Mathematics - MOST IMPORTANT UPSC EPFO Previous Year Questions

In a medium-size township, the trend of annual immigration is an addition of 20% of the population as it was at the beginning; also 15% of the population as it was at the beginning is estimated to relocate elsewhere every year. If the current population is 80000, what is the likely population three years hence?

For which time intervals, is the percentage rise of population the same for the following data?

In an office, 40% of the employees are men and the rest women. Half of the employees are tall and half short. If 10% of the employees are men and short, and 40 employees are women and tall, the number of tall men employees is

If the radius of a circle is reduced by 50%, its area will be reduced by

In an examination paper where maximum marks are 500, A got 10% marks less than B, B got 25% marks more than C, and C got 20% marks less than D. If A got 360 marks, what marks did D get?

There are two circles of radii $\displaystyle r_1$ and $\displaystyle r_2$ ($\displaystyle r_1 < r_2$). The area of the bigger circle is $\displaystyle \dfrac{693}{2}\text{ cm}^2$. The difference of their circumferences is 22 cm. What is the sum of the diameters of the two circles?

A cylindrical closed tank contains $\displaystyle 36\pi$ cubic metres of water, and is filled to half of its capacity. When the cylindrical tank is placed upright on its circular base on level ground, the height of the water in the tank is 4 metres. But when this tank is placed on its side on level ground, what will be the height of the surface of the water above the ground?

A rectangular garden is to be twice as long as its width. If 360 m of fencing including gates will totally enclose this garden, what is the length of the garden?

The original lay of a rectangular plot ABCD on open ground is 80 m long along AB, and 60 m wide along BC. Concreted pathways are intended to be laid on the inside of the plot all around the sides. The pathways along BC and DA are each 4 m wide. The pathways along AB and DC will mutually be of equal widths such that the un-concreted internal plot will measure three-fourth of the original area of the plot ABCD. What will be the width of each of these pathways along AB and DC?

Numbers $\displaystyle a_1, a_2, a_3, a_4, a_5, \dots, a_{24}$ are in arithmetic progression and $\displaystyle a_1 + a_5 + a_{10} + a_{15} + a_{20} + a_{24} = 225$. The value of $\displaystyle a_1 + a_2 + a_3 + a_4 + a_5 + \dots + a_{23} + a_{24}$ is

A certain sequence of integers is constructed as follows: Consider 0 and 1 as the first two numbers. The next, i.e. the third number is constructed by their sums, i.e. 1. This process of constructing the next number by the sum of the last two constructed numbers continues. Taking these numbers 0, 1, 1 as the first, second and third numbers in the sequence, what will be the 7th and 10th numbers, respectively?

In a race, the first four winners are to be awarded points. Each winner's points must be 5 more than that of the next position winner. Total sum of the points to be awarded is 50. What will be the points for the third position winner?

A firm is purchasing two items, both on credit on the same day. The credit term offered for the first item is $\displaystyle 2\frac{1}{2}/10$, $\displaystyle 1/20$, net 30; and the credit term offered for the second item is $\displaystyle 3/5$, $\displaystyle 2/15$, net 30. The declared purchase cost of item 1 is ₹ 60,000 and that of item 2 is ₹ 1,40,000. If both credits can be settled on the 14th day, what will be the total amount to be paid out?

There are 20 girls and 30 boys in a class, and their respective average marks are found to be 55 and 58. The average marks of the entire class are

Four quantities are such that their arithmetic mean (A.M.) is the same as the A.M. of the first three quantities. The fourth quantity is

Consider the sequential integers 27 to 93, both included in the sequence. The arithmetic average of these numbers will be

There are four identically sized and shaped balls in a box, with only its top open. Each ball is of a different colour, these being: Green, Red, White and Blue, only one ball of each colour. Without looking into the box, one ball is randomly picked out and its colour is noted; then it is returned to the box. What are the chances that, in two successive draws, one may get the white ball and the red ball — in whichever order?

The mean and standard deviation of a set of 16 non-zero positive numbers in an observation are 26 and 3.5 respectively. The mean and standard deviation of another set of 24 non-zero positive numbers without changing the circumstances of both sets of observations, are 29 and 3, respectively. The mean and standard deviation of their combined set of observations will respectively be

Which of the following is not an absolute measure of dispersion?

In a chess tournament, each of the six players will play with every other player exactly once. What is the number of matches that will be played during the tournament?