Explore topic-wise InterviewSolutions in Current Affairs.

The four lines drawing from the vertices of any tetrahedron to the centroid of the opposite faces meet in a point whose distance from each vertex is ‘k’ times the distance from each vertex to the opposite face, where k is

Let $\hat{\alpha },\hat{\beta },\hat{\gamma }$ be three unit vectors such that $\hat{\alpha }\times (\hat{\beta }\times \hat{\gamma })=\frac{1}{2}(\hat{\beta }+\hat{\gamma })$ where $\hat{\alpha }\times (\hat{\beta }\times \hat{\gamma })=(\hat{\alpha }.\hat{\gamma })\hat{\beta }-(\hat{\alpha }.\hat{\beta })\hat{\gamma }$. If $\hat{\beta }$ is not parallel to $\hat{\gamma }$, then the angle between $\hat{\alpha }$ and $\hat{\beta }$ is

From the following Receipts and Payments A/c of a club for the year ended 31st March, 2015 and from the informations supplied, prepare Income and Expenditure Account for the year ended 31st March, 2015 and the Balance Sheet as at that date :

$\begin{array}{cccc}\text{Receipts}& \text{Rs}& \text{Payments}& \text{Rs}\\ \text{Balance b/d}& 1,50,000& \text{Salaries}& 1,50,000\\ \text{Subscriptions :}& & \text{Entertainment Expenses}& 60,000\\ \text{2013-14}& 10,000& \text{Electric Charges}& 20,000\\ \text{2014-15}& 2,00,000& \text{General Expenses}& 30,000\\ \text{2015-16}& 20,000& \text{Investments}& 1,00,000\\ \text{Entertainment Receipts}& 1,00,000& \text{Printing and Stationery}& 20,000\\ \text{Sale of Old Furniture}& & \text{Newspapers}& 30,000\\ \text{(Costing Rs 10,000)}& 6,000& \text{Furniture}& 30,000\\ \text{Sale of Newspapers}& 4,000& \text{Miscellaneous Expenses}& 20,000\\ & & \text{Balance c/d}& 30,000\\ & \underset{–}{\overline{4,90,000}}& & \underset{–}{\overline{4,90,000}}\end{array}$

(i) The club has 250 members, each paying an annual subscription of Rs 1,000. Rs 5,000 are still in arrears for subscriptions of 2013-14. In 2013-14, 10 members had paid their subscriptions for 2014-15 as well.

(ii) Salaries paid include Rs 10,000 for 2013-14 and Rs 15,000 for 2015-16. Outstanding salaries for 2014-15 amounted to Rs 20,000.

(iii) On 1-4-2014 the club owned land and building valued at Rs 10,00,000 and furniture valued at Rs 1,10,000.

(iv) Interest for 3 months $6\%$ p.a. has accrued on investments.

${lim}_{h\to \infty }(a^{\frac{1}{x}}-1)x$

If one root of the equation $a{x}^2$+px + q = 0 be n times the other root, then

The real roots of the equation $7^{lo{g}_7(x^2-4x+5)}=x-1$ are

If $\frac{x}{a}+\frac{y}{b}=\sqrt{2}$ touches the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,$ then its eccentric angle $\theta$ is equal to

Let $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$ be three unit vectors, out of which vectors $\overrightarrow{b}$ and $\overrightarrow{c}$ are non-parallel. If $\alpha$ and $\beta$ are the angles which vector $\overrightarrow{a}$ makes with vectors $\overrightarrow{b}$ and $\overrightarrow{c}$ respectively and $\overrightarrow{a}\times (\overrightarrow{b}\times \overrightarrow{c})=\frac{1}{2}\overrightarrow{b}$, then $|\alpha -\beta |$ is equal to :

The domain of definition of the function $f\left(x\right)=log|x|$ is

Evaluate $\int \frac{\mathrm{dx}}{x^2-x+1}$

If $(cos\alpha +cos\beta {)}^2+(sin\alpha +sin\beta {)}^2=\lambda co{s}^2\left(\frac{\alpha -\beta }{2}\right)$, write tha value of $\lambda$

Let A = {x, y, z} and B = {a, b}. Find the total number of relations from A into B.

With reference to figure which of the following is possible?

If the distance between the foci of an ellipse is 6 and the length of the minor axis is 8, then the eccentricity Is

Let f and g be real functions defined by $f\left(x\right)=\sqrt{x+2}\mathrm{and}g\left(x\right)=\sqrt{4-x^2}.\mathrm{Then},\mathrm{the}\mathrm{domain}\mathrm{of}\mathrm{the}\mathrm{function}\left(\frac{f}{g}\right)\left(x\right)\mathrm{is}$

Equation of tangent drawn to circle $|z|=r$ at the point $A\left(z_0\right)$ is

Two dice are thrown simultaneously 500 times. Each time the sum of two numbers appearing on their tops is noted and recorded as given in the following table

$\begin{array}{cc}\text{Sum}& \text{Frequency}\\ 2& 14\\ 3& 30\\ 4& 42\\ 5& 55\\ 6& 72\\ 7& 75\\ 8& 70\\ 9& 53\\ 10& 46\\ 11& 28\\ 12& 15\end{array}$

If the dice are thrown once more, then what is the probability of getting a sum
(i) 3?
(ii) More than 10?
(iii) Less than or equal to 5?
(iv) Between 8 and 12?

Let $f\left(x\right)=\{\begin{array}{cc}{x}^{p}sin\frac{1}{x},& x\ne 0\\ 0,& x=0\end{array}$ then f(x) is continuous but not differential at x = 0 if

In $R^3$, consider the planes $P_1:y=0$ and $P_2:x+z=1.$ Let $P_3$ be a plane, different from $P_1$ and $P_2$, which passes through the intersection of $P_1$ and $P_2.$ If the distance of the point $(0,1,0)$ from $P_3$ is $1$ and the distance of a point $(\alpha ,\beta ,\gamma )$ from $P_3$ is $2$, then which of the following relations is/are true?

The equation of the lines joining the vertex of the parabola $y^2=6x$ to the points on it whose abscissa is 24, is

A ray emitting from the point $(-3,0)$ is incident on the ellipse $16x^2+25y^2=400$ at point $P$ with an ordinate $4.$ If the equation of the reflected ray after first reflection is $4x+3y=k,$ then the value of $k$ is

If (i, j)th element of matrix A is 2+3i , what is the corresponding element in A* or conjugate of A.

If $S=\frac{1^2}{1\cdot 3}+\frac{2^2}{3\cdot 5}+\frac{3^2}{5\cdot 7}+....+\frac{{1008}^2}{\left(2015\right)\cdot \left(2017\right)}$ such that $4S=1008+\frac{1000+p}{2000+q},$ $p\text{\&}q\in I^{+},$ then $q-p$ is

If $z_1=a+ib$ and $z_2=c+id$ are complex numbers such that $|z_1|=|z_2|=1$ and $R\left(z_1\overline{z_2}\right)=0$, then the pair of numbers $w_1=a+ic$ and $w_2=b+id$ satisfies

In a town of 10,000 families it was found that 40% families buy newspaper A, 20% buy newspaper B and 10% buy newspaper C, 5% buy A and B, 3% buy B and C and 4% buy A and C. If 2% buy all the three newspapers, then number of families which buy A only is ________.

In a triangle $\Delta ABC$, the sum of the lengths of two sides is represented by $p$ and the product of the lengths of the same two sides is $q$. Let $c$ be the third side. If $p^2=c^2+2q$, then the area of the circumcircle of $\Delta ABC$ is

Given $a{x}^2$ $+$ $bx$ $+c$ $\ge 0$ , $b{x}^2+cx+a\ge 0$ , $c{x}^2+ax+b\ge 0$ where $a\ne b\ne c$ and $a,b,cϵR$ . Now $\frac{a^2+b^2+c^2}{ab+bc+ca}$ cannot take the value(s)

Equation of the line passing through (1,1,1) and perpendicular to $2x-3y+z=0$ is

Let $f_k\left(x\right)=\frac{1}{k}({\sin }^{k}x+{\cos }^{k}x)$ where $x\in R$ and $k\ge 1$. Then $f_4\left(x\right)-f_6\left(x\right)$ equals:

The equations of tangents drawn from the point (2,3) to the ellipse $9x^2+16y^2=144$ are:

The mean square deviation of a set of $n$ observations $x_1,x_2,.......x_n$ about a point $c$ is defined as $\frac{1}{n}\sum _{i=1}^n(x_i-c{)}^2$. The mean square deviation about $–2$ and $2$ are $18$ and $10$ respectively, then standard deviation of this set of observations is

If $f\left(x\right)=\{\begin{array}{cc}2x+3& ,x\le 0\\ 3(x+1)& ,x>0\end{array}$ Find $li{m}_{x\to 0}f\left(x\right)$ and $li{m}_{x\to 1}f\left(x\right).$

If a, b, c are in G.P. then prove that : $\frac{a^2+ab+b^2}{bc+ca+ab}=\frac{b+a}{c+b}$

Chord of contact from any point on the line x + y = 4r to the circle $x^2+y^2=r^2$ (such that $r>0$) passes through the point (1, 1).What will be the value of r.

A student was asked to prove a statement P(n) by induction. He proved P(k + 1) is true whenever P(k) is true for all k > 5 $epsilon$ N and also (5) is true. On the basis of this he could conclude that P(n) is true.

Cheeck whether the relation R. defined in the set {1,2,3,4,5,6} as R ={(a,b):b=a+1} is reflexive, symmetric or transitive.

Given that the event A and B ar esuch that $P\left(A\right)=\frac{1}{2}P(A\cup B)=\frac{3}{5}andP\left(B\right)=p.$ Find p, if they are
independent

Find multiplicative inverse of the complex number $(2+\sqrt{3i}{)}^2.$