Maths PYQ — Page 5

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?

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?

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?

For any choices of values of X, Y and Z the 6-digit number of the form XYZXYZ is divisible by:

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?

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?

A number N is formed by writing 9 for 99 times, What is the remainder if N is divided by 13?

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?

What is the remainder if 2192 is divided by 6?

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?

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?

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 remainder when \(85 \times 87 \times 89 \times 91 \times 95 \times 96\)is divided by 100?

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?

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?

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?

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?

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?

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?

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?

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?

What is the number of selections of 10 consecutive things out of 12 things in a circle taken in the clockwise direction?

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?

If p, q, r and s are distinct single digit positive numbers, then what is the greatest value of (p + q) (r + s)?