Question

Assertion :In an examination of $9$ papers, a candidate has to pass in more papers than the numbers of papers in which he fails in order to be successful. The number of ways in which he can be unsuccessful is $256$ Reason: ${}^n{C}_0{+}^n{C}_1{+}^n{C}_2+...{+}^n{C}_n=2^n$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Reason by theory is true.

The candidate is unsucessful if he fails in $9$ or $8$ or $7$ or $6$ or $5$ papers.

$\therefore$The number of ways to be unsucessful ${}^9{C_9+}^9{C}_8{+}^9{C}_7{+}^9{C_6+}^9{C}_5$

${=}^9{C}_0{+}^9{C_1+}^9{C_2+}^9{C}_3{+}^9{C}_4=\frac{1}{2}({}^9{C}_0{+}^9{C}_1+...{+}^9{C}_9)$

$=\frac{1}{2}\times 2^9=2^8=256.$

Assertion is also correct.