Explore topic-wise InterviewSolutions in Current Affairs.

If f(x)=cos(log x), then prove that

f(1/x).f(1/y)-1/2(f(x/y)+f(xy))=0

In a YDSE setup, the distance between the plane of the slits and the screen is increased by $20\%$ and the distance between the slits is increased by $50\%$. Then the percentage change in fringe width is

Two ships are 10 km apart on a line joining south to north. The one farther north is steaming west at 20 km $h^{-1}$. The other is steaming north at 20 km $h^{-1}$. What is their distance of closest approach ?

If $x\ne 1$ and $f\left(x\right)=\frac{x+1}{x-1}$ is a real function, then f(f(f(2))) is

${lim}_{x\to 1}\frac{(2x-3)(\sqrt{x}-1)}{3x^2+3x-6}$

The principle value of the amplitude of (1 + i) is

A cow is tied to a post by a rope. If the cow moves along a circular path, always keeping the rope tight, and describes $88\text{m}$ when it traced out ${72}^{\circ }$ at the centre, then the length of the rope is
$(\pi =\frac{22}{7})$

There are three coloured dice of red, white and black colour. These dice are placed in a bag. One die is drawn at random from the bag and rolled, its colour and the number on its uppermost face is noted. Describe the sample space for this experiment.

The imaginary part of ${(\frac{1}{2}+\frac{1}{2}i)}^{10}$ is

If $X=\{x:x=8^n-7n-1,n\in N\}$ and $Y=\{y:y=49n-49,n\in N\},$ then which of the following is (are) TRUE?

The total number of $4$ letter words that can be formed from the string $"AABBBBCC"$ is

Integrate the following functions.
$\int \frac{x^2}{(2+3x^3{)}^3}dx.$

If the standard deviation of a variable X is $\sigma$ , then the standard deviation of variable $\frac{aX+b}{c}$ is

Integrate the following functions.
$\int \frac{x}{e^{x^2}}dx.$

Draw the graph of the function y = $a^x$ when 0 < a < 1.

A standard hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ of eccentricity 'e' is given as below.

Choose the correct options.[S is the focus and dotted line is a directrix.]

If the roots of $z^3+i{z}^2+2i$ = 0 represent the vertices of a triangle in the argand plane, then its area is

Find the following integrals.
$\int \frac{x^3+3x+4}{\sqrt{x}}dx.$

If $12$ persons are to be seated around a circular table such that the two secretaries of the chairman should be seated adjacent to the chairperson on both the sides and three particular boys should never seat together, then the total number of arrangements will be

What are the alternative definitions of money supply in India?

The middle term of expnsion of ${(\frac{10}{x}+\frac{x}{10})}^{10}$

Which of the following substitution on $\int \frac{1}{(x-1)\sqrt{x^2+x+1}}dx$ will lead to $-\frac{1}{\sqrt{3}}\int \frac{1}{\sqrt{(t+\frac{1}{2}{)}^2+\frac{1}{12}}}dt$ ?

Rolle's Theorem is not applicable to f(x) = |x| in (-2, 2), because:

Let f(x) = cos 2$\pi$ x+x-[x] ([.] denotes the greatest integer function). Then number of points in [0, 10] in which f (x) assume its local maximum value, is

Let $a=\hat{i}+4\hat{j}+2\hat{k},b=3\hat{i}-2\hat{j}+7\hat{k}$ and $c=2\hat{i}-\hat{j}+4\hat{k}$. Find a vector d which is perpendicular to both a and b and c.d = 15

In an entrance test there are multiple choice questions. There are four possible answers to each question of which one is correct. The probability that a student knows the answer to a question is 90$\%$. If he gets the correct answer to a question, then the probability that he was guessing, is

${lim}_{x\to 0}\frac{sin3x+7x}{4x+sin2x}$

If $\int \frac{x\cos \alpha +1}{(x^2+2x\cos \alpha +1{)}^{3/2}}dx=\frac{f\left(x\right)}{\sqrt{g\left(x\right)+1}}+C$, then $g\left(x\right)-2\cos \alpha f\left(x\right)$ is
(where $C$ is constant of integration)

A, B and C are partners sharing profits in 2 : 2 : 1 ratio. They admitted D for $\frac{1}{8}$ share which he acquired entirely from A. Calculate new profit sharing ratio.

Find the values of the following trigonometric ratios:

$\left(i\right)sin\frac{5\pi }{3}$

$\left(ii\right)sin{3060}^{\circ }$

$\left(iii\right)tan\frac{11\pi }{6}$

$\left(iv\right)cos(-{1125}^{\circ })$

$\left(V\right)tan{315}^{\circ }$

$\left(vi\right)sin{510}^{\circ }$

$\left(vii\right)cos{570}^{\circ }$

$\left(viii\right)sin(-{330}^{\circ })$

$\left(ix\right)cosec(-{1200}^{\circ })$

$\left(X\right)tan(-{585}^{\circ })$

$\left(xi\right)cos{855}^{\circ }$

$\left(xii\right)sin{1845}^{\circ }$

$\left(xiii\right)cos{1755}^{\circ }$

$\left(xiv\right)sin{4530}^{\circ }$

If ${\log }_{|\sin x|}(x^2-8x+23)>\frac{3}{{\log }_2|\sin x|}$, then the range of values of $x$ is

Which term is independent of x, in the expansion of ${(x-\frac{1}{3x^2})}^9?$

The total number of $4$ digit numbers that can be formed by using the digits $1,2,3,4,5,6$ and $7$ if at least one digit is repeated is

If k is a scalar and I is a unit matrix of order 3, then adj(kI) = [MP PET 1991;Pb. CET 2003]

The coordinates of an endpoint of the latusrectum of the parabola $(y-1{)}^2=4(x+1)$ are

One side of an equilateral triangle is $24$ cm. The midpoints of its sides are joined to form another triangle whose midpoints are in turn joined to form still another triangle this process continues indefinitely. The sum of the perimeters of all the triangles is

If $(x_1,y_1)$ and $(x_2,y_2)$ are two ordered pair which satisfies the condition in comprehension (where $x_1,x_2,y_1,y_2\text{/}ϵN$), then $\left(x_1{x}_2\right)/\left(y_1{y}_2\right)$ is

There are 5 books on Mathematics and 6 books on Physics in a book shop. In how many ways can a students buy : (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book?

Area of the region in which point $p(x,y,x>0$ lies; such that $y\le \sqrt{16-x^2}and\left|ta{n}^{-1}\left(\frac{y}{x}\right)\right|\le \frac{\pi }{3}$ is

a die is thrown thrice.Getting a 5 or 6 is considered as success.Find the probability of getting

(1-)exactly 2 successes

(2-)at most 2 successes

(3-)atleast 2 successes