Q If the product of n positive real numbers is unity then their sum is

# Q if the product of n positive real numbers is unity

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Q.If the product of n positive real numbers is unity, then their sum is necessarily 1. a multiple of n2. equal to n1n3. never less than n4. a positive integerSoln. (3) — The best way to do this is to take some value and verify.E.g. 2, 1/2 and 1. Thus, n = 3 and the sum of the three numbers = 3.5.Thus options 1, 2 and 4 get eliminated.Q.There are 8436 steel balls, each with a radius of 1 centimeter, stacked in a pile, with 1 ball on top, 3 balls in the second layer, 6 in the third layer, 10 in the fourth, and so on. The number of horizontal layers in the pile is1. 342. 383. 364. 32Soln. (3) — Assume the number of horizontal layers in the pile be n.So 84362)1n(n8436]nn[21284364)1n(n12)1n2()1n(n
Q.In the figure below, the rectangle at the corner measures 10 cm × 20 cm. The corner A of the rectangle is also a point on the circumference of the circle. What is the radius of the circle in cm?
Q.How many three digit positive integers, with digits x, y and z in the hundred’s, ten’s and unit’s place respectively, exist such that x < y, z < y and 0x ? ) )