Explore topic-wise InterviewSolutions in Current Affairs.

If the curve $\frac{x^2}{4}+y^2=1$ and $\frac{x^2}{a^2}+y^2=1$ for suitable values of ${}^{\prime }{a}^{\prime }$ cut on four concyclic points, the equation of the circle passing through these points is

$\text{if (gof)(x)=|sin x| and (fog)(x)=}{\left(sin\sqrt{x}\right)}^2\text{then}$

If a and b are two collinear vectors, then which of the following are incorrect:
(a) b = $\lambda a$, for some scalar $\lambda$
(b) $\hat{a}=\pm \hat{b}$
(c) The respective components of a and b are proportional.
(d) Both the vectors a and b have same direction but different magnitudes.

(i) Find the derivative of $\sqrt{\frac{(x-1)(x-2)}{(x-3)(x-4)}}$ + $\frac{sinx}{1+tanx}$

(ii) Evaluate ${lim}_{x\to 0}\frac{(1+x{)}^6-1}{(1+x{)}^2-1}$

If a convex polygon has $35$ diagonals, then the number of triangles formed by joining the vertices of the polygon is :

If $f\left(x\right)=\frac{sin\left(\pi \right[x-\pi \left]\right)}{1+\left[x^2\right]}$ (Where [.] denotes the G.I.F.,) then f(x) is

Integrate the function.
$\int x^2{e}^{x}dx.$

Find the acute angles A and B satisfying

1)cot(A+B)= 1 , cosec(A-B)= 2

2)secAcotB -secA-2cotB+2=0

Which of the following should be the FIRST sentence after rearrangement?

If $\alpha ,{\alpha }^2$ are the roots of the equation $x^2-90x+k=0$, find sum of all possible values of k.

Let $f\left(x\right)$ be a real valued function, then the domain of $f\left(x\right)=\sqrt{x-\sqrt{1-x^2}}$ is

The function f is

100 A.Ms are inserted between 20 and 80. Find the sum of first A.M and last A.M

if $f\left(x\right)=\sqrt{x}$, $g\left(x\right)=\frac{3x^2-x^6}{1-3x^4}$ and $h\left(x\right)=\tan x,$ then $(g\circ f\circ h)\left(\frac{\pi }{3}\right)$ is

If $\left({\log }_{5}x\right)\left({\log }_{x}3x\right)\left({\log }_{3x}y\right)={\log }_x{x}^3$, then $y$ equals

The equation of the transverse and conjugate axis of the hyperbola $16x^2-y^2+64x+4y+44=0$ are

The value of m for which the area of the triangle included between the axes and any tangent to the curve $x^{m}y=b^m$ is constant is

The horizontal range and maximum height for a projectile is same. The angle of projectile is

For any $\theta \in (\frac{\pi }{4},\frac{\pi }{2})$, the expression $3(\sin \theta -\cos \theta {)}^4+6(\sin \theta +\cos \theta {)}^2+4{\sin }^6\theta$ equals:

The minimum area of triangle formed by the tangents to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and coordinate axes is:

The vector equation of the plane through the point (2, 1, –1) and passing through the line of intersection of the plane $\overline{r}.(\hat{i}+3\hat{j}-\hat{k})=0$ and $\overline{r}=(\hat{j}+2\hat{k})=0$ , is :
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What is the meaning of '!' in numericals

If $P=\left[\begin{array}{ccc}1& \alpha & 3\\ 1& 3& 3\\ 2& 4& 4\end{array}\right]$ is the adjoint of a $3\times 3$ matrix $A$ and $|A|=4$, then $\alpha$ is equal to :

The binomial distribution for which mean = 6 and variance = 2, is

$\text{A point moves in a plane so that its distances PA and PB from two fixed points A and B in the plane satisfy the relation PA-PB}=k(k\ne 0),thenthelocusofPis$

In the expansion of $(1+x{)}^n$ the binomial coefficients of three consecutive terms are respectively 220, 495 and 792, find the value of n.

The numerator of the fraction $\frac{4x+1}{x^2+3x+2}$, can be expressed as
$\lambda \times \frac{d}{dx}\left(x^2+3x+2\right)+\mu$, the values of $\lambda \mathrm{and}\mu$ are?

Draw the graph of each of the following constant functions:

(i) $f\left(x\right)=2$ for all $xϵR$

(ii) $f\left(x\right)=0$ for all $xϵR$

(iii) $f\left(x\right)=-2$ for all $xϵR$

If $\int \frac{se{c}^{2}x-2010}{si{n}^{2010}x}dx=\frac{f\left(x\right)}{si{n}^{2010}x}+c$, then $f\left(\frac{\pi }{3}\right)=$ is

The proposition $p\to \sim (p\wedge \sim q)$

$\text{Express the det}A=\left|\begin{array}{ccc}a& bc& abc\\ b& ca& abc\\ c& ab& abc\end{array}\right|\text{as product of factors}$

The function $f\left(x\right)=|x|+|x-1|$ is not differentiable at

The sum of all real values of x satisfying the equation ${(x^2-5x+5)}^{x^2+4x-60}=1$ is:

If $\overrightarrow{a}\times (\overrightarrow{b}\times \overrightarrow{c})$ is perpendicular to $(\overrightarrow{a}\times \overrightarrow{b})\times \overrightarrow{c}$ then, we may have,

${}^n{C}_r÷{}^n{C}_{r-1}$ =