Read each question, consider the options, then reveal the correct answer and explanation.
100 MCQs10 per page4 of 10
MCQ 31Number System
The number 2/3 is rational. How should sqrt(2)/sqrt(3) be classified?
A rational number
Not a number
A natural periodic number
An irrational number
Correct answerD — An irrational number
Explanation
We can rewrite sqrt(2)/sqrt(3) as sqrt(6)/3 after rationalizing the denominator. Since 6 is not a perfect square, sqrt(6) is irrational, and dividing it by the nonzero rational number 3 remains irrational. Thus the expression is a valid real number but not a rational number.
MCQ 32Number System
How many rational numbers lie strictly between 1 and 1000?
998
999
Infinitely many
1000
Correct answerC — Infinitely many
Explanation
Between any two distinct real numbers there are infinitely many rational numbers. For example, between 1 and 1000 we can form 1 + 1/n for every integer n greater than 1, producing infinitely many distinct rational values. Rational numbers are dense on the real number line.
MCQ 33Problem Based On Ages
The average age of a five-member family is 24 years. The youngest member is presently 8 years old. What was the average age of the family members who existed at the time the youngest was born?
16 years
20 years
12 years
18 years
Correct answerB — 20 years
Explanation
The present total age is 5×24=120 years. Eight years ago, subtracting 8 years from all five current members gives a total of 80 years, but the youngest had just been born, so the four older members together accounted for those 80 years. Their average was 80/4=20 years.
MCQ 34Simple Interest
A finance company quotes 10% annual interest but adds the interest to the principal every six months. What is the effective annual interest rate?
10%
10.25%
10.5%
11%
Correct answerB — 10.25%
Explanation
A nominal annual rate of 10% applied every six months means 5% per half-year. The annual growth factor is 1.05²=1.1025, so the effective annual rate is 10.25%. Although the company describes the rate as simple interest, adding interest to principal creates compounding.
MCQ 35Discount
A shopkeeper earns 4% commission on notebooks sold at ₹457 each and 20% commission on pencil boxes sold at ₹80 each. If 10 notebooks and 6 pencil boxes are sold daily for 14 days, what total commission is earned?
₹3903.20
₹1956
₹1596
₹1496
Correct answerA — ₹3903.20
Explanation
Daily notebook commission is 10×457×0.04 = ₹182.80. Daily pencil-box commission is 6×80×0.20 = ₹96. Total daily commission is ₹278.80, and over 14 days it is 278.80×14 = ₹3903.20. The source used a 'none of these' option because none of its numerical choices matched.
MCQ 36Word Problems Based On Numbers
The difference between two numbers is 18. Four times the second number is 18 less than three times the first. What is the sum of the two numbers?
100
80
90
92
Correct answerC — 90
Explanation
Let the first number be x and the second y. Then x - y = 18 and 3x - 4y = 18. Substituting x = y + 18 into the second equation gives 3y + 54 - 4y = 18, so y = 36 and x = 54. Their sum is 90. The printed source options do not contain the mathematically correct answer.
MCQ 37Speed, Time And Distance
Two men start simultaneously from points A and B, 72 km apart, and walk toward each other. The man from A walks constantly at 4 km/h. The man from B walks at 2 km/h in the first hour, 2.5 km/h in the second, 3 km/h in the third, increasing by 0.5 km/h each hour. Where do they meet?
At the midpoint, 36 km from A
35 km from A
28 km from A
42 km from A
Correct answerA — At the midpoint, 36 km from A
Explanation
In 9 hours, the first man covers 9×4=36 km. The second man's hourly speeds form an arithmetic sequence from 2 to 6 km/h for 9 hours; its total distance is 9(2+6)/2=36 km. Their distances add to 72 km, so they meet after 9 hours exactly at the midpoint, 36 km from A.
MCQ 38Simple Interest
Rajnish invests in schemes P, Q, and R at 10%, 12%, and 15% simple interest. R is 150% of P and 240% of Q. If total annual interest is ₹3200, how much is invested in Q?
₹3050
₹5000
₹8000
₹9000
Correct answerB — ₹5000
Explanation
Let the investment in Q be q. Then R=2.4q and, because R=1.5P, P=1.6q. Annual interest is 0.10(1.6q)+0.12q+0.15(2.4q)=0.64q. Setting 0.64q=3200 gives q=₹5000. The source stem omitted one relationship that was used in its printed solution; it has been restored here.
MCQ 39Pipes And Cisterns
Two pipes fill a cistern in 14 and 16 hours. Because of a leak, when both are opened together the cistern takes 92 minutes longer than it otherwise would. How long would the leak alone take to empty a full cistern?
36 hours
42 hours
48 hours
1008/23 hours
Correct answerD — 1008/23 hours
Explanation
Without leakage, combined rate=1/14+1/16=15/112, so time=112/15 hours=7 h 28 min. Adding 92 min gives an actual filling time of exactly 9 hours, so net rate=1/9. Leak rate=15/112−1/9=(135−112)/1008=23/1008. Therefore leak time=1008/23 hours, about 43.83 hours.
MCQ 40Speed, Time And Distance
A train leaves Manipur at 6:00 am and reaches Dispur at 10:00 am. Another leaves Dispur at 8:00 am and reaches Manipur at 11:30 am. At what time do they cross?
7:56 am
7:56 pm
8:56 am
8:56 pm
Correct answerC — 8:56 am
Explanation
Let the distance be D. The first train's speed is D/4 and by 8:00 am it has covered D/2, leaving D/2 between the trains. The second train's speed is D/3.5=2D/7. Their relative speed is 15D/28, so meeting time after 8:00 is (D/2)/(15D/28)=14/15 hour=56 minutes.
