Management Exams (CAT) - Quantitative Aptitude (QA)

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Q1.

Algebra & Functions: In 'Quadratic & Higher Degree Polynomials, Descarte's Rule of Signs', if $f(x) + 2f(1/x) = 3x$ for all $x \neq 0$, what is the value of $f(2)$?

(A)

$-1$ ($f(2) + 2f(1/2) = 6$ and $f(1/2) + 2f(2) = 3/2 \implies 3f(2) = -3 \implies f(2) = -1$) (Quadratic & Higher Degree Polynomials, Descarte's Rule of Signs)

(B)

$2$

(C)

$1$

(D)

$-2$

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Q2.

Modern Math (Derangements): In how many ways can 5 distinct letters be placed into 5 addressed envelopes in 'Quadratic & Higher Degree Polynomials, Descarte's Rule of Signs' such that NO letter is placed into its correctly addressed envelope?

(A)

44 ways ($!5 = 5! [1 - 1/1! + 1/2! - 1/3! + 1/4! - 1/5!] = 120 [1/2 - 1/6 + 1/24 - 1/120] = 44$) (Quadratic & Higher Degree Polynomials, Descarte's Rule of Signs)

(B)

120 ways

(C)

60 ways

(D)

89 ways

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