Explore topic-wise InterviewSolutions in Current Affairs.

(1) A Boat takes 2 hours to go to 40 km down the stream and returns in 4 hours find the speed of the boat in still water and speed of the stream

(2) Ritu can row downstream 20 km in 2 hours and upstream 4 km in 2 hours find her speed of rowing in still water and speed of current

If $sin\theta +si{n}^2\theta +si{n}^3\theta =1$,then find the value of $co{s}^6\theta -4co{s}^4\theta +8co{s}^2\theta$.

To reach Allahabad from Delhi , Ved travels 600 km , partly by train and partly by car. He would take 8 hours, if he travels 120 km by train and remaining distance by car. On the other hand , if he travels 200 km by train and remaining by car, then he would take 20 minutes longer than the first case. Find the speeds of the train and car. Consider that the train and car travel with a uniform and the same speed each time .

Show that the number 143 and 187 are not co-primes

It take $12$ hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for $4$ hours and the pipe of smaller diameter for $9$ hours only half the pool can be filled .How long would it take for each pipe to fill the pool separately.

In Fig.1, PA and PB are two tangents drawn from an external point P to a circle with centre C radius 4 cm. if $PA\perp PB,$ then the length of each tangent is:

Find the value of K for which the points (2,5), (K, 11/2), (4,6) are collinear

Which geometric figures are always similar?

The slope of the line that is parallel to x – axis is _____.

For what value of k, the equation kx² - 6x - 2 = 0 has equal roots?

The angle formed by the line of sight with the horizontal, when the point being viewed is above the horizontal level is called:

Find the value of $\sqrt{4}$ using geometric method.

A box contains 90 disces which are numbered from 1 to 90. If one disc is drawn at random from the box, find rthe probability that it bears (i) a two-digit number, (ii) a perfect square number, (iii) a number divisible by 5.

Find the values of $cot\theta andcosec\theta$ in the figure given below.

In the following data the median of the runs scored by $60$ top batsmen of the world in one-day international cricket matches is $5000$. Find the missing frequencies $x$ and $y$.

How many terms aare there in the AP 41, 38, 35,..., 8?

Heights of students of Class X are given in the following frequency distribution :
$\begin{array}{cccccc}\text{Marks}& 150-155& 155-160& 160-165& 165-170& 170-175\\ \text{Number of}& & & & & \\ \text{students}& 15& 8& 20& 12& 5\end{array}$
Find the modal height.
Also, find the mean height. Compare and interpret the two measures of central tendency.

103×94

Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awanded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?

There is a coin. Ram attaches a conical attachment to one flat end of coin. The conical attachment has same radius as coin. What is the surface area of the combined solid?

The sum of the squares of two consecutive positive even numbers in 52. Find the numbers.

A cricket ball of radius r is exactly fitted in a cylindrical tin as shown in the figure below. The ratio of surface areas of the cricket ball to the surface area of tin is ___.

Is it possible to have two numbers whose HCF is 25 and LCM is 520?

Solve for x and y:

$\frac{x+y-8}{2}=\frac{x+2y-14}{3}=\frac{3x+y-12}{11}$

Solve the following systems of equations:

$\frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2$

$\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1$

If sec $\theta =\frac{5}{4}$, find the value of $\frac{sin\theta -2cos\theta }{tan\theta -cot\theta }$

Write the value of tan ${10}^o$ tan ${20}^o$ tan ${70}^o$ tan ${80}^o$.

The base BC of an equilateral triangle ABC lies on y-axis. The coordinates of point C are (0, -3). The origin is the midpoint of the base. Find the coordinates of the points A and B. Also, find the coordinates of another point D such that ABCD is a rhombus.

In the given figure, if $\angle AOD=$ ${135}^{\circ }$ then $\angle BOC$ is equal to

(a) ${25}^{\circ }$ (b) ${45}^{\circ }$ (c) ${52.5}^{\circ }$ (d) ${62.5}^{\circ }$

Two water taps together can fill a tank in 6 hours. The tap of larger diameter takes 9 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

The sum of two numbers is 48 and their product is 432 Find the numbers.

If $S_n$ denotes thesum of first n terms of an A.P., prove that $S_{12}=3(S_8-S_4)$.

If you write all the numbers from 300 to 400, how many times you have to write the number 3

4 tables and 3 chairs, together, cost Rs. 2,250 and 3 tables and 4 chairs cost Rs.1950.Find the cost of 2 chairs and 1 table.

If the sum of a certain number of terms starting from first term of an A.P. is 25,22,19,..., is 116. Find the last term.

Reflection of $(0,-12)$ in the y-axes is ___________

Factorise the following by splitting the middle term and find out the roots.
$2x^2+x–6=0$

What is the probability of an impossible event?

(a) $\frac{1}{2}$ (b) 0 (c) 1 (d) more than 1

If (x, y) be on the line joining the two points (1, -3) and (-4, 2), prove that x+ y+ 2 = 0.

The median of the following data is 16. Find the missing frequencies a and b if the total of frequencies is 70.
$\begin{array}{ccccccccc}\text{Class}& 0-5& 5-10& 10-15& 15-20& 20-25& 25-30& 30-35& 35-40\\ \text{Frequency}& 12& a& 12& 15& b& 6& 6& 4\end{array}$

Solve each of the following quadratic equations:
$ab{x}^2+(b^2-ac)x-bc=0$

If $a^2+b^2+c^2=1$, then $bc+ca+ab$ lies in the interval

Which of the following numbers is the fourth power of a natural number?