Explore topic-wise InterviewSolutions in Current Affairs.

If $a\le 0$ then the real roots of the equation $x^2-2a|x-a|-3a^2=0$ is/are

What should come in place of both x in the equation $\frac{x}{\sqrt{16}}=\frac{\sqrt{4}}{x}$ ?

(sin²A- cos²A) (1- 2sin² A. cos²A)=.

Find the value of $\underset{x\to \infty }{lim}\frac{\left[x\right]+\left[2x\right]+\left[3x\right]+....\left[nx\right]}{n^2}$ where [.] is an greatest integer function.

Locus of a point, whose chord of contact with respect to the circle $x^2+y^2=4$ is a tangent to hyperbola $xy=1$ is :

The maximum number of permutations of $2n$ letters in which there are only $a^{\prime }s$ and $b^{\prime }s,$ taken all at a time is given by

Find the remainder when 5k-1 is divided by 5, where k is a positive integer

The range of the function $f\left(x\right)=\left[\right\{2x+3\left\}\right]$ is
$\left(\right[.]$ represents the greatest integer function and $\left\{x\right\}$ is the fractional part of $x)$

The equation of the circle which passes through $(8,16)$ and touches the line $4x-3y=64$ at $(16,0)$ is

If $t^2+t+1=0$, then ${(t+\frac{1}{t})}^2+{(t^2+\frac{1}{t^2})}^2+{(t^3+\frac{1}{t^3})}^2....+{(t^{27}+\frac{1}{t^{27}})}^2$ is equal to

Choose the correct answer. The value of
${\int }_{\frac{-\pi }{2}}^{\frac{\pi }{2}}(x^3+xcosx+ta{n}^{5}x+1)dx$ is
$\text{(a) zero (b) 2 (c)}\pi \text{(d) 1}$

Find the equation of the plane through the intersection of the planes $\overrightarrow{r}.(\hat{i}+3\hat{j})-6=0$ and $\overrightarrow{r}.(3\hat{i}-\hat{j})-4\hat{k}=0$, whose perpendicular distance from origin is unity.

Find the equation of the hyperbola satisfying the given conditions.
Foci (4, 0), the latus rectum is of length 12.

If A is a square matrix of order 3 such that $|A|=2$ then the value of $|(adj{A}^{-1}{)}^{-1}|$ is ___ .

Prove the following:
$\frac{\text{cos 9x}-\text{cos 5x}}{\text{sin 17x}-\text{sin 3x}}=-\frac{\text{sin 2x}}{\text{cos 10x}}$

If $(p\wedge \sim r)\to (\sim p\vee q)$ is false, then the truth values of $p,q,r$ respectively, are

If $y=sin\left(sinx\right)and\frac{d^{2}y}{d{x}^2}+\frac{dy}{dx}tanx+f\left(x\right)=0,thenf\left(x\right)equals$

The complex number $z$ satisfying the equation $|z-i|=|z+1|=1$ is

Solution set of $\frac{(x-1)(x-2{)}^2(x-4)}{(x+2)(x-3)}\ge 0$ is :

If $xϵR$ and $nϵI$, then the determinant $\Delta =\left|\begin{array}{ccc}\sin \left(n\pi \right)& \sin x-\cos x& \log \left(\tan x\right)\\ \cos x-\sin x& \cos \left[\right(2n+1\left)\frac{\pi }{2}\right]& \log \left(\cot x\right)\\ \log \left(\cot x\right)& \log \left(\tan x\right)& \tan \left(n\pi \right)\end{array}\right|$

For real $x$, the greatest value of $\frac{x^2+2x+4}{2x^2+4x+9}$ is

The fundamental period of the function $\frac{|\sin x|+|\cos x|}{|\sin x-\cos x|}$ is

Find 2*2 matrix A such that. A[1 -2]. =6I₂ [ 1 4]

If the sides of a triangle are in GP and the largest angle is twice the smallest angle, then the common ratio, which is greater than 1, lies in the interval

Find the cofactor of the element $a_{32}$ in the matrix $\left[\begin{array}{ccc}5& 1& 2\\ 3& 2& 1\\ 9& 9& 5\end{array}\right]$

If 2√3 is the root of quadratic equation px²+qx+r=0 for (p,q,r) belongs to R , then find value of (p+q+r)

The number of ways in which the letters of the word ${}^{\prime }MADHUR{I}^{\prime }$ can be arranged so that vowels always occupy the beginning, middle and end places is

If f(x) = x - 1 ÷ x + 1 then f(2x) in terms of f(x) is?

If $\alpha$ is a complex, such that $\alpha$$z^2$ + z +$\overline{\alpha }$ = 0 has a real root. Then

If $\alpha ,\beta and\gamma$ are the roots of the equation $x^3+3x+2=0$ , Find the equation whose roots are $\alpha -\beta \left)\right(\alpha -\beta ),(\beta -\gamma \left)\right(\beta -\alpha ),(\gamma -\alpha \left)\right(\gamma -\beta$.

The focus and directrix of a parabola are (1,-1) and x+y+3=0. Its vertex is

How many three digit numbers are there with distinct digit with each digit odd?

The sum of the coefficients of all the integral powers of x in $(1+3\sqrt{x}{)}^{100}$ is

A father has three children with at least one boy. The probability that he has two boys and one girl is

Let $f\left(\frac{x+y}{2}\right)=\frac{1}{2}\left(f\right(x)+f(y\left)\right)$ for real x and y. If f' (0) = – 1 and f(0) = 1 then f(2) is

f(x) = {x} + {x + 1} + {x + 2} + .......+ {x + 999} then $\left[f\right(\sqrt{2}\left)\right]$ (where {.} denotes fractional part of x and [.] denotes greatest integer of x) is equal to

Consider the family of all circles whose centers lie on the straight line $y=x$. If this family of circles is represented by the differential equation $P{y}^{\prime \prime }+Q{y}^{\prime }+1=0$, where $P,Q$ are functions of $x,y\text{and}{y}^{\prime }(\text{here}{y}^{\prime }=\frac{dy}{dx},y^{\prime \prime }=\frac{d^{2}y}{d{x}^2}),$ then which of the following statements is (are) true ?

The coefficient of $x^{100}$ in the expansion of ${\sum }_{j=0}^{200}(1+x{)}^j$ is

The area of the region bounded by the curves $y=x^2$ and $y=\frac{2}{1+x^2}$ is

The portion of the tangent intercepted between the point of contact and the directrix of the parabola \( y^2 = 4ax\) subtends at the focus an angle of

If $\frac{1}{lo{g}_3\pi }+\frac{1}{lo{g}_4\pi }>x$, then x be

If either $\text{a = 0 or b = 0}$, then $a\times b=0$. Is the converse true? Justify your answer with an example.

The distance between the parallel lines 8x+6y+5=0 and 4x+3y-25=0 is

How many of the following statements are correct?

1. $\int x^{2}dx=x^3$

2. $\int sinxdx=cosx$

3. $\int e^{x}dx=Inx$

4. $\int \frac{1}{x}dx=x^0$

5. $\int tanxdx=se{c}^{2}x$