Explore topic-wise InterviewSolutions in Current Affairs.

Find the sum of the series when n = 10. $\frac{C_1}{C_0}$ + 2 $\frac{C_2}{C_1}$ + 3 $\frac{C_3}{C_2}$ + ...............+ n $\frac{C_n}{C_{r-1}}$

The product of the length of the perpendiculars drawn from the point (1,1) to the pair of lines x^2 + xy - 6y^2 = 0 is?

Let $f\left(x\right)=\frac{x^2-1}{x},g\left(x\right)=\frac{x+2}{x-3}$ then domain of $\frac{f\left(x\right)}{g\left(x\right)}$ is

Find the value of $\underset{x\to 0}{lim}\frac{sinx}{x}$

Suppose $f\left(x\right)=e^{ax}+e^{bx}$, where $a\ne b$, and that $f"\left(x\right)-2f"\left(x\right)-15f\left(x\right)=0$ for all x. Then the product ab is equal to

The equation of plane through the intersection of planes (x+y+z =1) and (2x +3y - z+4) =0 is

A grain wholesaler earns a profit of 12 Rs per bag of wheat sold and a loss of 8 Rs per bag of rice sold.

(a) If he sells 1500 bags of wheat and 2050 bags of rice in a month, what is his profit or loss?

(b) What is the number of wheat bags he must sell to have neither profit nor loss, if the number of rice bags sold is 2400 bags?

Let $a,b,c>0,a+b+c=15$.
The least value of $E=\frac{a^3}{a^2+ab+b^2}+\frac{b^3}{b^2+bc+c^2}+\frac{c^3}{c^2+ca+a^2}$ is___

If $4^{th}$ term in the expansion of ${(2+\frac{3}{8}x)}^{10}$ is numerically greatest term . Then the range of $x$ is

Find the orthogonal trajectory of $x^2+y^2=c$

The angle between the tangents drawn from a point P to a circle is ${60}^{\circ }$ and the length of theTangent from the circle $2\sqrt{3}$ units. Then the radius of the circle is

If $\alpha ,\beta$ are the solutions of $\cot x=-\sqrt{3}$ in $[0,2\pi ]$ and $\alpha ,\gamma$ are the solutions of $\text{cosec}x=-2$ in $[0,2\pi ],$ then

${\int }_0^{\frac{\pi }{2}}{e}^{x}sinxdx=$ [Roorkee 1978]

If $\sum _{r=0}^{44}{}^{49-r}{C}_5={}^{50}{C}_x$, then the value(s) of $x$ is/are

If tan A, tan B are the roots of $x^2-Px+Q=0$ the value of $si{n}^2$ (A+B)=(where P, Q $ϵ$ R)

A tangent to the parabola $x^2=4ay$ meets the hyperbola $x^2-y^2=a^2$ at two points P and Q, then midpoint of P and Q lies on the curve

The locus of the orthocentre of the triangle formed by the lines $(1+p)x-py+p(1+p)=0,$$(1+q)x-qy+q(1+q)=0$ and $y=0,$ where $p\ne q,$ is

If step II of a given input is ‘fear 116 1468 say 1124 get 148 horn’ then

which of the following is step Vl?

The slope of a line passing through P$(2,3)$ and intersecting the line, $x+y=7$ at a distance of 4 units from P, is:

The value of integral ${\int }_1^{e^6}\left[\frac{logx}{3}\right]dx$, where [.] denotes the greatest integer function, is

The value of the expression $\cos {20}^{\circ }\cos {100}^{\circ }+\cos {100}^{\circ }\cos {140}^{\circ }-\cos {140}^{\circ }\cos {200}^{\circ }$ is

The locus of midpoint of chord of the circle $x^2+y^2-2x-2y-2=0$, which makes an angle of ${120}^{\circ }$ at the centre, is

A double ordinate $PQ$ of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is such that $\Delta OPQ$ is equilateral, $O$ being the centre of the hyperbola. Then the eccentricity $e$ satisfies the relation

The number of ordered triplets of natural numbers $(a,b,c)$ for which $abc\le 11$ is

Show that the path of a moving point such that its distances from two lines $3x-2y=5$ and $3x+2y=5$ are equal is a straight line.

Find the length and the foot of perpendicular from the point $(1,\frac{3}{2},2)$ to the plane 2x-2y+4z+5=0.

Given $\Delta$$=\left|\begin{array}{ccc}P& 2-i& i+1\\ 2+i& q& 3+i\\ 1-i& 3-i& r\end{array}\right|$, $\Delta$ is

The first three of four given numbers are in G.P. and their last three are in A.P., with common difference 6. If first and fourth numbers are equal, then the first number is

Area of a rectangle having vertices $A(-\hat{i}+\frac{1}{2}\hat{j}+4\hat{k}),B(\hat{i}+\frac{1}{2}\hat{j}+4\hat{k}),C(\hat{i}-\frac{1}{2}\hat{j}+4\hat{k})$ and $D(-\hat{i}-\frac{1}{2}\hat{j}+4\hat{k})$ is

a) $\frac{1}{2}$
b) 1
c) 2
d) 4

The lines joining the origin and the common points of $(x-3{)}^2+(y-4{)}^2=r^2$ and $4x+3y=24$ are at right angles then $|r|$ = __________

The number of integral solutions of the equation $x+y+z+t=20,$ such that $x\ge 0,y\ge 1,z\ge 2,t\ge 3,$ is

A (p, 0), B(4, 0), C(5, 6), D(1, 4) are the vertices of a quadrilateral ABCD. If $\angle$ ADC is obtuse, the maximum integral value of p is

Let the two vertices of a triangle are $(2,-1)$ and $(3,2)$ and third vertex lies on the line $x+y=5$. If the area of triangle is $4\text{sq. units}$, then the coordinates of the third vertex is/are

If the angle of intersection of the circles $x^2+y^2+x+y=0$ and $x^2+y^2+x-y=0$ is $\theta$, then the equation of the line passing through $(1,2)$ and making an angle $\theta$ with the $y$-axis is

Differentiate each the following from first principles :

$\left(i\right)xsinx$

$\left(ii\right)x+cosx$

$\left(iii\right)sin(2x-3)$

$\left(iv\right)\sqrt{sin2x}$

$\left(v\right)\frac{sinx}{x}$

$\left(vi\right)\frac{cosx}{x}$

$\left(vii\right)x^{2}sinx$

$\left(viii\right)\sqrt{sin(3x+1)}$

$\left(ix\right)sinx+cosx$

The equation of the directrix of a hyperbola is x-y+3 =0.Its ficys us(-1,1) and eccentricity 3.Find the equation of the hyperbola.

What can be said regarding a line if its slope is

(i) zero (ii) positive (iii) negative ?

The value/s of $\theta$ lying between 0 and $\frac{\pi }{2}$ and satisfying the equation $\left|\begin{array}{ccc}1+si{n}^2\theta & co{s}^2\theta & 4sin4\theta \\ si{n}^2\theta & 1+co{s}^2\theta & 4sin4\theta \\ si{n}^2\theta & co{s}^2\theta & 1+4sin4\theta \end{array}\right|=0,are$

The value of the limit $\underset{x\to e}{\lim }\frac{\log x-1}{x-e}$ is

Find the equation of a curve passing through the point (0,2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5.

If $xsin(a+y)+sina.cos(a+y)=0$, then prove that
$\frac{dy}{dx}=\frac{si{n}^2(a+y)}{sina}$

Solve the equation $z+\sqrt{2}|z+1|+i=0$ for complex value of z.

Evaluate:
$\left|\begin{array}{ccc}x+4& x& x\\ x& x+4& x\\ x& x& x+4\end{array}\right|$