CSAT Maths questions from IAS 2023.
A 3-digit number ABC, on multiplication with D gives 37DD where A, B, C and D are different non-zero digits. What is the value of A + B + C?
A, B, C working independently can do a piece of work in 8, 16 and 12 days respectively. A alone works on Monday, B alone works on Tuesday, C alone works on Wednesday; A alone, again works on Thursday and so an. Consider the following statements: 1. The work will be finished on Thursday. 2. The work will be finished in 10 days. Which. of the above statements is/are correct?
A box contains 14 black balls, 20 blue balls, 26 green balls, 28 Yellow balls, 38 red balls 54 white balls. Consider the following Statements: 1. The smallest number n such that any n balls drawn from the box randomly must contain one full group of at least one colour is 175. 2. The smallest number m such that any m balls drawn from the box randomly must contain at least one ball of each colour is 167. Which of the above statements is/are correct?
A flag has to be designed with 4 horizontal strips using some or all of the colour red, green and yellow. What is the number of different ways in which this can be done so that no two adjacent stripes have the same colour?
A number N is formed by writing 9 for 99 times, What is the remainder if N is divided by 13?
A principal P becomes Q in 1 year when compounded half-yearly with R% annual rate of interest. If the same principal P becomes Q in 1 year when compounded annually with S% annual rate of interest, then which one of the following is correct?
A rectangular floor measures 4 m in length and 2.2 m in breadth. Tiles of size 140cm by 60 cm have to be laid such that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. What is the maximum number of tiles that can be accommodated on the floor?
AB and CD are 2-digit numbers, Multiplying AB with CD results in a 3-digit number DEF. Adding DEF to another 3-digit number GHI results in 975. Further A, B, C, D, E, F, G, H, I are distinct digits. If E = 0, F = 8, then what is A + B + C equal to?
ABCD is a square. One point on each of AB and CD; and two distinct points on each of BC and DA are chosen. How many distinct triangles can be drawn using any three points as vertices out of these six points?
Consider the following in respect of prime number p and composite number c. 1. \(\frac{p + c}{p - c}\)can be even 2. 2p + c can be odd 3. pc can be odd. Which of the statements given above are correct?
D is a 3-digit number such that the ratio of the number of the sum of its digits is least. What is the difference between the digit at the hundred’s place and the digit at the unit’s place of D?
Each digit of a 9-digit number is 1. It is multiplied by itself. What is the sum of the digits of the resulting number?
For any choices of values of X, Y and Z the 6-digit number of the form XYZXYZ is divisible by:
How many distinct 8-digit numbers can be formed by rearranging the digits of the number 11223344 such that odd digits occupy odd positions and even digits occupy even positions?
How many natural numbers are there which give a remainder of 31 when 1186 is divided by these natural numbers?
If ABC and DEF are both 3-digit numbers such that A, B, C, D, E and F are distinct non-zero digits such that ABC + DEF = 1111, then what is the value of A + B + C + D + E + F?
If p, q, r and s are distinct single digit positive numbers, then what is the greatest value of (p + q) (r + s)?
In an examination, the maximum marks for each of the four papers namely P, Q, R and S are 100. Marks scored by the students are in integers. A student can score 99% in n different ways. What is the value of n?
In how many ways can a batsman score exactly 25 runs by scoring single runs, fours and sixes only, irrespective of the sequence of scoring shots?
Let pp, qq and rr be 2-digit numbers where p < q < r. If pp + qq + rr = tt0, where tt0 is a 3-digit number ending with zero, consider the following statements: 1. The number of possible values of p is 5. 2. The number of possible values is/are correct?
Let x be a positive integer such that 7x + 96 is divisible by x. how many value of x are possible?
Raj has ten pairs of red, nine pairs of white and eight pairs of black shoes in a box. If he randomly picks shoes one by one (without replacement) from the box to get a red pair of shoes to wear, what is the maximum number of attempts he has to make?
There are four letters and four envelopes and exactly one letter is to be put in exactly one envelop with the correct address. If the letters are randomly inserted into the envelopes, then consider the following statements: 1. It is possible that exactly one litter goes into an incorrect envelope. 2. There are only six ways in which only two letters can go into the correct envelopes. Which of the statements given above is/are correct?
There are large numbers of silver coins weighing 2 gm, 5 gm, 10 gm, 25 gm, 50 gm each. Consider the following statements: 1. To buy 78 gm of coins one must buy at least 7 coins. 2. To weigh 78 gm using these coins one can use less than 7 coins. Which of the statements given above is/are correct?
There are three traffic signals. Each signal changes colour from green to red and then form red to green. The first signal takes 25 seconds, the second signal takes 39 seconds and the third signal takes 60 seconds to change the colour from green to red. The durations for green and red colour are time. At 2:00 p.m. they together turn green. At what time will they change to green next, simultaneously?
Three of the five positive integers p, q, r, s, t are even and two of them are odd (not necessarily in order). Consider the following: 1. p + q + r – s – t is definitely even 2. 2p + q + 2r – 2s + t is definitely odd. Which of the above statements is/are correct?
What is the number of selections of 10 consecutive things out of 12 things in a circle taken in the clockwise direction?
What is the remainder if 2192 is divided by 6?
What is the remainder when \(85 \times 87 \times 89 \times 91 \times 95 \times 96\)is divided by 100?
What is the sum of all 4-digit numbers less than 2000 formed by the digits 1, 2, 3 and 4, where none of the digits is repeated?
What is the sum of all-digit number less than 2000 formed by the digits 1, 2, 3 and 4, where none of the digit is repeated?
What is the sum of all digits which appear in all the integers from 10 to 100?
What is the unit digit in the expansion of \((57242)^{9 \times 7 \times 5 \times 3 \times 1}\)?