CAT Progression

Reading Test 1

Question No : 1

Q.1 For a real number x, if 1/2, (log₃(2^x - 9))/log₃4, and (log₅(2^x + 17/2))/log₅4 are in an arithmetic progression, then the common difference is:

Question No : 2

Q.2 For some positive and distinct real numbers x,y and z, if 1/(√y + √z) is the arithmetic mean of 1/(√x + √z) and 1/(√x + √y), then the relationship which will always hold true is

Question No : 3

Q.3 Let both the series a₁, a₂, a₃... and b₁, b₂, b₃... be in arithmetic progression such that the common differences of both the series are prime numbers. If a₅ = b₉, a₁₉ = b₁₉ and b₂ = 0, then a₁₁ equals

Question No : 4

Q.4The value of 1 + (1 + 1/3)1/4 + (1 + 1/3 + 1/9)1/16 + (1 + 1/3 + 1/9 + 1/27)1/64 + ---------- is

Question No : 5

Q.5 Let a_n = 46 + 8n and b_n = 98 + 4n be two sequences for natural numbers N ≤ 100. Then the sum of all terms common to both the sequences is:

Question No : 6

Q.6 A lab experiment measures the number of organisms at 8 am every day. Starting with 2 organisms on the first day, the number of organisms on any day is equal to 3 more than twice the number on the previous day. If the number of organisms on the n^th day exceeds one million, then the lowest possibl value of n is

Question No : 7

Q.7 Three posiive integers x, y and z are in arithmetic progression. If y-x > 2 and xyz = 5(x + y + z), then z-x equals

Question No : 8

Q.8 Let a_n and b_n be two sequences such that a_n = 13 + 6(n - 1) and b_n = 15 + 7(n - 1) for all natural numbers n. Then, the largest three digit integer that is common to both these sequences, is

Question No : 9

Q.9 The average of a non-decreasing sequence of N numbers a₁, a₂,...,a_N is 300. If a₁ is replaced by 6a₁, the new average becomes 400. Then, the number of possible values of a₁, is

Question No : 10

Q.10 For any natural number n, suppose the sum of the first n terms of an arithmetic progression is (n + 2n²). If n^th term of the progression is divisible by 9, then the smallest possible value of n is

Question No : 11

Q.11 On day one, there are 100 particles in a laboratory expreiment. On day n, where n ≥2, one out of every n aricles produces another particle. If the total number of particles in the laboratory experiment increases to 1000 on day m, then m equals

Question No : 12

Q.12 Consider the arithmetic progression 3,7,11,... and let A_n denote the sum of the first n terms of this progression. Then the value of 1/25 ∑²⁵_n=1 A_n is

Question No : 13

Q.13 Consider a sequence of real numbers x₁, x₂, x₃, ... such that x_n+1 = x_n + n - 1 for all n ≥ 1. If x₁ = -1 then x₁₀₀ is equal to

Question No : 14

Q.14 For a sequence of real numbers x₁, x₂,...x_n, if x₁ - x₂ + x₃ - ... + (-1)^n-1x_n = n² + 2n for all natural numbers n, then the sum x₄₉ + x₅₀ equals

Question No : 15

Q.15 If x₀ = 1, x₁ = 2, and x_n+2 = ((1 + x_n+1)/x_n), n = 0,1,2,3,...., then x₂₀₂₁ is equal to

Question No : 16

Q.16 The natural numbers are divided into groups as (1), (2,3,4), (5,6,7,8,9), ... and so on. Then, the sum of the numbers in the 15th group is equal to