গাণিতিক যুক্তি

১. Find the value of ( √ 3 +1) (10+ √ 12 ) ( √ 12 -2) (55- √ 3 )

২. A circle is inscribed in a right triangle whose legs measure 9 and 12. Find the radius of the circle.

৩. In a geometric progression, the 3rd term is 12 and the 6th term is 96. Find the sum of the first 8 terms.

৪. The present age of a father and his son are in ratio 7 : 2. Five years ago the ratio was 6 : 1. Find the sum of their present ages.

৫. How many positive divisors of 7200 are perfect squares?

৬. For x > 0, what is the minimum value of x+ 16 x ?

৭. A cistern is normally filled in 6 hours, but a leak makes it take 8 hours. How long would the leak alone take to empty a ful cistern?

৮. Nasif's watch gains 4 minutes per hour. It was correct at 2:00 pm yesterday. When it displays 6:00 am today. What is the accurate time?

৯. ab is negative and a2+b2 is greater than o, but less than 114. What is the minimum value of ab?

১০. If positive integers m and n satisfy m + n < 10, how many distinct values can mn assume?

১১. Find the smallest positive integer that leaves remainder 3 when divided by 7, remainder 4 when divided by 9, and remainder 8 when divided by 11.

১২. A circular garden's diameter has endpoints at coordinates (2, 3) and (8, 11). Find its area in terms of π.

১৩. Nasrin and Farid can finish a project in 12 and 18 days. They work together for 4 days, then Nasir in leaves. How many more days does Farid need?

১৪. In a factory, yield drops 10% each stage: cutting, sewing, finishing. To ship 729 flawless:, shirts, how many starting materials (in shirts) are needed?

১৫. The total number of legs of a group of cows and chickens is 14 more than twice the total number of their heads. How many cows are there in that group?