Maths PYQ — Page 7

What is the remainder when \(91 \times 92 \times 93 \times 94 \times 95 \times 96 \times 97 \times 98 \times 99\)is divided by 1261?

The digits 1 to 9 are arranged in three rows in such a way that each row contains three digits, and the number formed in the second row is twice the number formed in the first row; and the number formed in the third row is thrice the number formed in the first row. Repetition of digits is not allowed. If only three of the four digits 2, 3, 7 and 9 are allowed to use in the first row, how many such combinations are possible to be arranged in the three rows?

There are eight equidistant points on a circle. How many right-angled triangle can be drawn using these points as vertices and taking the diameter as one side of the triangle?

If \(15 \times 14 \times 13 \times ... \times 3 \times 2 \times 1 = 3^{m} \times n\) where m and n are positive integers, then what is the maximum value of m?

Let A, B and C represent distinct non zero digits. Suppose x is the sum of all possible 3-digit numbers formed by A, B and C without repetition. Consider the following statements: 1. The 4-digit least value of x is 1332. 2. The 3-digit greatest value of x is 888. Which of the above statements is/are correct?

A man started from home to 14:30 hours and drove to village, arriving there when the village clock indicated 15:15 hours. After staying for 25 minutes, he drove back by a different route of length 1:25 times the first route at a rate twice as fast reaching home at 16:00 hours. As compared to the clock at home, the village clock is

X and Y run a 3 km race along a circular course of length 300 m. Their speeds are in the ratio 3 : 2. If they start together in the same direction, how many times would the first one pass the other (the start-off is not counted as passing)?

On one side of a 1.01 km long road, 101 plants are planted at equal distance from each other. What is the total distance between 5 consecutive plants?

Consider the following statements in respect of two natural numbers p and q such that p is prime number and q is a composite number: 1. p × q can be an odd number. 2. q/p can be a prime number. 3. p + q can be a prime number. Which of the above statements are correct?

There are two containers X and Y. X contains 100ml of milk and y contains 100ml of water. 20ml of milk from X is transferred to Y. After mixing well, 20 ml of the mixture in Y is transferred back to X. If m denotes the proportion of milk in X and n denotes the proportion of water in Y, then which one of the following is correct?

One non-zero digit, one vowel and one consonant from English-alphabet (in capital) are to be used in forming passwords, such that each password has to start with a vowel and end with a consonant. How many such passwords can generated?

What is the number of numbers of the form XY, where X and Y are distinct non-zero digits?

Using 2, 2, 3, 3, 3, as digits, how many distinct numbers greater than 30000 can be formed?

At which one of the following times, do the hour hand and the minute hand of the clock make an angle of 180° with each other?

A cubical vessel of side 1m is filled completely with water. How many millilitres of water is contained in it (neglect thickness of the vessel)?

A pie diagram shows the percentage distribution of proteins, water and other dry elements in the human body. Given that proteins correspond to 16% and water corresponds to 70%. If both proteins and the other dry elements correspond to p%, then what is the central angle of the sector representing p on the pie diagram?

A person X from a place A and another person Y from a place B set out at the same time to walk towards each other. The places are, separated by a distance of 15 km. X walks with a uniform speed of 1.5 km/hr and Y walks with a uniform speed of 1 in the first hour, with a uniform speed of 1:25 km/hr in the second hour and with a uniform speed of 1-5 km/hr in the third hour and so on. Which of the following is/are correct? 1. They take 5 hours to meet. 2. They meet midway between A and B. Select the correct answer using the code given below

There are two Classes A and B having 25 and 30 students respectively. In Class-A the highest score is 21 and lowest score is 17. In Class-B the highest score is 30 and lowest score is 22. Four students are shifted from Class-A to Class-B. 1. The average score of Class-B will definitely decrease. 2. The average score of Class-A will definitely increase. Which of the above statements is/are correct?

When a certain number is multiplied by 7, the product entirely comprises ones only (1111…). What is the smallest such number?

A boy plays with a ball and he drops it from a height of 1.5 m. Every time the ball hits the ground, it bounces back to attain a height 4/5th of the previous height. The ball does not bounce further if the previous height is less than 50 cm. What is the number of times the ball hits the ground before the ball stops bouncing?

If 32019 is divided by 10, then what is the remainder?

If the price of an article is decreased by 20% and then the new price is increased by 25%, then what is the net change in the price?

The difference between a 2-digit number and the number obtained by interchanging the positions of the digit is 54. Consider the following statements: 1. The sum of the two digits of the number can be determined only if the product of the two digits is known. 2. The difference between the two digits of the number can be determined. Which of the above statements is/are correct?

Consider the following statements: 1. The sum of 5 consecutive integers can be 100. 2. The product of three consecutive natural numbers can be equal to their sum. Which of the above statements is/are correct?