In the following passage, some words have been deleted. Read the passage carefully and select the most appropriate option to fill in each blank. When Mr. Smith went to a restaurant one day, he left his coat near the door. There was (1)________ in the pockets when he left it, so he was very surprised when he took his coat after his meal and found the (2)________ full of jewellery. There was a waiter near the door, so Mr. Smith said to him, “Somebody has made a mistake. He has put some (3)________ in my coat. Take it, and when he comes back, give it to him.” The waiter took it and went away. Suddenly another man came in with a (4)________ just like Mr. Smith’s. “I am sorry,” said the man , “I made a mistake. I took your coat and you have got mine. Please give me my coat and jewellery.” Mr. Smith answered.” I gave the jewellery to the waiter. He will give it to you.” Mr. Smith called the manager of the restaurant; but the manager said, “We have (5)________ waiters here. We have only waitresses.” “You gave the jewellery to a thief!” shouted the other man. “I shall send for the police!” Mr. Smith paid the man a lot of money for the jewellery.
Simplify: 12(1−m)(m−n)(n−1)(1−m)3+(m−n)3+(n−1)3
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 41.
a3 + b3 = (a + b)(a2 - ab + b2)
Using this in the given expression,
12(1−m)(m−n)(n−1)(1−m+m−n)((1−m)2−(1−m)(m−n)+(m−n)2)+(n−1)3
⇒ 12(1−m)(m−n)(n−1)(1−n)(1−2m+m2−m+n+m2−mn+m2−2mn+n2)+(n−1)3
⇒ 12(1−m)(m−n)(n−1)−(n−1)(1−3m+3m2+n−3mn+n2)+(n−1)3
⇒ 12(1−m)(m−n)(n−1)−(n−1)(1−3m+3m2+n−3mn+n2−(n−1)2)
⇒ 12(1−m)(m−n)(n−1)−(n−1)(1−3m+3m2+n−3mn+n2−n2+2n−1)
⇒ 12(1−m)(m−n)(n−1)−(n−1)(−3m+3m2+3n−3mn)
⇒ 12(1−m)(m−n)(n−1)−3(n−1)(m(m−1)−n(m−1))
⇒ 4(1−m)(m−n)(n−1)(n−1)(1−m)(m−n) = 41