CAT 2021 Quant x maro G Strategy

The number of integers n that satisfy the inequalities |n − 60| < |n − 100| < |n − 20| is.

If r is a constant such that |x² − 4 x − 13| = r has exactly three distinct real roots, then the value of r is

If x_0 = 1, x_1 = 2, and x_(n + 2) = 1+xⁿ+1/xⁿ, n = 0, 1, 2, 3,..., then x_(2021) is equal to?

If log₂[3 + log₃{4 + log₄(x − 1)}] − 2 = 0 then 4x equals TITA

Consider the pair of equations: x² − xy − x = 22 and y² − xy + y = 34. If x > y, then x − y equals

Three positive integers x, y and z are in arithmetic progression. If y − x > 2 and xyz = 5(x + y + z), then z − x equals

For all real values of x, the range of the function f(x) = x2+2x+42x2+4x+9 is.

For all possible integers n satisfying 2.25 ≤ 2 + 2n + 2 ≤ 202, the number of integer values of 3 + 3n + 1 is

For all real numbers x the condition |3x − 20| + |3x − 40| = 20 necessarily holds if.

Suppose one of the roots of the equation a x2 − b x + c = 0 is 2 + √3, where a, b and c are rational numbers and a ≠ 0. If b = c3 then |a| equals

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

If f(x)=x²−7x and g(x)=x+3 , then the minimum value of f(g(x))−3x is

For a real number a, if log15a+log32a/(log15a)(log32a)= = 4 then a must lie in the range

If 3x+2|y|+y=7 and x+|x|+3y=1 , then x+2y is

Consider a sequence of real numbers x1,x2,x3,… such that xn+1=xn+n−1 for all n≥1. If x1=−1 then x100 is equal to

The number of distinct pairs of integers (m, n) satisfying |1+mn| < |m+n| < 5 is