Explore topic-wise InterviewSolutions in Current Affairs.

A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is ${\tan }^{-1}\left(\frac{1}{2}\right)$. Water is poured into it at a constant rate of $5$ cubic meter per minute. Then the rate (in m/min), at which the level of water is rising at the instant when the depth of water in the tank is $10m$; is :

If $cosA=mcosB$, then write the value of $cot\frac{A+B}{2}cot\frac{A-B}{2}$

If the data $x_1,x_2,....,x_{10}$ is such that the mean of first four of these is $11,$ the mean of the remaining six is $16$ and the sum of squares of all of these is $2,000;$ then the standard deviation of this data is :

If A+B+C=90degrees then sin2A+sin2B+sin2C=?

Options 1)cosAcosBcosC

2)2cosAcosBcosC

3)3cosAcosBcosC

4)4cosAcosBcosC

Answer is option 4

Study the following information and answer the questions given below

1. A, B, C, D, E, and F are six members of a family.

2. One is a student, one housewife, one doctor, one teacher, one lawyer and one engineer.

3. There are two married couples in the family.

4. B is a teacher and the mother of C.

5. D is the grandmother of C and is a housewife.

6. F is a lawyer and is the father of A.

7. C is the brother of A.

8. E is the father of F and is a doctor.

Q65. How many female members are there in the family?

integrate 4ax+2b/(ax^2 +bx+c)^10 using substitution

The value(s) of $x$ for which the expression $y=|x+2|+|x-7|$ is minimum is/are

PQ is a double ordinate of the parabola $y^2=4ax$. If the normal at a point P intersects the line passing through Q and parallel to axis of the parabola at G. Then locus of G is a parabola with

If the roots of the equation $x^2+ax+b=0arec\&d$ , then one of the roots of equation $x^2+(2c+a)x+c^2+ac+b=0$ is

If $tan\theta =\frac{a}{b},thenthevalueofE=\frac{asin\theta -bcos\theta }{asin\theta +bcos\theta }is-$

Trigonometric series of the form
$\frac{\sin (A-B)}{\cos A\cdot \cos B}+\frac{\sin (B-C)}{\cos B\cdot \cos C}+\frac{\sin (C-D)}{\cos C\cdot \cos D}$
$=\tan A-\tan D$
As we know that,
$\frac{\sin (A-B)}{\cos A\cdot \cos B}=\tan A-\tan B$
Based on the above given information, find $n^{\text{th}}$ term of the series
$\frac{\sin x}{\cos 3x}+\frac{\sin 3x}{\cos 9x}+\frac{\sin 9x}{\cos 27x}+\cdots$ upto $n$ terms

If $sinA=nsinB,then\frac{n-1}{n+1}tan\frac{A+B}{2}=$

If a and b are the real and imaginary part of the square root of the complex number 8 - 15i, then a$\times$b is _____?

How many onto functions from set A to set A can be formed for the set A = { 1,2,3,4,5,......n} ?

The sum of the series $1+\frac{1}{5}+\frac{1.3}{5.10}+\frac{\mathrm{1.3.5}}{\mathrm{5.10.15}}+....$ is equal to

Solution of $lo{g}_{x^2+6x+8}lo{g}_{x^2+2x+3}(x^2-2x)=0is$

The solution of $5^{{\log }_{a}x}+5x^{{\log }_{a}5}=3(a>0,a\ne 1)$ is

The three normals from a point to the parabola $y^2=4ax$ cut the axes in points, whose distances from the vertex are in A.P., then the locus of the point is

If the line 3x + 4y - 1 = 0 touches the circle $(x-1{)}^2+(y-2{)}^2=r^2$, then the value of r will be

Equation of the circle with centre (1,2) and passing through (2,1) is

The angle made by the tangent to the circle $x^2+y^2-8x+6y+20$ = 0 at (3,-1) with the positive direction of the x-axis is

The centre of circle passing through (0, 0) and (1, 0) and touching the circle $x^2+y^2=9$ is
(2002)

An ordinary cubical die has four blank faces, one face marked 2 and another marked 3. Then the probability of obtaining 12 in 5 throws is

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 ${lim}_{x\to 0}{\left[\frac{(a^x+b^x)}{2}\right]}^{\frac{2}{x}}=6$ is

If $a\ne 0$ and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas $y^2=4ax$ and $x^2=4ay$ , then

If $a,b,c$ are in A.P., then $a^3+c^3-8b^3$ is equal to

The normals at two points P and Q of a parabola $y^2=4x$ meet at $(x_1,y_1)$ on the parabola. Then $P{Q}^2$ =

Let A(1, 2) and B(7, 10) are two points. If P(x, y) is a point such that the $\angle APB$ is ${60}^{\circ }$ and the area of the $△APB$ is maximum, then which of the following is/are true.

The angle between curves $y^2=4x$ and $x^2+y^2=5$ at (1,2) is

Two tangents are drawn to the parabola $y^2=8x$ which meets the tangent at vertex at $P$ and $Q$ respectively. If $PQ=4\text{units}$, then the locus of the point of intersection of the two tangents is

The equation of the hyperbola whose asymptotes are $3x+4y–2=0,2x+y+1=0$ and which passes
through the point (1, 1) is

If $a\ast b=\frac{ab}{10};a,b\in Q^{+}$, then $(5\ast 8{)}^{-1}=$______

Which of the following is/are irrational numbers ?

A variable line $L$ is drawn through $O(0,0)$ to meet the lines $L_1:x+2y-3=0$ and $L_2:x+2y+4=0$ at points $M$ and $N$ respectively. A point $P$ is taken on line $L$ such that $\frac{1}{O{P}^2}=\frac{1}{O{M}^2}+\frac{1}{O{N}^2}$. Then the locus of $P$ is

The number of real roots of the equation
$\left|\begin{array}{ccc}{x}^2+1& 2x^3& x\\ 2x^3& x& x^2+1\\ x& x^2+1& 2x^3\end{array}\right|=0$ is

The coefficient of the term independent of $x$ in the expansion ${(\sqrt{\frac{x}{3}}+\frac{\sqrt{3}}{x^2})}^{10}$ is

Two numbers are selected randomly from the set S = {1, 2, 3, 4, 5, 6} without replacement one by one. The probability that minimum of the two numbers is less than 4, is