SSC CHSL 2023 PYQ — Question 65

SSC CHSL - 07 Aug 2023 - Shift 3 • Quantitative Aptitude • Q65

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.

At one end of diameter PQ of a circle of radius 8 cm  a tangent APB is drawn to the circle. Find the length of the chord RS, which is parallel to AB and at a distance of 12 cm from P.

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e.  838\sqrt3 cm.

According to the given question,

Let the diameter PQ cuts the chord RS at right angle in two equal parts at T.

Now, applying Pythagoras theorem in triangle OTS, 

OS2 = OT2 + ST2

⇒ 82 = 42 + ST2

⇒ ST2 = 64 - 16

⇒ ST2 = 48

⇒ ST = 434 \sqrt{3}

Also, RS = 2ST 

⇒ RS = 838\sqrt{3} cm