Explore topic-wise InterviewSolutions in Current Affairs.

Which of the following magnetic moment values will correspond to the highest ionization energy for Mn species?

If $y=si{n}^{-1}(x\sqrt{1-x}+\sqrt{x}\sqrt{1-x^2})$ then $\frac{dy}{dx}=$

The value of $\underset{n\to \infty }{lim}\underset{k=1}{\sum ^n}(\frac{n-k}{n^2})\cos \frac{4k}{n}=\frac{1}{a}(1-\cos c),$ then

Four identical dice are rolled once. Probability that atleast 3 different numbers appear on them is

The projection of the line segment joining the points (–1, 0, 3) and (2, 5, 1) on the line whose direction ratios are 6, 2, 3 is

A vector which makes equal angles with the vectors $\frac{1}{3}(\hat{i}-2\hat{j}+2\hat{k}),\frac{1}{5}(-4\hat{i}-3\hat{k}),\hat{j}.$ is

A box contains 24 identical balls of which 12 are white and 12 black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the $4^{th}$ time on the $7^{th}$ draw is

The minimum value of the expression for $\frac{9x^{2}si{n}^{2}x+4}{xsinx}forxϵ(0,\pi )is$

In $△ABC$, if $A,B$ and $C$ represent the angles of a triangle, then the maximum value of $\sin \frac{A}{2}+\sin \frac{B}{2}+\sin \frac{C}{2}$ is

Find the mean deviation from the mean for the following data :

(i) $\begin{array}{ccccccc}{x}_i& 5& 7& 9& 10& 12& 15\\ f_i& 8& 6& 2& 2& 2& 6\end{array}$

(ii) $\begin{array}{cccccc}{x}_i& 5& 10& 15& 20& 25\\ f_i& 7& 4& 6& 3& 5\end{array}$

(iii) $\begin{array}{cccccc}{x}_i& 10& 30& 50& 70& 90\\ f_i& 4& 24& 28& 16& 8\end{array}$

(iv) $\begin{array}{cccccc}\text{Size}& 20& 21& 22& 23& 24\\ \text{Frequency}& 6& 4& 5& 1& 4\end{array}$

(v) $\begin{array}{ccccccccc}\text{Size}& 1& 3& 5& 7& 9& 11& 13& 15\\ \text{Frequency}& 3& 3& 4& 14& 7& 4& 3& 4\end{array}$

If $y=x^{(\log x{)}^{\log \left(\log x\right)}}$, then $\frac{dy}{dx}$ is

Find the distance of the point of intersection of the lines $2x+3y=21$ and $3x-4y+11=0$ from the line $8x+6y+5=0$.

Which of the following statements are correct?

1 . if sin θ = sin α ⇒ θ = nπ + $(-1{)}^n$α where α ∈ [ - $\frac{\pi }{2}$ , $\frac{\pi }{2}$] n ∈ I

2 . if cos θ = cos α ⇒ 2nπ±α where α ∈ [0,π] n ∈​ I

3 . if tan θ = tan α ⇒ θ = nπ + α where α ∈ (- $\frac{\pi }{2}$ , $\frac{\pi }{2}$ ) n ∈​ I

If $\alpha ,\beta \ne 0,$ and $f\left(n\right)={\alpha }^n+{\beta }^n$ and
$\left|\begin{array}{ccc}3& 1+f\left(1\right)& 1+f\left(2\right)\\ 1+f\left(1\right)& 1+f\left(2\right)& 1+f\left(3\right)\\ 1+f\left(2\right)& 1+f\left(3\right)& 1+f\left(4\right)\end{array}\right|=K(1-\alpha {)}^2(1-\beta {)}^2(\alpha -\beta {)}^2$, then $K$ is equal to:

A curve is represented by y = sin x. If x is changed from $\frac{\pi }{3}$ to $\frac{\pi }{3}+\frac{\pi }{100}$, find approximately the change in y.

${lim}_{x\to 2}\frac{\sqrt{x^2+1}-\sqrt{5}}{x-2}$

The equation of the straight line which passes through the point $(-4,3)$ such that the portion of the line between the axes is divided internally by the point in the ratio 5 : 3 is

If $\overrightarrow{a}=\hat{i}+2\hat{j}+2\hat{k}$ and $\overrightarrow{b}=3\hat{i}+6\hat{j}+2\hat{k}$, then the vector in the direction of $\overrightarrow{a}$ and having magnitude as $|\overrightarrow{b}|$, is

If $\Delta =\left|\begin{array}{ccc}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3\end{array}\right|$ $A_i,B_i,C_i$ are respectively are cofator of $a_i,b_i,c_i$-- for all i = 1, 2, 3, then

$\left|\begin{array}{ccc}{A}_1& B_1& C_1\\ A_2& B_2& C_2\\ A_3& B_3& C_3\end{array}\right|$

Two dice are thrown simultaneously, The probability of obtaining total score of seven is

The shortest distance between the line $y=x$ and the curve $y^2=x-2$ is:

If $x=2\cos 2t,y=\sin 2t$ then -

If $P\left(A\right)=65,P\left(B\right)=80$, then $P(A\cap B)$ lies in the interval

The common tangent to the circles $x^2+y^2=4$ and $x^2+y^2+6x+8y-24=0$ also passes through the point :

The variance of 1, 2, 3, 4, 5 is

The eccentricity of the conic$9x^2-16y^2=144$ is

If 1,2,1 are the direction ratios of a line then the direction cosines of this line is equal to

If $\frac{\pi }{2}<\theta <\frac{3\pi }{2}$, then write the value of $\sqrt{\frac{1+cos2\theta }{2}}$

The product of three consecutive terms of a $\text{G.P.}$ is $512.$ If $4$ is added to each of the first and the second of these terms, then the three terms now form an $\text{A.P.}$ Then the sum of the original three terms of the given $\text{G.P.}$ is:

Let $S_1,S_2,...S_n$ be squares such that for each $n\ge 1$, the length of a side of $S_n$ equals the length of the diagonal of $S_{n+1}$. If the length of a side of $S_1$ is $10$ cm, then the least value of $n$ for which the area of $S_n$ less that 1 sq cm

If $\overrightarrow{a}=x\hat{i}+(x-1)\hat{j}+\hat{k}$ and $\overrightarrow{b}=(x+1)\hat{i}+\hat{j}+a\hat{k}$ always make an acute angle with each other for every value of $xϵR$, then

The domain of the function $f\left(x\right)=3-\frac{1}{[x+3]}$ is
(where [.] denotes the greatest integer function)

Let $z_1=10+6i$ and $z_2=4+6i,$ where $i=\sqrt{-1}.$ If $z$ is any complex number such that $\arg \left(\frac{z-z_1}{z-z_2}\right)=\frac{\pi }{4},$ then the value of $|z-7-9i|$ is

The product $\cos \left(\frac{2\pi }{2^{64}-1}\right)\cos \left(\frac{2^2\pi }{2^{64}-1}\right)\cdots \cos \left(\frac{2^{64}\pi }{2^{64}-1}\right)$ equals

If $f\left(A\right)=\sum _{r=1}^8\tan rA\cdot \tan (r+1)A$ then

Let ${\cos }^{-1}\left(\frac{y}{b}\right)=\log {\left(\frac{x}{n}\right)}^n$ . Then

$(\text{Here}{y}_2\equiv \frac{d^{2}y}{d{x}^2},y_1\equiv \frac{dy}{dx})$

The number of arbitrary constants in the particular solution of a differential equation of third order is
(a) 3
(b) 2
(c) 1
(d) zero