IAS 2020 — Maths

Let p, q, r and s be natural numbers such that \[p - 2016 = q + 2017 = r - 2018 = s + 2019\] Which one of the following is the largest natural number?

As a result of 25% hike in the price of rice per kg, a person is able to purchase 6 kg less rice for Rs 1200. What was the original price of rice per kg.

The average score of a batsman after his 50th innings was 46.6. After 60th innings, his average score increases by 2.6. What was his average score in the last ten innings?

For what value of n, the sum of digits in the number (10n + 1) is2?

How many different 5-letter words (with or without meaning) can be constructed using all the letters of the word ‘DELHI’ so that each word has to start with D and end with I?

A shop owner offers the following discount options on an article to a customer: 1. Successive discounts of 10% and 20%, and then pay a service tax of 10%. 2. Successive discounts of 20% and 10%, and then pay a service tax of 10%. 3. Pay a service tax of 10% first, then successive discounts of 20% and 10%. Which one of the following is correct?

If 1 litre of water weighs 1kg, then how many cubic millimetres of water will weigh 0.1 gm?

A frog tries to come out of a dried well 4.5m deep with slippery walls. Every time the frog jumps 30 cm, slides down 15 cm. What is the number of jumps required for the frog to come out of the well?

A person bought a car and sold it for Rs 3,00,000. If he incurred a loss of 20%, then how much did he spend to buy the car?

Consider the following data: | Average Marks in English | Average marks in Hindi Girls | 9 | 8 Boys | 8 | 7 Overall average marks | 8.8 | X What is the value of x in the above table?

What is the remainder when \(51 \times 27 \times 35 \times 62 \times 75\)is divided by 100?

The average age of a teacher and three students is 20 years. If all the three students are of same age and the difference between the age of the teacher and each student is 20 years, then what is the age of the teacher?

A man takes halftime in rowing a certain distance downstream than upstream. What is the ratio of the speed in still water to the speed of current?

How many zeroes are there at the end of the following product? \(1 \times 5 \times 10 \times 15 \times 20 \times 25 \times 30 \times 35 \times 40 \times 45 \times 50 \times 55 \times 60\)

Let A3BC and DE2F be four-digit numbers where each letter represents a different digit greater than 3. If the sum of the numbers is 15902, then what is the difference between the values of A and B?

If you have two straight sticks of length 7.5 feet and 3.25 feet, what is minimum length can you measure?

What is the largest number among the following?

In adult population of a city, 40% men and 30% women are married. What is the percentage of married adult population if no man marries more than one woman and no woman marries more than one man; and there are no widows and widowers?

A sum of Rs 2,500 is distributed among X, Y and Z in the ratio \(\frac{1}{2}:\frac{3}{4}:\frac{5}{6}.\) What is the difference between the maximum share and the minimum share?

In the sum ⊗ + 1 ⊗ + 5 ⊗ + ⊗ ⊗ + ⊗ 1 = 1 ⊗ ⊗ For which digit-does the symbol ⊗ stand?

Let XYZ be a three-digit number, where (X + Y + Z) is not a multiple of 3. Then (XYZ + YZX + ZXY) is not divisible by

A bottle contains 20 litres of liquid A., 4 litres of liquid A is taken out of it and replaced by same quantity of liquid B. Again 4 litres of the mixture is taken out and replaced by same quantity of liquid B. What is the ratio of quantity of liquid A to that of liquid B in the final mixture?

How many five-digit prime numbers can be obtained by using all the digit 1, 2, 3, 4 and 5 without repetition of digits?

How many pairs of natural numbers are there such that the difference of whose squares is 63?

Let x, y be the volumes; m, n be the masses of two metallic cubes P and Q respectively. Each side of Q is two times that of P and mass of q is two times that of P. Let u = m/x and v = n/y. Which one of the following is correct?

Which one of the following will have minimum change in its value if 5 is added to both numerator and the denominator of the fractions \(\frac{2}{3},\frac{3}{4},\frac{4}{5}\)and \(\frac{5}{6}\)?

In a class, there are three groups, A, B and C. If one student from group A and two students from group B are shifted to group C, then what happens to the average weight for the students of the class?

The recurring decimal representation 1.272727… is equivalent to

A vessel full of water weighs 40 kg. If it is one-third filled, its weight becomes 20kg. What is the weight of the empty vessel?

How many different sums can be formed with the denominations ₹50, ₹100, ₹200, ₹500 and ₹2000 taking at least three denominations at a time?

Consider the following statements: 1. The minimum number of points of intersection of a square and a circle is 2. 2. The maximum number of points of intersection of a square and a circle is 8. Which of the above statements is/are correct?

What is the greatest length x such that \(3\frac{1}{2}\)m and \(8\frac{3}{4}\)m are integral multiple of x?

Consider the following data: Year | Birth rate | Death rate 1911–1921 | 48.1 | 35.5 1921–1931 | 46.4 | 36.3 1931–1941 | 45.2 | 31.2 1941–1951 | 39.9 | 27.4 1951–1961 | 41.7 | 22.8 1961–1971 | 41.1 | 18.9 1971–1981 | 37.1 | 14.8 For which period was the natural growth rate maximum?

A car travels from a place X to place Y at an average speed of v km/hr, from Y to X at an average speed of 2v km/hr, again from X to Y at an average speed of 3v km/hr and again from Y to X at an average speed of 4v km/hr. Then the average speed of the car for the entire journey

What is the least four-digit number when divided by 3, 4, 5 and 6 leaves a remainder 2 in each case?

A digit n > 3 is divisible by 3 but not divisible by 6. Which one of the following is divisible by 4?

A person X can complete 20% of work in 8 days and another person Y can complete 25% of the same work in 6 days. If they work together, in how many days will 40% of the work be completed?

One page is torn from a booklet whose pages are numbered in the usual manner starting from the first page as 1. The sum of the numbers on the reaming page is 195. The torn page contains which of the following numbers?

How many integers are there between 1 and 100 which have 4 as a digit but are not divisible by 4?