An electric device makes a beep after every 60 seconds. Another device makes a beep after every 62 seconds. They beeped together at 11:00 AM. At what time will they beep together again?

Divide a line segment of length 9 cm internally in the ratio 4 : 3.

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of drawing

(i) an ace (ii) a red king (iii) a diamond

OR

Two different dice are thrown together. Find the probability that the numbers obtained

(i) have a sum less than 7 (ii) is a doublet of odd numbers

If α and β are the zeroes of the polynomial f(x) = x² + x – 2, find the value of .

A bookseller buys a number of books for ₹ 1760. If he had bought 4 more books for the same amount, each book would have cost ₹ 22 less. How many books did he buy?

OR

A two-digit number is such that product of its digits is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.