Find the compound interest on ₹13000 at 10% per annum for 2 years.
Correct answer: ₹2860
Explanation: CI=13000×(1.1²−1)=2730.
Question 102 · Hard
A boat travels 42 km downstream in 3 hours and 30 km upstream in 5 hours. Find the speed of the stream.
Correct answer: 4 km/h
Explanation: Downstream=14, upstream=6. Stream=(14−6)/2=4 km/h.
Question 103 · Hard
If α and β are the roots of x²−11x+k=0 and α²+β²=65, find k.
Correct answer: 28
Explanation: 121−2k=65 ⇒ k=28.
Question 104 · Hard
The average of 15 observations is 48. If one observation 72 is replaced by 57, find the new average.
Correct answer: 47
Explanation: Total decreases by 15. Average decreases by 1. New average =47.
Question 105 · Hard
A train crosses a 240 m platform in 24 seconds and a pole in 12 seconds. Find the speed of the train.
Correct answer: 72 km/h
Explanation: Let length=L. L/v=12 and (L+240)/v=24. Hence v=20 m/s =72 km/h.
Question 106 · Hard
A and B can complete a work in 18 and 30 days respectively. They work together for 6 days, then A leaves. In how many more days will B finish the remaining work?
Correct answer: 14
Explanation: Work done in 6 days = 8/15. Remaining = 7/15. B alone takes (7/15)/(1/30)=14 days.
Question 107 · Hard
A shopkeeper marks an article 60% above the cost price and allows successive discounts of 10% and 20%. Find the profit percentage.
If α and β are the roots of x²−13x+k=0 and α²+β²=97, find k. / यदि α तथा β, x²−13x+k=0 के मूल हैं तथा α²+β²=97 है, तो k का मान ज्ञात करें।यदि α तथा β, x²−13x+k=0 के मूल हैं तथा α²+β²=97 है, तो k का मान ज्ञात करें।
Correct answer: 36
Explanation: Apply Vieta's formulas.
Question 109 · Hard
The HCF and LCM of two numbers are 18 and 1260 respectively. If one number is 180, find the other number. / दो संख्याओं का HCF 18 तथा LCM 1260 है। यदि एक संख्या 180 है, तो दूसरी संख्या ज्ञात करें.दो संख्याओं का HCF 18 तथा LCM 1260 है। यदि एक संख्या 180 है, तो दूसरी संख्या ज्ञात करें।