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 $=\left(2^7-8\right)^2\left(2^4-5\right)\left(3^5-11\right)$