Two right circular cones, whose heights are different, have the same slant height. The product of their base radii is equal to the product of their heights. If the baseradius and the height of one of the cones are 5 cm and 6 cm respectively, then find the sum of the volumes (in sq. cm) of the two cones

Four vacuum cleaners, A, B, C and D are used to clean IIM Lucknow’s library. A is twice as fast as B while C is twice as fast as D and B is thrice as fast as D. Acleans (1/8)th of the building, B cleans (1/4)th, C cleans (3/8) th and D cleans the rest. The machines work one after the other and in all it takes 130 hours for themto clean the whole library. The time taken by each of A, B, C and D to clean the library individually (in hours) is

If a positive integer ‘n’ is subtracted from the squares of three consecutive terms of an Arithmetic Progression, the numbers obtained are 120, 232 and 376respectively. What is the sum of the digits of ‘n’?

Three varieties of rice with Cost Price (in Rs./kg) 28, 36 and 45 are mixed in the ratio a : b : c respectively. It is known that a, b and c are in Geometric Progression where a < b < c. The Cost Price (in Rs./kg) of the mixture becomes 40. What would have been the Cost Price (in Rs./kg) of the mixture had the three varieties been mixed in the ratio c : a : b?

If α and β are the roots of the equation

The roots of x3- ax2 + bx- c = 0 are p, q and r while the roots of x3 + dx2 + ex − 90 = 0 are p + 3, q + 3 and r + 3. What is the value of 9a + 3b + c?

A class photograph has to be taken. The front row consists of 5 girls who are sitting. 14 boys are standing behind. The two corner positions are reserved for the 2tallest boys. In how many ways can the students be arranged?

In Delhi Public school, Lucknow, 30% of students are below 8 years of age. The number of students above 8 years of age is (2/3) of the number of students of 8 years which is 42. What is the total number of students in the school?

If N is the greatest possible number which leaves remainders of 3 and 7 when it divides 171 and 247 respectively, what is the remainder when N divides 700?

To bake a cake, we need 250 gm of flour, 250 gm of butter, 25 gm of raisins, 25 gm of cashew nuts, 25 gm of cherries, 25 gm of almonds, 10 gm of sodiumbicarbonate and 250 gm equivalent of eggs. If the 25 gm of almonds are substituted with 15 more grams of cashew, the increase in the percentage of cashew, in percentage points, approximately is