Polynomials || Quantitative Aptitude || CAT 2021 || 14 May (App update required to attempt this test)

Given that x²⁰¹⁸ y²⁰¹⁷ = 1/2 and x²⁰¹⁶ y²⁰¹⁹ = 8, the value of x² + y³ is

Consider the four variables A, B, C and D and a function Z of these variables, Z = 15A² – 3B⁴ + C + 0.5D It is given that A, B, C and D must be non-negative integers and thatall of the following relationships must hold:

i) 2A + B ≤ 2

ii) 4A + 2B + C ≤ 12

iii) 3A + 4B + D ≤ 15

If Z needs to be maximised, then what value must D take?

If 16a⁴ + 36a²b² + 81b⁴ = 77 and 4a² + 9b² – 6ab = 7, then what is the value of 3ab?

If  ; then how can we write 3x⁴+5x³−2x²+5x+3 = 0 in terms of y?

Given that x⁸ – 47x⁴ + 1 = 0, x > 0. What is the value of (x³ – x^–3)?

Suppose there is a polynomial p(x) = x⁴ - 8x³ - px² + qx + 16 that has positive real roots. Find pq:

Let p be any root, real or complex, of the equation xⁿ + x^n–1 + x^n–2 + ….+ 1 = 0. Then (p²ⁿ⁺² + 3)(p³ⁿ⁺³ – 4) equals. n is odd natural number.

The factors of x³⁹−x³²+x¹⁷−1 is/are:

Find the number of ordered pairs ( x² , y) that satisfy the equation x³ + y³ + 36 xy = 1728, where x and y are positive whole numbers.