Explore topic-wise InterviewSolutions in Current Affairs.

Solve
system of linear equations, using matrix method.

x −
y + 2z = 7

3x
+ 4y − 5z = −5

2x
− y + 3z = 12

The interior of building is in the form of a right circular cylinder of radius 7m and height 6m, surmounted by a right circular cone of same radius and of vertical angle ${60}^{\circ }$. Find the cost of painting the building from inside at the rate of Rs 30 per $m^2$

Determine if f
defined by

is a continuous function?

Let $p,q,r$ be all distinct real numbers and the vectors $p\hat{i}+p^2\hat{j}+(1+p^3)\hat{k},q\hat{i}+q^2\hat{j}+(1+q^3)\hat{k},$ and $r\hat{i}+r^2\hat{j}+(1+r^3)\hat{k}$ are coplanar. Then $pqr$ equals

At what points on the curve $x^2+y^2-2x-4y+1=0$ are the tangents parallel to the y axis?

If $f\left(x\right)$ and $g\left(x\right)$ are differentiable functions such that $f(x+y)=f\left(x\right)f\left(y\right)\forall x,y\in R$ and $f\left(x\right)=1+\sin \left(3x\right)g\left(x\right),$ then $f^{\prime }\left(x\right)$ is equal to

Let $x,y$ and $z$ be positive real numbers. Suppose $x,y$ and $z$ are the lengths of the sides of a triangle opposite to its angles $X,Y$ and $Z,$ respectively. If

$\tan \frac{X}{2}+\tan \frac{Z}{2}=\frac{2y}{x+y+z}$,

then which of the following statements is/are TRUE?

The Newton-Raphson iteration formula for finding $\sqrt[3]{3c}$ where c > 0 is,

If $\alpha ,\beta ,\gamma$ are three angles given by $\alpha =2ta{n}^{-1}(\sqrt{2}-1),\beta =3si{n}^{-1}\frac{1}{\sqrt{2}}+si{n}^{-1}\left(\frac{-1}{2}\right)and\gamma =co{s}^{-1}\left(\frac{1}{3}\right),$ then

If $A=\left[\begin{array}{cccc}1& 0& 2& 3\\ 4& 2& 6& 4\end{array}\right]$ then fourth element of second column of $A^T$ =

If $A=\{1,2,3\},B=\{4,5,6,7,8\},$ $C=\{4,8,12,16,20\},$ then $n\left[\right(A\times B)\cup (A\times C\left)\right]=$

If $d\ne 0$ and $a(a+d),(a+d)(a+2d),(a+2d)a$ are in G.P., then the common ratio is

The value of ${\cos }^2{45}^{\circ }-{\sin }^2{15}^{\circ }$ is:

Convert the following products into factorials:
(i) 5.6.7.8.9.10 (ii) 3.6.9.12.15.18
(iii) (n+1)(n+2)(n+3) ...(2n) (iv) 1.3.5.7.9 ...(2n-1)

For two sets $A$ and $B$, $(A\cup B)\cap (A^{\prime }\cup B^{\prime })=$

Cards are drawn from a pack of 52 cards one by one. The probability that exactly 10 cards will be drawn before the first ace cards is

Ben bought $20$ packets of candy for distributing among his classmates on his birthday. Each packet contains $8$ chocalates. Find total number of chocalates Ben bought

The order of differential equation of family of curves given by $y=a_1(a_2+a_3)\cdot \cos (x+a_4)-a_5{e}^{x+a_6},$ is

If ${\int }_0^{\pi }xf\left(sinx\right)dx=A{\int }_0^{\frac{\pi }{2}}f\left(sinx\right)dx,$ then A is equals to

Given the function $f\left(x\right)=\frac{1}{1-x},$ the number of point(s) of discontinuity of the composite function $y=f^{3n}\left(x\right),$ where, $f^n\left(x\right)=fof\cdots of\left(n\text{times}\right)\left(x\right),(n\in N)$ is

Three critics review a book. Odds in favour of the book are $5:2,4:3$ and $3:4$, respectively for the three critics. The probability that majority are in favor of the book is:

The equation of common tangent to the circles $x^2+y^2=4$ and $x^2+y^2-6x-8y-24=0$ is

Which of the following is the identity pair of addition and multiplication in order?

If f : D $\to$R $f\left(x\right)=\frac{x^2+bx+c}{x^2+b_{1}x+c_1},where\alpha ,\beta$ are th roots of the equation $x^2+bx+c=0$ and ${\alpha }_1,{\beta }_1$ are the roots of $x^2+b_{1}x+c_1=0$. Now, answer the following question for f(x). A combination of graphical and analytical approach may be helpful in solving these problems. If ${\alpha }_{1}and{\beta }_1$ are real, then f(x) has vertical asymptote at $x=({\alpha }_1,{\beta }_1$).

If the equations $x^2$ + bx + c = 0 and $x^2+b_{1}x+c_1=0$ do not have real roots, then

Find the equation of the planes that passes through the sets of three points.
(1,1,0),(1,2,1),(-2,2,-1)

The equation of the circle which is touched by $y=x$, has its centre on the positive direction of the $x$-axis and cuts off a chord of length $2$ units along the line $\sqrt{3}y-x=0$, is

If the terms of a G.P. are a, b and c, respectively. Prove that

For the
differential equation
find
the solution curve passing through the point (1, –1).

Solve the following system of equations in R.
$|3-4x|\ge 9$

If the distance of the point $P(1,–2,1)$ from the plane $x+2y–2z=\alpha$, where $\alpha >0$, is $5$, then the foot of the perpendicular from $P$ to the plane is

The minimum value of $\frac{(6+x)(11+x)}{(2+x)},x\ge 0$ is

The equation of the hyperbola whose directrix is $x+2y=1$, focus $(2,1)$ and eccentricity $2$ is

Find the values of
is
equal to

(A) (B) (C) (D) 1