Explore topic-wise InterviewSolutions in Current Affairs.

Let P(x) be a quadratic in 'x' satisfying P(0) = $co{s}^3{40}^{\circ },P\left(1\right)=cos{40}^{\circ }si{n}^2{40}^{\circ },P\left(2\right)=0$. Then P(3) equals

In a triangle $ABC$, $\angle BAC={90}^{\circ };$ $AD$ is the altitude from $A$ on to $BC.$ Draw $DE$ perpendicular to $AC$ and $DF$ perpendicular to $AB.$ Suppose $AB=15$ and $BC=25.$ Then the length of $EF$ is

For positive integers the value of the expression $(1+i{)}^{n_1}+(1+i^3{)}^{n_1}+(1+i^5{)}^{n_2}+(1+i^7{)}^{n_2}$where $i=\sqrt{-1}$is a real number if and only if

The point A(sin θ, cosθ) is 3 units away from the point B $(2cos{75}^{\circ },2sin{75}^{\circ })$. If $0^{\circ }\le \Theta <{360}^{\circ }$, then $\Theta$ is _____ degree

The range of the function $f\left(x\right)=\frac{x+3}{|x+3|},x\ne -3$ is

The order of the differential equation is

[MP PET 1994]

The equation of the ellipse whose vertices are ( ±5,0) and foci are ( ± 4 , 0 ) is

Find the equation of the line passing through the point (3,0,1) and parallel ti the planes x+2y=0 and 3y-z=0.

Find the area of the triangle with vertices A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5)

Equation of the parabola with focus (3,-4) and directrix x+y+7=0

The expression for $n^{th}$ term of an AP is

A function $f:R\to R^{+}$ satisfies $f(x+y)=f\left(x\right)f\left(y\right)\forall x,yϵR.$ If $f^{\prime }\left(0\right)=2$ then$\forall x,yϵR$, $f^{\prime }\left(x\right)=$

A perpendicular is drawn from a point on the line $\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z}{1}$ to the plane $x+y+z=3$ such that the foot of the perpendicular $Q$ also lies on the plane $x-y+z=3$. Then the co-ordinates of $Q$ are :

Given that the equation $z^2+(p+iq)z+r+is$=0 where p,q,r,s are real and non-zero has a real root, then

If the permutations of a, b, c, d, e taken all together be written down in alphabetical order as in dictionary and numbered, find the rank of the permutation debac.

If ${\sum }_{r=1}^{20}\left(r\right)=a,{\sum }_{r=1}^{20}\left(r^2\right)=b$ then the sum of products of $1,2,3,\dots 20$ taking two at a time is

An angle between the lines whose direction cosines are given by the equations, $l+3m+5n=0$ and $5lm-2mn+6nl=0$, is :

Prove that:
(i) $\frac{sinA+sin3A}{cosA-cos3A}=cotA$
(ii) $\frac{sin9A-sin7A}{cos7A-cos9A}=cot8A$
(iii) $\frac{sinA-sinB}{cosA-cosB}=tan\frac{A-B}{2}$
(iv) $\frac{sinA+sinB}{sinA-sinB}tan\left(\frac{A+B}{2}\right)cot\frac{A+B}{2}$
(v) $\frac{cosA+cosB}{cosB-cosA}=cot\frac{A+B}{2}cot\frac{A-B}{2}$

If x sin (a + y) + sin a cos (a + y) = 0, then the value of $\frac{\mathrm{dy}}{\mathrm{dx}}$ is

The complete set of values of $x$ satisfying $5x+2<3x+8$ and $\frac{x+2}{x-1}<4,$ is

Differentiate the following functions with respect to x :

$\frac{xsinx}{1+cosx}$

If P(n) is the statement "n^2 + n is even", and if P (r) is true, then P (r + 1) is true.

Number of real normals to the parabola $y^2=16x,$ passing through $(4,0)$ is

If $\sqrt{2}\sin A=\sin B-{\sin }^{3}B$ and $\sqrt{2}\cos A=\cos B+{\cos }^{3}B$, then the possible value(s) of $\sin (A-B)$ is/are

The $n^{\text{th}}$ term of a sequence of numbers is $a_n$ and given by the formula $a_n=a_{n-1}+2n$ for $n\ge 2$ and $a_1=1.$
The sum of first $20$ terms is

Find the angle between the following pair of lines

$\frac{x-2}{2}=\frac{y-1}{5}=\frac{z+3}{-3}and\frac{x+2}{-1}=\frac{y-4}{8}=\frac{z-5}{4}$

$\frac{x}{2}=\frac{y}{2}=\frac{z}{1}and\frac{z-5}{4}=\frac{y-2}{1}=\frac{z-3}{8}$

Six balls are placed randomly into six cells. Then the probability that exactly one cell remains empty is

Find area of the triangle with vertices at the points in each of the following

(-2,-3), (3,2), (-1,-8)

Choose the correct answer.

$Iff(a+b-x)=f\left(x\right),then{\int }_a^{b}xf\left(x\right)dxisequalto\left(a\right)\frac{a+b}{2}{\int }_a^{b}f(b-x)dx\left(b\right)\frac{a+b}{2}{\int }_a^{b}f(b+x)dx\left(c\right)\frac{b-a}{2}{\int }_a^{b}f\left(x\right)dx\left(d\right)\frac{a+b}{2}{\int }_a^{b}f\left(x\right)dx$

If $2\tan A+\cot A=\tan B$, then the value of $\cot A+2\tan (A-B)$ is

By using properties of definite integrals, evaluate the integrals
${\int }_0^4|x-1|dx.$

If $f\left(x\right)=3\left[x\right]+1,g\left(x\right)=4[x-1]-10$, then the values of $x$ for which $f\left(x\right)=g\left(x\right)$ is
(where [.] denotes the greatest integer function)

The value of $a$ for which $\underset{x\to 0}{lim}\frac{(e^x-1{)}^2}{\sin \frac{x}{a}\log (1+\frac{x}{2})}=8$, is

Let the volume of tetrahedron $ABCD$ is $81$ cubic units and $G_1$, $G_2$, $G_3$ are centroids of triangular faces $ABC,ABD$ and $ACD$ respectively, then volume of tetrahedron $A{G}_1{G}_2{G}_3$ is -

A circle has its centre at the vertex of the parabola $x^2=4y$ and the circle cuts the parabola at the ends of its latus rectum. The equation of the circle is

The circle $x^2+y^2-8x=0$ and hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$ intersect at the points A and B.
Equation of the circle with AB as its diameter is

Prove that in any $△$ABC, $cosA=\frac{b^2+c^2-a^2}{2bc}$, where a, b and c are the magnitudes of the sides opposite to the vertices A, B and C, respectively.