Explore topic-wise InterviewSolutions in Current Affairs.

Find the root of the equation.

X-1/x=3,x≠0.

The vertices of an acute angled triangle are $A(x_1,x_1\tan \alpha ),B(x_2,x_2\tan \beta )$ and $C(x_3,x_2\tan \gamma ).$ If origin is the circumcentre of $△ABC$ and $H(a,b)$ be its orthocentre, then $\frac{b}{a}$ equals to

(where $x_1,x_2,x_3$ are positive)

The equation of the plane containing the line $\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}$ and passing through the point $(0,7,-7)$ is

If $f:R\to R,g:R\to R,h:R\to R$ be three functions given by $f\left(x\right)=x^2-1,g\left(x\right)=\sqrt{x^2+1},$ $h\left(x\right)=\{\begin{array}{cc}0,& x\le 0\\ x,& x>0\end{array}$ then $\left(hofog\right)\left(x\right)=$

The root(s) of the equation $({\log }_{3}x{)}^2-{\log }_{3}x=6$ is/are

If $(\overrightarrow{a},\overrightarrow{b})=\frac{\pi }{6},\overrightarrow{c}$ is perpendicular to $\overrightarrow{a}$and$\overrightarrow{b},\left|\overrightarrow{a}\right|=3,\left|\overrightarrow{b}\right|=4,\left|\overrightarrow{c}\right|=6,$$\text{then}\left|\left[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\right]\right|$ is equal to

In each of
the following cases, state whether the function is one-one, onto or
bijective. Justify your answer.

(i) f:
R → R defined by f(x) = 3 − 4x

(ii) f:
R → R defined by f(x) = 1 + x²

If 7 points out of 12 are in the straight line, then the numbers of triangles formed by joining them is

Question : 6

If the perimeter of a regular hexagon is x metres, then the length of each of its sides is

(a) $x+6$ metres

(b) $x÷6$ metres

(c) $x-6$ metres

(d) $6÷x$ metres

The diameter of the circle $9x^2+y^2$ = $4(X^2-Y^2)-8X$ is

The number of integral values of $a$ such that the difference between the roots of the equation $x^2+ax-a=0$ is less than $1,$ is

The angle between the curves $y^2=4x$ and $x^2=2y-3$ at the point $(1,2)$ is

Set of values of $\alpha$ for which the point $(\alpha ,1)$ lies inside the curves $c_1:x^2+y^2-4=0$ and $c_2:y^2=4x$ is

Number of five digit numbers that contain digit $7$ exactly once (repetition of digits is allowed) is

If $\left(\sqrt{3}\right)bx+ay=2ab$ is tangent to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ , then eccentric angle $\theta$ is

A manufacturer of air plane parts makes a certain engine that has a probability $p$ of failing on any given flight. There are two planes fitted with this type of engine. One plane has $3$ such engines and other plane has $5$. A plane crashes if more than half the engines fitted in it fail. If the two planes have the same probability of crashing, then the possible value of $p$ are

If a, b and c are real numbers, and,

Show that
either a + b + c = 0 or a = b = c.

From the following system of unknown vectors $(\overrightarrow{a}$ and $\overrightarrow{b}$ are given vectors$)\overrightarrow{x}+\overrightarrow{y}=\overrightarrow{a},\overrightarrow{x}\times \overrightarrow{y}=\overrightarrow{b},\overrightarrow{x}.\overrightarrow{a}=1$ and

$\overrightarrow{x}=\frac{\overrightarrow{a}+\lambda (\overrightarrow{a}\times \overrightarrow{b})}{|\overrightarrow{a}{|}^2}$. Then $\lambda$ is

For any two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$, which of the following are ture ?

What are ordered set of components

y = mx is a chord of a circle of radius a and the diameter of the circle lies along x-axis and one end of this chord in origin .The equation of the circle described on this chord as diameter is

Show that ${lim}_{x\to 0}{e}^{\frac{-1}{x}}$ does not exist.

If the maximum and the minimum values of $1+\sin (\frac{\pi }{4}+\theta )+2\cos (\frac{\pi }{4}-\theta )$ for all real values of $\theta$ are $\lambda$ and $\mu$ respectively, then $\lambda -\mu$ is

If $\frac{3\pi }{4}<\alpha <\pi$, then $\sqrt{cose{c}^2\alpha +2cot\alpha }$ is equal to

If the normal at the point $P(a{p}^2,2ap)$ meets the parabola at $Q(a{q}^2,2aq)$ such that the lines joining the origin to $P$ and $Q$ are at right angle, then

Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length $2\sqrt{7}$ on y-axis is (are)

If

$f\left(x\right)=\{\begin{array}{cc}x+a\sqrt{2}\sin x,& 0\le x<\frac{\pi }{4}\\ 2x\cot x+b,& \frac{\pi }{4}\le x<\frac{\pi }{2}\\ a\cos 2x-b\sin x,& \frac{\pi }{2}\le x\le \pi \end{array}$ is continuous in $[0,\pi ],$ then

If $f\left(x\right)=\left|\begin{array}{ccc}1& x& x+1\\ 2x& x(x-1)& x(x+1)\\ 3x(x-1)& x(x-1)(x-2)& x(x-1)(x+1)\end{array}\right|$ where $x\in R,$ then the value of $f\left(100\right)$ is