Explore topic-wise InterviewSolutions in Current Affairs.

^{_{​​​​​​A rod AB of length 4 units moves horizontally with its left end A always on the circle} ​​​}x _{​​​​​​}²+y²-4x-18y-29=0 then the locus of the circle is

Line of intersection of the planes $x+2y=0$ and $y-3z+3=0$ is

Check the injectivity and surjectivity of the following functions:
$\left(i\right)f:Z\to Z$ given by $f\left(x\right)=x^3$

Prove that the function f given by $f\left(x\right)=log\left(sinx\right)$ is strictly increasing on $(0,\frac{\pi }{2})$ and strictly decreasing on $(\frac{\pi }{2},\pi )$.

If ${\sum }_{r=0}^n\left(\frac{r+2}{r+1}\right){}^n{C}_r=\frac{2^8-1}{6}$ then n is

Find the local maxima and local minima, if any of the following function. Also, find the local maximum and the local minimum values, as the case may be as follows.

$f\left(x\right)=sinx-cosx,0<x<2\pi$

Calculate the area under the curve $y=2\sqrt{x}$ included between the lines x = 0 and x = 1.

Consider $P$ is a point on $y^2=4ax,$ if the normal at $P,$ the axis and the focal radius of $P$ form an equilateral triangle. Then coordinates of $P$ are

Find the particular solution of differential equation : $2y{e}^{\frac{x}{y}}dx+(y-2x{e}^{\frac{x}{y}})dy=0$ given that x = 0 when y = 1.

The vectors $\lambda \hat{i}+\hat{j}+2\hat{k},\hat{i}+\lambda \hat{j}-\hat{k}and2\hat{i}-\hat{j}+\lambda \hat{k}arecoplanar,if$

(a) $\lambda =-2$ (b) $\lambda =0$

(a) $\lambda =1$ (b) $\lambda =-1$

Evaluate $\underset{x\to 0}{lim}\frac{(1-cosx\sqrt{cos2x})}{x^2}$

Let f(x) = $x^2$-1, 0<x<2
and 2x+3, 2$\le$x<3, The quadratic equation whose roots are ${lim}_{x\to 2^{-}}f\left(x\right),and{lim}_{x\to 2^{+}}f\left(x\right)$

An aeroplane flying at a height of $9000\text{m}$ vertically above from the ground, passes another aeroplane when the angles of elevation of the two aeroplanes from a point on the ground are ${60}^{\circ }$ and ${30}^{\circ }$ respectively. Then the vertical distance between the aeroplanes at that instant is

Find the principal values of the following questions:

$ta{n}^{-1}(-\sqrt{3})$

The domain of the function $f\left(x\right)=\log (1-x)+\sqrt{x^2-1}$ is

If the latus rectum of an ellipse be equal to half of its minor axis, then its eccentricity is

The number of ways in which the time table for Monday can be made if there must be $5$ lessons to be taught that day (Algebra, Geometry, Calculus, Trigonometry, Vector) and topics Algebra and Geometry cannot immediately follow each other are

If $|x-1|+|x+1|=2$, then $x$ belongs to

A father left a will of Rs $16,400$ for his two sons aged $17$ and $18$ years. They must get equal amounts when they are $20$ years at $5$ compound interest. Find the present share of the elder son.

Don't we consider a joker card in a deck of cards while solving a problem? Why? Are there any special cases where we should consider joker in our deck? In such questions how many jokers shall we consider 1or 2 ? Could you please explain me with an example please for the special case.

Regards,

Lakshit

Solution set of $\frac{3x-4}{2}\ge \frac{x+1}{4}-1$ is

cos ^2 A (3 - 4 cos ^2 A)^2 + sin ^2 A( 3 - 4 sin ^2 A) ^2 equal to

The roster form of the set $\{x:x$ is a two-digit natural number such that sum of its digits is $9\}$

If $(P_3,P_4)$ share a flat, then the other flat $P_4$ shares will be

If A = ${20}^{\circ }$ and B = ${25}^{\circ }$, Find the value of tanA + tanB + tanAtanB.

The value of $cosAcos({60}^{\circ }-A)cos({60}^{\circ }+A)$ is equal to

The cross product $(2\hat{i}+3\hat{j}+4\hat{k})\times (\hat{i}-\hat{j}+\hat{k})$ is .

Let R be the feasible region (convex polygon) for a linear programming problem and let,

Z = + be the objective function. When Z has an optimal value (maximum or minimum), where the variables and are subject to constraints described by linear inequalities, this optimal value must occur at ____________of the feasible region.

The equations of the tangents drawn to the curve y² - 2x³ - 4y + 8 = 0 from the point (1, 2) is... .

Let $A,B$ are two points on the curve $y={\log }_{1/2}(x-\frac{1}{2})+{\log }_2\sqrt{4x^2-4x+1}$ and $A$ is also on the circle whose radius is $\sqrt{10}$ and centre at $O(0,0)$. $B$ lies inside the circle such that its abscissa is integer, then

The time taken for 10% completion of a first order reaction is $20\text{min}$. How much time does it take for 19% completion?

1. undefined

Find all the cube root of $-4\sqrt{2}-4\sqrt{2}i$

If $A=\left[\begin{array}{ccc}1& 2& 1\\ 0& 1& -1\\ 3& -1& 1\end{array}\right]$, then

Let $p$ and $q$ be any two logical statements and $r$ be the statement $p\to (\sim p\vee q).$ If $r$ has the truth value $\text{F},$ then the truth values of $p$ and $q$ are, respectively

If 0 $<$ c $<$ b $<$a and the roots α,β of the equation are imaginary then

If three lines are non concurrent and no two of them are parallel, number of circles drawn touching all the three lines

If $(4co{s}^2{40}^{\circ }-3)(3–4si{n}^2{40}^{\circ })=a+bcos{20}^{\circ }$ then $|a|+|b|$ =

Three boys and three girls are to be seated around a circular table. Among them, the boy $X$ does not want any girl neighbour and the girls $Y$ does not want any boy neighbour. Then the number of possible arrangements is

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

Three athletes A, B and C participate in a race. Both A and B have the same probability of winning the race and each is twice as likely to win as C. The probability that B or C wins the race is

Let ABCD be a quadrilateral with area 18, with side AB parallel to CD and AB = 2CD. Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is

A bag contains n white and n black balls. Pairs of balls are drawn without replacement until the bag is empty.The probability that each pair consists of one white and one black ball is