Explore topic-wise InterviewSolutions in Current Affairs.

The mean of 5 obsservations is 4.4 and their variance is 8.24. If three of the observations are 1, 2 and 6, find the other two observations.

Three coins are tossed simultaneously. List the sample space for the event.

The tangent at A (2, 4) on y = $x^3$ -2$x^2$ + 4 cuts the x axis at T then AT =

Let $S_k=\frac{1+2+3+....+k}{k}.$ If
$S_1^2+S_2^2+...+S_{10}^2=\frac{5}{12}A$, then $A$ is equal to:

Differentiate the following functions with respect to x :

$(2x^2+1)(3x+2)$

If tan $x=\frac{b}{a}$, then find the value of $\sqrt{\frac{a+b}{a-b}}+\sqrt{\frac{a-b}{a+b}}$.

Coefficient of $x^{17}$ in the expansion of $(1+x^5+x^7{)}^{20}$ is $\lambda$, then $\frac{\lambda }{380}$ is equal to ___

The value of ${\sin }^{-1}\left(\frac{12}{13}\right)-{\sin }^{-1}\left(\frac{3}{5}\right)$ is equal to :

The equation of the circle which cuts orthogonally each of the three circles given below:
$x^2+y^2-2x+3y-7=0$, $x^2+y^2+5x-5y+9=0$ and $x^2+y^2+7x-9y+29=0$

If we convert the denominator of the integral into a perfect square, $\int \frac{1}{x^2-x+1}dx$ then the correct integral will be

If $3(2-x)\ge 2(1-x)$ and $x\in R$, then $x\in$

A beam is supported at its ends by two supports which are $12\text{m}$ apart. Since the load is concentrated at its centre, there is a deflection of $3\text{cm}$ at the centre and the deflected beam is in the shape of a parabola. Then distance from the centre where deflection is $1\text{cm},$ is

$L:x^2+2gxy+y^2=0$ represents the equation of pair of straight lines passing through the origin. If $L$ makes an acute angle of $\theta$ with the straight line $y=x$, then

Assume that a bag contains 4 red squares, 3 red rectangles, 5 blue squares and 4 blue circles. An object is taken out from the bag. What is the probability of taking out a blue square?

If the line $y=\sqrt{3}x$ cuts the curve $x^3+y^3+3xy+5x^2+3y^2+4x+5y-1=0$ at points $A,B,C$ then $\left(\text{where O is origin}\right)$

Evaluate: $\int \frac{1}{co{s}^{4}x+si{n}^{4}x}dx.$

Find $\frac{dy}{dx}$in the following questions:

$si{n}^{2}y+cosxy=k$

Let $f:R\to R:f\left(x\right)=x+2$ and $g:R-\left\{2\right\}\to R:g\left(x\right)=\frac{x^2-4}{x-2}$
Show that $f\ne g$. Re-define f and g such that f = g

Give the proforma of a Bills Payable

If the 8th term of an H.P. is 1/2 and the 14th term is 1/3, then the 20th term is

Find the harmonic mean of 1, $\frac{1}{2}$,$\frac{1}{3}$.

The AM between m and n and the GM between a and b are each equal to \frac{ma+nb}{m+n}. What are m and n in terms of a and b?

Number of points from where perpendicular tangents to the curve $\frac{x^2}{16}-\frac{y^2}{25}=1$ can be drawn, is:

Given positive integers r > 1, n > 2 and the coefficients of $(3r{)}^{th}$ and $(r+2{)}^{th}$ terms in the Binomial expansion of $(1+x{)}^{2n}$ are equal, then:

Find the sum of 40 terms of the series 1 + 5 + 12 + 22 + 35 + .................

A particle moves along the curve $y=x^2+2x$, then the point on the curve such that x and y coordinates of the particle changes with same rate is

How many odd numbers less than 1000 can be formed by using the digits 0, 3, 5, 7 when repetition of digits is not allowed ?

Let A = {1,2,3,4,5,6,7}. P={1,2}, Q = {3, 7}. Write the elements of the set R so that P, Q and R form a partition that results in equivalence relation.

If the median AD of a triangle ABC is perpendicular to AB then the value of tan A+ 2tan B

Factories:

$12x^2-25x+12$

f a function $f:[-2a,2a]\to R$ is an odd function such that $f(2a-x)=f\left(x\right),\forall xϵ[a,2a]$ and left hand derivative at x = a is 0 then find left hand derivative at x = -a

If $\alpha ,\beta ,\gamma$ are the roots of the equation $x^3$ + px + q = 0, then the value of the determinant $\left|\begin{array}{ccc}\alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta \end{array}\right|$ is

For $xϵR,f\left(x\right)=|log2-sinx|andg\left(x\right)=f\left(f\right(x\left)\right)$ then:

To verify Lagrange's Mean value Theorem which one is essential.

Integrate the following functions w.r.t. x.

$\int \frac{cosx}{\sqrt{4-si{n}^{2}x}}dx.$

Find the locus of a point such that the line segments having end points(2,0) and (-2,0) subtend a right angle at that point.