Question

A test paper has four sections A, B, C, D having 7,4,5, 7 questions respectively. Each question in section $C$ has an altemate. The number of ways in which student can attempt the question paper, taking atleast two questions from each section is

• A. $2^{22}$
• B. ${\left(2^7-1\right)}^2\left(2^4-1\right)\left(2^5-1\right)$
• C. ${\left(2^7-8\right)}^2\left(2^4-5\right)\left(3^5-1\right)$
• D. ${\left(2^7-8\right)}^2\left(2^4-5\right)\left(3^5-11\right)$

Answer 1

Answer: (D)

Number of ways of selecting at least two questions from
section $A$ or $D=2^7-{}^7{C}_0-{}^7{C}_1=2^7-8$
From section $B=2^4-{}^4{C}_0-{}^4{C}_1=2^4-5$
From section $C\Rightarrow 3^5-1-{}^{10}{C}_1=3^5-11$
$\therefore$ Total number of ways $={\left(2^7-8\right)}^2\left(2^4-5\right)\left(3^5-11\right)$