Question

In a class test, Renu score (out of 50) marks, which is equal to the coefficient of $x^2$ in the expansion of $(1+x{)}^7$. But she reported to her parents that she had scored 70% marks in the test.
(i) What is the actual score of Renu in the test?
(ii) What value is shown here by Renu?

Answer 1

(i) Actual score of Renu in the test= Coefficient of $x^2$ in the expansion of $(1+x{)}^7$

$=7_{C_2}=\frac{7!}{2!5!}=\frac{7\times 6}{2\times 1}=$ 21 marks

Since, she got 21 marks out of 50. So, score in percentage

$=\frac{21}{50}\times 100=42\%$

Hence, Renu score 42%. But she reported her parents that she got 70%.

(ii) The value shown by Renu is dishonesty.