Explore topic-wise InterviewSolutions in Current Affairs.

If the centre of the sphere $x^2+y^2+z^2-2x-4y-6z=0$

is (a,b,c) , find the value of a+b+c

Write the value of ${lim}_{x\to 0^{-}}x-\left[x\right].$

If a and b are chosen randomly from the set consisting of numbers $1,2,3,4,5,6$ with replacement. Then the probability that $\underset{x\to 0}{lim}{\left(\frac{a^x+b^x}{2}\right)}^{\frac{2}{x}}=6$ is

If $x_1,x_2,x_3,x_4$ are four positive real numbers such that $x_1+\frac{1}{x_2}=4,x_2+\frac{1}{x_3}=1,x_3+\frac{1}{x_4}=4$ and $x_4+\frac{1}{x_1}=1,$ then

The quadratic equation $x^2-7x+12=0$ can be simplified to , and it's corresponding roots will be .

The value of $\sum _{r=0}^n(-1{)}^r\frac{{}^n{C}_r}{r+2}$ is equal to .

The number of common solution(s) of $y=\cos x$ and $y=x^2+1$ is

The statement $(p\wedge \sim q)\vee q\vee (\sim p\wedge q)$ is equivalent to

When two projectiles are fired from complementary angles having times of flight T_1, ​T₂ and maximum heights H₁ , H₂ respectively.

Which of the following is correct?

1) R= gT₁T₂/2

2)R= 4√H₁H₂

_{​​​​​​}3) angle of protection=tan^-1*T ₁/T₂

4) angle of projection= tan^-1*H₁/H₂

$IfP(Q-r)x^2+Q(r-P)x+r(P-Q)=0hasequalrootsthen\frac{2}{Q}=(whereP,Q,rϵR)$

The solution $(x,y)$ of $\left[\begin{array}{cc}12& 3\\ 2& -3\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}15\\ 13\end{array}\right]$ is

Let $h\left(x\right)=\sec \left\{\frac{{\tan }^{-1}\left(\cos \right({\sin }^{-1}x\left)\right)+{\cot }^{-1}\left(\sin \right({\cos }^{-1}x\left)\right)}{3}\right\},$

where $x\in [-1,1],$ then which of the following option(s) is(are) correct?

1. 40

Let $y=y\left(x\right)$ be the solution of the differential equation $x\tan \left(\frac{y}{x}\right)dy=(y\tan \left(\frac{y}{x}\right)-x)dx,$$-1\le x\le 1,$ $y\left(\frac{1}{2}\right)=\frac{\pi }{6}.$ Then the area of region bounded by the curves $x=0,$ $x=\frac{1}{\sqrt{2}}$ and $y=y\left(x\right)$ in the upper half plane is

Let $f\left(x\right)$ is a polynomial of degree $4$, with $f\left(2\right)=-1,f^{\prime }\left(2\right)=0,f^{\prime \prime }\left(2\right)=2,f^{\prime \prime \prime }\left(2\right)=-12,f^{\prime \prime \prime \prime }\left(2\right)=24,$ then the value of $f^{\prime \prime }\left(1\right)$ is -

The slope of the normal to the curve $x=a(\theta +sin\theta ),y=acos\theta at\theta =\frac{\pi }{4}$ is

If the axes are shifted to $(-2,-3)$ and then rotated through $\frac{\pi }{4}$ in anticlockwise direction, then transformed equation of $x^2-y^2+2x+4y=0$ is

The minimum value of $f\left(x\right)=a^{a^x}+a^{1-a^x}$, where $a,x\in R$ and $a>0$, is equal to:

In the given number line, the positions of A and B are and respectively.

Probability that a random chosen three digit number has exactly 3 factors is

The plane $4x+7y+4z+81=0$ is rotated through a right angle about its line of intersection with the plane $5x+3y+10z=25$. If the equation of plane in its new position is $x-4y+6z=k$, then the value of $k$ is equal to

Question 4 (xi)

Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.

(xi) $a,a^2,a^3,a^4,\dots$

If y = $ta{n}^{-1}\sqrt{\left(\frac{1+sinx}{1-sinx}\right)},\frac{\pi }{2}<x<\pi$, then $\frac{dy}{dx}$ equals

Find a
particular solution of the differential equation
,
given that y = 0 when

If the straight line x cos $\alpha$ + y sin $\alpha$ = p touches the curve $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,$ then prove that $a^{2}co{s}^2\alpha +b^{2}si{n}^2\alpha =p^2$.

Integrate the function.
$\int \frac{xco{s}^{-1}x}{\sqrt{1-x^2}}dx.$