Explore topic-wise InterviewSolutions in Current Affairs.

The integral $\underset{\frac{\pi }{4}}{\overset{\frac{\pi }{2}}{\int }}{e}^x\left(\ln \right(\cos x\left)\right)(\cos x\sin x-1){\text{cosec}}^{2}xdx$ is equal to

If exhaustive value of x satisfying $|si{n}^{-1}x|+|ta{n}^{-1}x|+|co{s}^{-1}x|=|\pi -co{t}^{-1}x|$ belongs to $[\alpha ,\beta ]$, then $\alpha and\beta$ will be

The differential equation of all the straight lines which are at a constant distance of ${}^{\prime }{a}^{\prime }$ from the origin is

Let$P=(-1,0),Q=(0,0)$ and $R=(3,3\sqrt{3})$ be three points, Then the equation of the bisector of the angle PQR is -

The equation of the plane which is parallel to y-axis and cuts off intercepts of length 2 and 3 from x-axis and z-axis is

If $f\left(x\right)$ is a polynomial satisfying $f\left(x\right)\cdot f\left(\frac{1}{x}\right)=f\left(x\right)+f\left(\frac{1}{x}\right)$ and $f\left(2\right)=17$, then the value of $f\left(3\right)$ is

There are 3 bags which are known to contain 2 white and 3 black balls; 4 white and 1 black balls and 3 white and 7 black balls respectively. A ball is drawn at random from one of the bags and found to be a black ball. Then the probability that it was drawn from the bag containing the most black balls is

f(x) = $\{\begin{array}{c}x+1,ifx\ge 1\\ x^2+1,ifx<1\end{array}$

A committee of two persons is selected from two men and two women. What is the probability that the committee will have

(i) no man?

(ii) one man?

(iii) two men?

If $X$ and $Y$ are two sets, then $X\cap (Y\cup X{)}^C$ equals to

The area (in sq. units) of the region $\left\{\right(x,y):y^2\ge 2xand{x}^2+y^2\le 4x,x\ge 0,y\ge 0\}$ is :

If the centroid of the triangle ABC is (1, 1, 1 ) . If the coordinates A and B are (3, -5, 7) and (-1, 7, -6) respectively, then the coordinates C is

The distance of the point $(2,3)$ from the line $2x–3y+9=0$, measured along the line $x–y+1=0$ is

The value of ${\cos }^3\frac{\pi }{8}\cos \frac{3\pi }{8}+{\sin }^3\frac{\pi }{8}\sin \frac{3\pi }{8}$ is :

The sum of real values of $K$ for which the equation $x^3-Kx+K–1=0$ has exactly two distinct real solutions.

If two perpendicular lines are having slopes m${}_1$ and m${}_2$. Then (m${}_1$m${}_2$)${}^n$ will be ( n$>$0)

If the sides of a triangle ABC, are a, b, $\sqrt{a^2+b^2+ab}$ then the greatest angle of the triangle is -

Consider a branch of the hyperbola $x^2-2y^2-2\sqrt{2}x-4\sqrt{2}y-6=0$ with vertex at the point A. Let B be one of the end points of its latusrectum. If C is the focus of the hyperbola nearest to the point A, then the area of the $\Delta ABC$ is

The condition for the point (a, b) to be collinear with the points, (2, 3) and (5, 8), is

Let $A+B+C=\pi$ and $\alpha ={\sin }^3(B+C)\cdot \sin (2C+A),\beta ={\sin }^3(A+C)\cdot \sin (2A+B),\gamma ={\sin }^3(A+B)\cdot \sin (2B+C)$
are roots of the cubic equation $x^3+a{x}^2+bx+c=0$, then the value of $a$ is

The order and degree of the differential equation are

[MP PET 1993]

$\left(a\right)Provethat{\int }_0^{2a}f\left(x\right)dx=2{\int }_0^{a}f\left(X\right)dx,iff(2a-x)=f\left(x\right)andevaluate{\int }_0^{2\pi }co{s}^{5}xdx$
$iff(2a-x)=-f\left(x\right)$

(b) Find the values of a and b such that the function defined by

$f\left(x\right)=\{\begin{array}{cc}5,& ifx\le 2\\ ax+b& if2<x<10isacontinousfunction\\ 21,& ifx\ge 10\end{array}$

How many words can be formed from e letters of the word 'SUNDAY'? How many of these begin with D?

If the parabolas
$25\left\{\right(x-3{)}^2+(y+2{)}^2\}=(3x-4y-2{)}^2,y^2=\lambda x$
are equal, then $\lambda$ is

In how many ways can the letters of the word 'INTERMEDIATE' be arranged so that :

(i) the vowels always occupy even places ?

(ii) the relative order of vowels and consonants do not alter ?

Write the area of the circle passing through (-2, 6) and having its centre at (1, 2).

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of :

(i) exactly 3 girls ?

(ii) at least 3 girls ?

(iii) at most 3 girls ?

The area of the region
$A=\left\{(x,y):0\le y\le x|x|+1\text{and}-1\le x\le 1\right\}$ in sq. units, is :

$\frac{a+b}{c}=\frac{cos\left(\frac{A-B}{2}\right)}{sin\frac{C}{2}}$

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola.The roadway which is horizontal and 100 m long is supported by vertical lines wires attached to the cable,the longest wire being 30 m and the shortest wire being 6 m.Find the length of a supporting wire attached to the roadway 18 m from the middle.

Find the equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.

The sum of three numbers a, b, c in A.P. is 18. If a and b are each increased by 4 and c is increased by 36, the new numbers form a G.P. Find a, b, c.

There are 10 persons named $P_1,P_2,P_3,....,P_{10}.$ Out of 10 persons, 5 persons are to be arranged in a line such that is each arrangement $P_1$ must occur whereas $P_4$ and $P_5$ do not occur. Find the number of such possible arrangements.

If ${\theta }_1,{\theta }_2,{\theta }_3,\dots \dots {\theta }_n$ are in A.P, whose common difference is d, show that $sec{\theta }_{1}sec{\theta }_2+sec{\theta }_{2}sec{\theta }_3+\dots \dots +sec{\theta }_{n-1}sec{\theta }_n=\frac{tan{\theta }_n-tan{\theta }_1}{sind}$

Length of side of an equilateral triangle inscribed in a parabola $y^2-2x-2y-3=0$ whose one angular point is vertex of the parabola is

The value of $si{n}^2{5}^{\circ }+si{n}^2{10}^{\circ }si{n}^2{15}^{\circ }+...+si{n}^2{85}^{\circ }+si{n}^2{90}^{\circ }$ is

Decide among the following sets , which are subsets of which :

A = {x : x satisfies $x^2-8x+12=0$},

B = {2, 4, 6}, C = {2, 4, 6, 8, .....}, D = {6}.

If A = {2, 3}, B = {4, 5} and C = {5, 6}, find $A\times (B\cap C),(A\times B)\cup (A\times C).$

$If{e}^{sinx}-e^{-sinx}-4=0,then,x=$

Let the unit vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are perpendicular and the unimodulus vector $\overrightarrow{c}$ inclined at an angle $\alpha$ to $\overrightarrow{a}$ and $\overrightarrow{b}$. If $\overrightarrow{c}=l\overrightarrow{a}+m\overrightarrow{b}+n(\overrightarrow{a}\times \overrightarrow{b})$, then

Let $f$ be a real valued function defined as $f\left(x\right)=x^2+x^2\underset{-1}{\overset{1}{\int }}t\cdot f\left(t\right)dt+x^3\underset{-1}{\overset{1}{\int }}f\left(t\right)dt.$ Then which of the following hold(s) good ?

The number of integers greater than a million (Ten lakhs) that can be formed using the digits
$2,3,0,3,4,2,3$ is

Words are formed using all letters of the word 'JEEADVANCED'.
Let $a$ denotes the number of words in which all the vowels are together.
Let $b$ denotes the number of words in which vowels as well as consonants are separated.
Let $c$ denotes the number of words which begin and end with vowels.

If $\alpha ,\beta ,\gamma$ are the roots of $x^3-x^2-1=0$, then

Let $a,r,s$ and $t$ be non –zero real numbers. Let $P(a{t}^2,2at),Q,R(a{r}^2,2ar)$ and $S(a{s}^2,2as)$ be distinct points on the parabola $y^2=4ax$. Suppose that $PQ$ is the focal chord and lines $QR$ and $PK$ are parallel, where $K$ is point $(2a,0)$.
The value of $r$ is