Q: A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
Solution: Total number of balls = (2 + 3 + 2) = 7. Let S be the sample space. Then, n(S) = Number of ways of drawing 2 balls out of 7 =7C2 = 21 Let E = Event of drawing 2 balls, none of which is blue. n(E) = Number of ways of drawing 2 balls out of (2 + 3) balls =5C2 = 10 Therefore, P(E) = n(E)/n(S) = 10/ 21. The correct answer is: A) 10/21
Q: How many ways can 10 letters be posted in 5 post boxes, if each of the post boxes can take more than 10 letters ?
Solution: Each of the 10 letters can be posted in any of the 5 boxes. So, the first letter has 5 options, so does the second letter and so on and so forth for all of the 10 letters. i.e. 5*5*5*….*5 (upto 10 times) = 5 ^ 10. The correct answer is: A) 5^10
Q: A man invests Rs.5000 for 3 years at 5% p.a. compound interest reckoned yearly. Income tax at the rate of 20% on the interest earned is deducted at the end of each year. Find the amount at the end of the third year
Solution: 5% is the rate of interest. 20% of the interest amount is paid as tax. i.e 80% of the interest amount stays back. if we compute the rate of interest as 80% of 5% = 4% p.a., we will get the same value. The interest accrued for 3 years in compound interest = 3 x simple interest on principal + 3 x interest on simple interest + 1 x interest on interest on interest. = 3 x (200) + 3 x (8) + 1 x 0.32 =600 + 24 + 0.32 = 624.32 The amount at the end of 3 years = 5000 + 624.32 = 5624.32 The correct answer is: A) Rs.5624.32
Q: The base of a parallelogram is twice its height. If the area of the parallelogram is 72 sq. cm, find its height
Solution: Let the height of the parallelogram be x. cm. Then, base = (2x) cm. 2x×x=72=>2x2=72=>x=6 The correct answer is: A) 6
Q: Which of the following has the most number of divisors?
Solution: 99 = 1 x 3 x 3 x 11 101 = 1 x 101 176 = 1 x 2 x 2 x 2 x 2 x 11 182 = 1 x 2 x 7 x 13 So, divisors of 99 are 1, 3, 9, 11, 33, .99 Divisors of 101 are 1 and 101 Divisors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88 and 176 Divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182. Hence, 176 has the most number of divisors. The correct answer is: C) 176
Q: A is twice efficient as B and together they do the same work in as much time as C and D together. If C and D can complete the work in 20 and 30 daysrespectively, working alone ,then in how many days A can complete the work individually:
Solution: A + B = C + D | | | | Ratio of efficiency 10x + 5x 9x + 6x |________| |_________| 15x 15x Therefore , ratio of efficiency of A:C =10:9 Therefore, ratio of days taken by A:C = 9:10 Therefore, number of days taken by A = 18 days The correct answer is: B) 18 days
Q: The population of a town was 3600 three years back. It is 4800 right now. What will be the population three years down the line, if the rate of growth of population has been constant over the years and has been compounding annually?
Solution: The population grew from 3600 to 4800 in 3 years. That is a growth of 1200 on 3600 during three year span. Therefore, the rate of growth for three years has been constant. The rate of growth during the next three years will also be the same. Therefore, the population will grow from 4800 by 4800*13= 1600 Hence, the population three years from now will be 4800 + 1600 = 6400 The correct answer is: B) Rs,6400
Q: Find the length of the longest pole that can be placed in a room 12 m long 8m broad and 9m high.
Solution: Length of longest pole = Length of the diagonal of the room 122+82+92=289 = 17m The correct answer is: D) 17m
Q: A clock is set right at 5 a.m. The clock loses 16 minutes in 24 hours.What will be the true time when the clock indicates 10 p.m. on 4th day?
Solution: Time from 5 am. on a day to 10 pm. on 4th day = 89 hours. Now 23 hrs 44 min. of this clock = 24 hours of correct clock. 356/15 hrs of this clock = 24 hours of correct clock 89 hrs of this clock = (24 x 31556 x 89) hrs of correct clock. = 90 hrs of correct clock. So, the correct time is 11 p.m. The correct answer is: A) 11pm
Q: At what time between 3 and 4 o’clock will the minute hand and the hour hand are on the same straight line but facing opposite directions ?
Solution: On straight line means 180 degree angle.180 = 11/2 min – 30 hrs180 = 11/2 m – 30 × 3180 = 11/2 m – 90(180 + 90) 2 = 11 mm = 540/11 = 49 1/11 minutes. The correct answer is: C) 3:49 1/11
| You Have Score | /10 |