$. Then, the points $E_3,F_3$, and $G_3$ lie on the curve

If ${}^5{C}_r=r\cdot {}^5{C}_{r-1}$, then the number of value(s) of $r$ is

A manufacturer has three machine operators A, B an C. The first operatot A produces 1% defective items, where as the other two operators B anc C produce 5% of the time, B on the job for 30% of the time and C on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A?

Prove that $si{n}^{-1}\frac{8}{17}+si{n}^{-1}\frac{3}{5}=si{n}^{-1}\frac{77}{85}.$

Choose the correct answer in the following questions :
The slope of the tangent to the curve $x=t^2+3t-8,y=2t^2-2t-5$ at the point (2, -1) is
(a) $\frac{22}{7}$ (b) $\frac{6}{7}$
(c) $\frac{7}{6}$ (d) $\frac{-6}{7}$

For each of the following compound statement first identify the connecting words and then break it into component statements.

(i) All rational numbers are real and all real numbers are not complex.

(ii) Square of an integer is positive or negative.

(iii) The sand heats up quickly in the sun and does not cool down fast at night.

(iv) x = 2 and x = 3 are the roots of the equation $3x^2-x-10=0$.

Show that the set of letters needed to spell "CATARACT" and the set of letters needed to spell "TRACT" are equal.

The slope of a straight line passing through $A(-2,3)$ is $-\frac{4}{3}$. The point(s) on the line that are $10$ units away from $A$ is/are

An open cylindrical can has to be made with $100$ square units of tin. If its volume is maximum, then the ratio of its base radius and the height is

Find the locus of the mid-point of the portion of the line x cos $\alpha +ysin\alpha =p$ which is intercepted between the axes.

The number of ways of choosing triplet $(x,y,z)$ such that $z>max\text{of}(x,y)$ and $x,y,z\in \{1,2,...,n,n+1\}$ is

The value of $\sum _{k=1}^{10}(\sin \frac{2k\pi }{11}-i\cos \frac{2k\pi }{11})$ is

Which of the following is true if A and C are coefficient and augmented matrices respectively for a system of linear equation. Here n = number of unknowns

Integrate the rational functions.
$\int \frac{3x-1}{(x+2{)}^2}dx.$

If A and B are symmetric matrices, prove that AB-BA is a skew -symmetric matrix.

A hyperbola has its centre at the origin, passes through the point $(4,2)$ and has transverse axis of length $4$ unit along the $x-$axis. Then the eccentricity of the hyperbola is

$\text{In any}△ABC,a(bcosC-ccosB)equals$

which one of the following statements are correct?
1) Equation of a circle with centre $(h,k)$ and radius r is given by $(x-h{)}^2+(y-k{)}^2=r^2$
2) Equation of circle with $A(x_1,y_1)$ and $B(x_2,y_2)$ as extremities of diameter is given by

$(x-x_1)(y-y_1)+(x-x_2)(y-y_2)=0$

In the expansion $(1+x{)}^5=1+5x+a{x}^2......x^5$, find the value of a

If boys and girls sit alternately then the number of ways in which 3 boys and 3 girls can be seated in a row is

Find the number of solutions of cos(x)+cos(2x)+cos(3x)+cos(4x)+cos(5x)=5 in the interval [0,2π]

Find derivative with respect to x of 2√cot(x^2​​​) ? Please give in detail

If y = sin $\left(x^{\circ }\right),find\frac{dy}{dx}$ .

If $f\left(x\right)={lim}_{n\to \infty }{e}^{xtan\left(1/n\right)ln\left(1/n\right)}$ and $\int \frac{f\left(x\right)}{\sqrt[3]{3si{n}^{11}xcosx}}dx=g\left(x\right)+C$, then

The perpendicular distance of a point P (7,5 ,-2) from the plane -2x +7y -4z + 5 = 0 is units.

The maximum distance between the points $(a\cos \alpha ,a\sin \alpha )$ and $(a\cos \beta ,a\sin \beta )$ is

Number of terms in the expansion of $(a+b+c+d+e{)}^5$ is

The vector c directed along the internal bisector of the angle between the vectors $a=7\hat{i}-4\hat{j}-4\hat{k}$ and $b=-2\hat{i}-\hat{j}+2\hat{k}$ with $|c|=5\sqrt{6}$, is

Express $\frac{{(cos\theta +isin\theta )}^4}{{i(cos\theta +isin\theta )}^{-4}}$ in a + ib form.

The condition that the line $\frac{x}{p}+\frac{y}{p}=1$ o be tangent to $\frac{x^z}{a^z}+\frac{y^z}{b^z}=1$ is

A boy is standing on the edge of the roof at height of $78.4m$. He throws a ball vertically upwards with velocity of $19.6m{s}^{-1}$. After how much time the ball will reach the ground? (Take $g=9.8m{s}^{-2}$)

The ellipse $E_1:\frac{x^2}{9}+\frac{y^2}{4}=1$ is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse $E_2$ passing through the point (0,4) circumscribes the rectangle R. The Eccentricity of the ellipse $E_2$ is

Sixteen players $P_1.P_2.\dots \dots \dots P_{16}$ play in a tournament. They are divided into eight pairs at random.From each pair a winner is decided on the basis of a game played between the two players of the pair.Assuming that all the players are of equal strength, the probability that exactly one of the two players $P_1$ and $P_2$ is among the eight winners is

If $x^2+y^2+px+3y-5=0$ and $x^2+y^2+5x+py+7=0$ cut orthogonally, then p is

The general solution of the differential equation $(y^2+e^{2x})dy-y^{3}dx=0$ (C being the constant of integration), is

The equation $z\overline{z}+a\overline{z}+\overline{a}z+b$ = 0, b$\in$R represents a circle if