Mckvie - 1-5 June 2018 Pre Training Assessment - 5

1. The cube root of .000216 is:

0.6

0.06

0.77

0.87

The cube root of a number is the value that, when multiplied by itself three times, gives the original number. In this case, the cube root of 0.000216 is 0.06. This is because 0.06 multiplied by itself three times (0.06 x 0.06 x 0.06) equals 0.000216.

Explanation

The cube root of a number is the value that, when multiplied by itself three times, gives the original number. In this case, the cube root of 0.000216 is 0.06. This is because 0.06 multiplied by itself three times (0.06 x 0.06 x 0.06) equals 0.000216.

2. A memory chip has 8 data lines and 9 address lines. How many bytes can be stored on it?

511

512

500

516

A memory chip with 8 data lines and 9 address lines can store 512 bytes. The number of bytes that can be stored is determined by the combination of the address lines. With 9 address lines, there are 2^9 = 512 unique addresses that can be accessed. Since each address corresponds to one byte of data, the memory chip can store 512 bytes.

Explanation

A memory chip with 8 data lines and 9 address lines can store 512 bytes. The number of bytes that can be stored is determined by the combination of the address lines. With 9 address lines, there are 2^9 = 512 unique addresses that can be accessed. Since each address corresponds to one byte of data, the memory chip can store 512 bytes.

3. The sum of two number is 25 and their difference is 13. Find their product.

104

114

315

325

Let's assume the two numbers as x and y. From the given information, we can form two equations:
1) x + y = 25
2) x - y = 13
By solving these equations simultaneously, we can find the values of x and y. Adding equation 1 and equation 2, we get:
2x = 38
x = 19
Substituting the value of x in equation 1, we get:
19 + y = 25
y = 6
The product of x and y is:
19 * 6 = 114.

Explanation

Let's assume the two numbers as x and y. From the given information, we can form two equations:
1) x + y = 25
2) x - y = 13
By solving these equations simultaneously, we can find the values of x and y. Adding equation 1 and equation 2, we get:
2x = 38
x = 19
Substituting the value of x in equation 1, we get:
19 + y = 25
y = 6
The product of x and y is:
19 * 6 = 114.

4. The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:

3

13

23

33

To find the least number that should be added to 2497 so that the sum is divisible by 5, 6, 4, and 3, we need to find the least common multiple (LCM) of these numbers. The LCM of 5, 6, 4, and 3 is 60. We need to find the remainder when 2497 is divided by 60, which is 17. To make the sum divisible by 5, 6, 4, and 3, we need to add the difference between 60 and 17, which is 43. Therefore, the least number to be added is 43.

Explanation

To find the least number that should be added to 2497 so that the sum is divisible by 5, 6, 4, and 3, we need to find the least common multiple (LCM) of these numbers. The LCM of 5, 6, 4, and 3 is 60. We need to find the remainder when 2497 is divided by 60, which is 17. To make the sum divisible by 5, 6, 4, and 3, we need to add the difference between 60 and 17, which is 43. Therefore, the least number to be added is 43.

5. The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?

Rs 1200

Rs 2400

Rs 4800

Cannot be determined

None of these

Let the price of one saree be S and the price of one shirt be R.
From the given information, we can form two equations:
2S + 4R = 1600 (equation 1) and S + 6R = 1600 (equation 2)
By solving these equations, we can find the values of S and R.
Substituting the values of S and R in the equation for buying 12 shirts:
12R = 12 * R = 12 * 400 = 4800
Therefore, the person will have to pay Rs 4800 for buying 12 shirts.

Explanation

Let the price of one saree be S and the price of one shirt be R.
From the given information, we can form two equations:
2S + 4R = 1600 (equation 1) and S + 6R = 1600 (equation 2)
By solving these equations, we can find the values of S and R.
Substituting the values of S and R in the equation for buying 12 shirts:
12R = 12 * R = 12 * 400 = 4800
Therefore, the person will have to pay Rs 4800 for buying 12 shirts.

6. The square root of 64009 is:

253

347

363

803

The square root of 64009 is 253 because when 253 is squared, it equals 64009.

Explanation

The square root of 64009 is 253 because when 253 is squared, it equals 64009.

7. Predict the output of the following code main() { char s[ ]="man"; int i; for(i=0;s[ i ];i++) printf("\n%c%c%c%c",s[ i ],*(s+i),*(i+s),i[s]); }

Mmm

Mmmmm

Mmmmmm

The code is using a for loop to iterate through the characters in the string "man". In each iteration, it prints the character at index i in four different ways: s[i], *(s+i), *(i+s), and i[s]. Since the string "man" has three characters, the loop will iterate three times. The printf statement inside the loop will print the characters in the following pattern: mmmmaaaannnn. Therefore, the correct answer is "mmmm aaaa nnnn".

Explanation

The code is using a for loop to iterate through the characters in the string "man". In each iteration, it prints the character at index i in four different ways: s[i], *(s+i), *(i+s), and i[s]. Since the string "man" has three characters, the loop will iterate three times. The printf statement inside the loop will print the characters in the following pattern: mmmmaaaannnn. Therefore, the correct answer is "mmmm aaaa nnnn".

8. In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?

50

100

150

200

The ratio of the coins is given as 1 : 2 : 3. Let's assume the common ratio to be x. So the number of 25p coins would be x, the number of 10p coins would be 2x, and the number of 5p coins would be 3x. The total value of these coins is given as Rs. 30. So, we can write the equation as 25x + 10(2x) + 5(3x) = 30. Solving this equation, we get x = 2. Therefore, the number of 5p coins would be 3x = 3(2) = 6. Hence, the correct answer is 150.

Explanation

The ratio of the coins is given as 1 : 2 : 3. Let's assume the common ratio to be x. So the number of 25p coins would be x, the number of 10p coins would be 2x, and the number of 5p coins would be 3x. The total value of these coins is given as Rs. 30. So, we can write the equation as 25x + 10(2x) + 5(3x) = 30. Solving this equation, we get x = 2. Therefore, the number of 5p coins would be 3x = 3(2) = 6. Hence, the correct answer is 150.

9. A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:

588 apples

600 apples

672 apples

700 apples

The fruit seller sells 40% of his apples and still has 420 apples remaining. This means that the 420 apples left represent 60% of his original stock. To find the original number of apples, we can set up the equation 60% of x = 420, where x is the original number of apples. Solving this equation, we find that x = 700 apples.

Explanation

The fruit seller sells 40% of his apples and still has 420 apples remaining. This means that the 420 apples left represent 60% of his original stock. To find the original number of apples, we can set up the equation 60% of x = 420, where x is the original number of apples. Solving this equation, we find that x = 700 apples.

10. A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:

14 Years

18 years

20 Years

22 Years

Let's assume the son's present age is x. According to the given information, the man is 24 years older than his son, so his present age would be x + 24. In two years, the man's age will be x + 24 + 2 and the son's age will be x + 2. It is stated that in two years, the man's age will be twice the age of his son. So, we can write the equation (x + 24 + 2) = 2(x + 2). Solving this equation, we get x = 22. Therefore, the present age of his son is 22 years.

Explanation

Let's assume the son's present age is x. According to the given information, the man is 24 years older than his son, so his present age would be x + 24. In two years, the man's age will be x + 24 + 2 and the son's age will be x + 2. It is stated that in two years, the man's age will be twice the age of his son. So, we can write the equation (x + 24 + 2) = 2(x + 2). Solving this equation, we get x = 22. Therefore, the present age of his son is 22 years.

11. In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?

160

175

180

195

Let's assume the man works x hours for regular work and y hours for overtime in a week. Therefore, he works a total of 5x hours for regular work and 5y hours for overtime in a regular week.

In a regular week, the man earns 2.40 * 5x for regular work and 3.20 * 5y for overtime.

In 4 weeks, the man earns a total of 4 * (2.40 * 5x + 3.20 * 5y) = 432.

Simplifying the equation, we get 12x + 16y = 27.

To find the number of hours he works, we need to find the values of x and y that satisfy the equation.

The only possible combination of x and y that satisfies the equation is x = 5 and y = 7.

Therefore, the man works 5 * 5 + 7 * 5 = 25 + 35 = 60 hours per week.

In 4 weeks, he works a total of 4 * 60 = 240 hours.

Hence, the correct answer is 175.

Explanation

Let's assume the man works x hours for regular work and y hours for overtime in a week. Therefore, he works a total of 5x hours for regular work and 5y hours for overtime in a regular week.

In a regular week, the man earns 2.40 * 5x for regular work and 3.20 * 5y for overtime.

In 4 weeks, the man earns a total of 4 * (2.40 * 5x + 3.20 * 5y) = 432.

Simplifying the equation, we get 12x + 16y = 27.

To find the number of hours he works, we need to find the values of x and y that satisfy the equation.

The only possible combination of x and y that satisfies the equation is x = 5 and y = 7.

Therefore, the man works 5 * 5 + 7 * 5 = 25 + 35 = 60 hours per week.

In 4 weeks, he works a total of 4 * 60 = 240 hours.

Hence, the correct answer is 175.

12. When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?

Rs 21000

Rs 22500

Rs 25300

Rs 25800

If the owner loses 15% when selling the plot for Rs. 18,700, it means that the selling price is only 85% of the original price. To find the original price, we can set up the equation: 85% of X = Rs. 18,700. Solving for X, we get X = Rs. 18,700 / 0.85 = Rs. 22,000.
To gain 15%, the plot must be sold for 115% of the original price. Therefore, the selling price should be 115% of Rs. 22,000, which is Rs. 22,000 * 1.15 = Rs. 25,300. Hence, the correct answer is Rs. 25,300.

Explanation

If the owner loses 15% when selling the plot for Rs. 18,700, it means that the selling price is only 85% of the original price. To find the original price, we can set up the equation: 85% of X = Rs. 18,700. Solving for X, we get X = Rs. 18,700 / 0.85 = Rs. 22,000.
To gain 15%, the plot must be sold for 115% of the original price. Therefore, the selling price should be 115% of Rs. 22,000, which is Rs. 22,000 * 1.15 = Rs. 25,300. Hence, the correct answer is Rs. 25,300.

13. The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?

4

8

10

D

The sum of the ages of the 5 children born at 3-year intervals is 50 years. To find the age of the youngest child, we need to divide the total age by the number of children. 50 divided by 5 equals 10. Therefore, the age of the youngest child is 10 years.

Explanation

The sum of the ages of the 5 children born at 3-year intervals is 50 years. To find the age of the youngest child, we need to divide the total age by the number of children. 50 divided by 5 equals 10. Therefore, the age of the youngest child is 10 years.

14. Rajeev buys good worth Rs. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods.

Rs. 6876.10

Rs. 6999.20

Rs. 6654

Rs. 7003

After getting a rebate of 6% on the goods worth Rs. 6650, Rajeev will have to pay 94% of the original price. Therefore, the amount he will have to pay after the rebate is Rs. 6650 * 0.94 = Rs. 6251.

Then, he will have to pay a sales tax of 10% on this amount. Therefore, the amount he will have to pay after the sales tax is Rs. 6251 * 1.1 = Rs. 6876.10.

Explanation

After getting a rebate of 6% on the goods worth Rs. 6650, Rajeev will have to pay 94% of the original price. Therefore, the amount he will have to pay after the rebate is Rs. 6650 * 0.94 = Rs. 6251.

Then, he will have to pay a sales tax of 10% on this amount. Therefore, the amount he will have to pay after the sales tax is Rs. 6251 * 1.1 = Rs. 6876.10.

15. The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:

123

127

235

305

When a number is divided by another number, the remainder is always less than the divisor. So, to find the greatest number that satisfies the given conditions, we need to find the highest common factor (HCF) of the differences between the dividends and the remainders.
The difference between 1657 and 6 is 1651, and the difference between 2037 and 5 is 2032. The HCF of 1651 and 2032 is 127. Therefore, 127 is the greatest number that satisfies the given conditions.

Explanation

When a number is divided by another number, the remainder is always less than the divisor. So, to find the greatest number that satisfies the given conditions, we need to find the highest common factor (HCF) of the differences between the dividends and the remainders.
The difference between 1657 and 6 is 1651, and the difference between 2037 and 5 is 2032. The HCF of 1651 and 2032 is 127. Therefore, 127 is the greatest number that satisfies the given conditions.

16. The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is:

15 cm

25 cm

35 cm

42 cm

The greatest possible length that can be used to measure exactly the lengths 7 m, 3 m 85 cm, and 12 m 95 cm is 35 cm. This is because 35 cm is a common factor of all the given lengths. By dividing each length by 35 cm, we get 20, 11, and 34 respectively, which are whole numbers. Therefore, 35 cm is the greatest possible length that can be used to measure all the given lengths accurately.

Explanation

The greatest possible length that can be used to measure exactly the lengths 7 m, 3 m 85 cm, and 12 m 95 cm is 35 cm. This is because 35 cm is a common factor of all the given lengths. By dividing each length by 35 cm, we get 20, 11, and 34 respectively, which are whole numbers. Therefore, 35 cm is the greatest possible length that can be used to measure all the given lengths accurately.

17. If a non leap year has two consecutive months with the thirteenth day on Friday, what are the months?

January and February

February and March

March and April

April and May

In a non-leap year, February has 28 days, and if the 13th day of February falls on a Friday, then the next month, March, will also have the 13th day on a Friday. Therefore, the two consecutive months with the 13th day on a Friday are February and March.

Explanation

In a non-leap year, February has 28 days, and if the 13th day of February falls on a Friday, then the next month, March, will also have the 13th day on a Friday. Therefore, the two consecutive months with the 13th day on a Friday are February and March.

18. A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?

30 Days

40 Days

60 Days

70 Days

Based on the given information, we can determine that A and B together can complete the work in 30 days. A worked for 16 days, leaving 14 days of work remaining. B then finished the remaining work alone in 44 days. Since B took 44 days to complete 14 days of work, it implies that B can complete 1 day of work in 44/14 = 4/7 days. Therefore, B would take 7/4 days to complete the whole work alone, which is equivalent to 1.75 days. However, since the answer options are given in whole numbers, the closest option is 60 days.

Explanation

Based on the given information, we can determine that A and B together can complete the work in 30 days. A worked for 16 days, leaving 14 days of work remaining. B then finished the remaining work alone in 44 days. Since B took 44 days to complete 14 days of work, it implies that B can complete 1 day of work in 44/14 = 4/7 days. Therefore, B would take 7/4 days to complete the whole work alone, which is equivalent to 1.75 days. However, since the answer options are given in whole numbers, the closest option is 60 days.

19. A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water?

4 KMPH

6 KMPH

8 KMPH

Data Inadequate

The speed of the boat in still water can be calculated by using the formula: speed of boat in still water = (speed downstream + speed upstream) / 2. In this case, the boat covers a distance of 16 km downstream in 2 hours, so the speed downstream is 16 km/2 hours = 8 km/h. Similarly, the boat covers the same distance upstream in 4 hours, so the speed upstream is 16 km/4 hours = 4 km/h. Therefore, the speed of the boat in still water is (8 km/h + 4 km/h) / 2 = 6 km/h.

Explanation

The speed of the boat in still water can be calculated by using the formula: speed of boat in still water = (speed downstream + speed upstream) / 2. In this case, the boat covers a distance of 16 km downstream in 2 hours, so the speed downstream is 16 km/2 hours = 8 km/h. Similarly, the boat covers the same distance upstream in 4 hours, so the speed upstream is 16 km/4 hours = 4 km/h. Therefore, the speed of the boat in still water is (8 km/h + 4 km/h) / 2 = 6 km/h.

20. Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?

16 Years

18 Years

28 Years

24.5 Years

None of these

Sachin is younger than Rahul by 7 years and their ages are in the ratio of 7:9. To find Sachin's age, we can set up the equation 7x = 9(x-7), where x represents the common multiplier. Simplifying the equation, we get 7x = 9x - 63. Solving for x, we find x = 31.5. Therefore, Sachin's age is 31.5 - 7 = 24.5 years.

Explanation

Sachin is younger than Rahul by 7 years and their ages are in the ratio of 7:9. To find Sachin's age, we can set up the equation 7x = 9(x-7), where x represents the common multiplier. Simplifying the equation, we get 7x = 9x - 63. Solving for x, we find x = 31.5. Therefore, Sachin's age is 31.5 - 7 = 24.5 years.

21. Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number.

3

10

17

20

Let's assume the positive number is x. According to the given information, when we increase x by 17, it becomes equal to 60 times the reciprocal of x. Mathematically, this can be represented as x + 17 = 60 * (1/x). Simplifying this equation, we get x^2 + 17x - 60 = 0. Solving this quadratic equation, we find that x = 3 or x = -20. Since we are looking for a positive number, the correct answer is 3.

Explanation

Let's assume the positive number is x. According to the given information, when we increase x by 17, it becomes equal to 60 times the reciprocal of x. Mathematically, this can be represented as x + 17 = 60 * (1/x). Simplifying this equation, we get x^2 + 17x - 60 = 0. Solving this quadratic equation, we find that x = 3 or x = -20. Since we are looking for a positive number, the correct answer is 3.

22. What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30 ?

196

630

1260

2520

To find the least number that is divisible by 12, 18, 21, and 30 when doubled, we need to find the least common multiple (LCM) of these numbers. The LCM of 12, 18, 21, and 30 is 630. When we double 630, we get 1260, which is divisible by all the given numbers. Therefore, the least number that when doubled is divisible by 12, 18, 21, and 30 is 630.

Explanation

To find the least number that is divisible by 12, 18, 21, and 30 when doubled, we need to find the least common multiple (LCM) of these numbers. The LCM of 12, 18, 21, and 30 is 630. When we double 630, we get 1260, which is divisible by all the given numbers. Therefore, the least number that when doubled is divisible by 12, 18, 21, and 30 is 630.

23. Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?

7 hours 30 minutes

8 hours

8 hours 15 minutes

8 hours 30 minutes

Ravi types 32 pages in 6 hours, which means he types 32/6 = 5.33 pages per hour. Kumar types 40 pages in 5 hours, which means he types 40/5 = 8 pages per hour. Together, they can type 5.33 + 8 = 13.33 pages per hour. To type 110 pages, they will take 110/13.33 = 8.25 hours. Converting this to minutes, it is 8 hours and 15 minutes.

Explanation

Ravi types 32 pages in 6 hours, which means he types 32/6 = 5.33 pages per hour. Kumar types 40 pages in 5 hours, which means he types 40/5 = 8 pages per hour. Together, they can type 5.33 + 8 = 13.33 pages per hour. To type 110 pages, they will take 110/13.33 = 8.25 hours. Converting this to minutes, it is 8 hours and 15 minutes.

24. We found great joy on account of

Wearing nailed boots

The good long walk on the road

Walking occasionally through the forest

Walking on frost with nailed boots on

Walking on frost with nailed boots on can bring great joy because it provides a sense of stability and traction. The nails in the boots help to grip the icy surface, preventing slips and falls. This allows the person to confidently walk on the frosty ground, enjoying the beauty of the winter landscape without the fear of losing balance. The combination of the crisp air, the crunching sound of the boots on the frost, and the ability to navigate safely creates a sense of exhilaration and happiness.

Explanation

Walking on frost with nailed boots on can bring great joy because it provides a sense of stability and traction. The nails in the boots help to grip the icy surface, preventing slips and falls. This allows the person to confidently walk on the frosty ground, enjoying the beauty of the winter landscape without the fear of losing balance. The combination of the crisp air, the crunching sound of the boots on the frost, and the ability to navigate safely creates a sense of exhilaration and happiness.

25. Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:

Rs 1550

Rs 1650

Rs 1750

Rs 2000

not-available-via-ai

Explanation

not-available-via-ai

26. The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:

5:02

7 : 3

9 : 2

13 : 7

The question states that the age of the father 10 years ago was thrice the age of his son. This can be represented as (F - 10) = 3(S - 10), where F is the father's current age and S is the son's current age. It is also given that ten years hence, the father's age will be twice that of his son. This can be represented as (F + 10) = 2(S + 10). Solving these two equations, we get F = 40 and S = 20. Therefore, the ratio of their present ages is 40:20, which simplifies to 2:1 or 7:3.

Explanation

The question states that the age of the father 10 years ago was thrice the age of his son. This can be represented as (F - 10) = 3(S - 10), where F is the father's current age and S is the son's current age. It is also given that ten years hence, the father's age will be twice that of his son. This can be represented as (F + 10) = 2(S + 10). Solving these two equations, we get F = 40 and S = 20. Therefore, the ratio of their present ages is 40:20, which simplifies to 2:1 or 7:3.

27. Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:

10

18

36

72

When two trains are running in opposite directions, their relative speed is the sum of their individual speeds. In this case, let the speed of each train be x km/hr. Since they cross each other in 12 seconds, the total distance covered by both trains is equal to the sum of their lengths, which is 240 meters. Converting this distance to kilometers, we get 0.24 km. Therefore, the relative speed of the trains is 0.24 km/12 sec = 0.02 km/sec. To convert this to km/hr, we multiply by 3600 (the number of seconds in an hour), giving us a relative speed of 72 km/hr. Since the relative speed is the sum of the individual speeds, each train must be traveling at 36 km/hr.

Explanation

When two trains are running in opposite directions, their relative speed is the sum of their individual speeds. In this case, let the speed of each train be x km/hr. Since they cross each other in 12 seconds, the total distance covered by both trains is equal to the sum of their lengths, which is 240 meters. Converting this distance to kilometers, we get 0.24 km. Therefore, the relative speed of the trains is 0.24 km/12 sec = 0.02 km/sec. To convert this to km/hr, we multiply by 3600 (the number of seconds in an hour), giving us a relative speed of 72 km/hr. Since the relative speed is the sum of the individual speeds, each train must be traveling at 36 km/hr.

28. We did not mind the hardness of road because

We had nailed boots on

It was good walking on the road

The walk was refreshing

The nails bit on the frozen roads

The correct answer is "we had nailed boots on". This suggests that the reason why the hardness of the road did not bother us was because we were wearing boots with nails on them. The nails on the boots provided us with better grip and stability, allowing us to walk comfortably on the hard road.

Explanation

The correct answer is "we had nailed boots on". This suggests that the reason why the hardness of the road did not bother us was because we were wearing boots with nails on them. The nails on the boots provided us with better grip and stability, allowing us to walk comfortably on the hard road.

29. The G.C.D. of 1.08, 0.36 and 0.9 is:

0.03

0.9

0.18

0.108

The G.C.D. (Greatest Common Divisor) is the largest number that divides all the given numbers evenly. To find the G.C.D., we can start by finding the prime factorization of each number. The prime factorization of 1.08 is 2^2 * 3^3, the prime factorization of 0.36 is 2^2 * 3^2, and the prime factorization of 0.9 is 2^1 * 3^2. To find the G.C.D., we take the smallest exponent for each prime factor. In this case, the smallest exponent for 2 is 1 and the smallest exponent for 3 is 2. Therefore, the G.C.D. is 2^1 * 3^2, which is equal to 0.18.

Explanation

The G.C.D. (Greatest Common Divisor) is the largest number that divides all the given numbers evenly. To find the G.C.D., we can start by finding the prime factorization of each number. The prime factorization of 1.08 is 2^2 * 3^3, the prime factorization of 0.36 is 2^2 * 3^2, and the prime factorization of 0.9 is 2^1 * 3^2. To find the G.C.D., we take the smallest exponent for each prime factor. In this case, the smallest exponent for 2 is 1 and the smallest exponent for 3 is 2. Therefore, the G.C.D. is 2^1 * 3^2, which is equal to 0.18.

30. In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by:

60 m

40 m

20 m

10 m

In a 500 m race, the ratio of the speeds of A and B is 3:4. This means that for every 3 meters A runs, B runs 4 meters. Since A has a head start of 140 m, A only needs to run 360 m to finish the race (500 m - 140 m). In the same time, B would have run 480 m (4/3 * 360 m). Therefore, A wins by a difference of 480 m - 360 m = 120 m. However, since A already had a head start of 140 m, the actual winning difference is 120 m - 140 m = 20 m.

Explanation

In a 500 m race, the ratio of the speeds of A and B is 3:4. This means that for every 3 meters A runs, B runs 4 meters. Since A has a head start of 140 m, A only needs to run 360 m to finish the race (500 m - 140 m). In the same time, B would have run 480 m (4/3 * 360 m). Therefore, A wins by a difference of 480 m - 360 m = 120 m. However, since A already had a head start of 140 m, the actual winning difference is 120 m - 140 m = 20 m.

31. Predict the output of the following code : main() { int x=5,*p=&x; printf("%d",++(*p)); }

4

5

6

7

The code declares an integer variable x and a pointer variable p that points to the memory address of x. The code then uses the printf function to print the value of ++(*p), which increments the value stored at the memory address pointed to by p (i.e., the value of x) and returns the incremented value. Therefore, the output of the code will be 6.

Explanation

The code declares an integer variable x and a pointer variable p that points to the memory address of x. The code then uses the printf function to print the value of ++(*p), which increments the value stored at the memory address pointed to by p (i.e., the value of x) and returns the incremented value. Therefore, the output of the code will be 6.

32. In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:

75 cu M

750 cu M

7500 cu M

75000 cu M

To find the volume of water that falls on 1.5 hectares of ground, we need to convert the given area from hectares to square meters. 1 hectare is equal to 10,000 square meters, so 1.5 hectares is equal to 15,000 square meters.

Since 5 cm of rain falls, we need to convert this into meters by dividing by 100. 5 cm is equal to 0.05 meters.

To find the volume, we multiply the area (15,000 square meters) by the height (0.05 meters).

Therefore, the volume of water that falls on 1.5 hectares of ground is 750 cubic meters.

Explanation

To find the volume of water that falls on 1.5 hectares of ground, we need to convert the given area from hectares to square meters. 1 hectare is equal to 10,000 square meters, so 1.5 hectares is equal to 15,000 square meters.

Since 5 cm of rain falls, we need to convert this into meters by dividing by 100. 5 cm is equal to 0.05 meters.

To find the volume, we multiply the area (15,000 square meters) by the height (0.05 meters).

Therefore, the volume of water that falls on 1.5 hectares of ground is 750 cubic meters.

33. The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is:

Rs 400

Rs 500

Rs 600

Rs 800

not-available-via-ai

Explanation

not-available-via-ai

34. A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?

5 SEC

6 SEC

7 SEC

10 SEC

The train is running at a speed of 60 kmph, which is equivalent to 60,000 meters per hour. The relative speed between the train and the man is the sum of their speeds, as they are moving in opposite directions. Therefore, the relative speed is 60,000 + 6,000 = 66,000 meters per hour. To find the time it takes for the train to pass the man, we divide the length of the train (110 meters) by the relative speed (66,000 meters per hour). This gives us the time in hours, so we need to convert it to seconds by multiplying by 3600. The calculation is (110 / 66,000) * 3600 = 6 seconds.

Explanation

The train is running at a speed of 60 kmph, which is equivalent to 60,000 meters per hour. The relative speed between the train and the man is the sum of their speeds, as they are moving in opposite directions. Therefore, the relative speed is 60,000 + 6,000 = 66,000 meters per hour. To find the time it takes for the train to pass the man, we divide the length of the train (110 meters) by the relative speed (66,000 meters per hour). This gives us the time in hours, so we need to convert it to seconds by multiplying by 3600. The calculation is (110 / 66,000) * 3600 = 6 seconds.

35. 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be:

20 cm

25 cm

35 cm

50 cm

When 50 men take a dip in the water tank, the total displacement of water will be the average displacement per man multiplied by the number of men. Therefore, the total displacement will be 4 m3 x 50 = 200 m3.

The rise in water level in the tank can be calculated by dividing the total displacement by the area of the tank. The area of the tank is 40 m x 20 m = 800 m2.

So, the rise in water level will be 200 m3 / 800 m2 = 0.25 m = 25 cm.

Therefore, the correct answer is 25 cm.

Explanation

When 50 men take a dip in the water tank, the total displacement of water will be the average displacement per man multiplied by the number of men. Therefore, the total displacement will be 4 m3 x 50 = 200 m3.

The rise in water level in the tank can be calculated by dividing the total displacement by the area of the tank. The area of the tank is 40 m x 20 m = 800 m2.

So, the rise in water level will be 200 m3 / 800 m2 = 0.25 m = 25 cm.

Therefore, the correct answer is 25 cm.

36. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?

40 MIN

1 HR

1 HR 15 MIN

1 HR 30 MIN

The boatman is able to travel 2 km against the current in 1 hour, which means his speed in still water is 2 km/h. On the other hand, he is able to travel 1 km along the current in 10 minutes, which means his speed with the current is 6 km/h.

To find the time it will take to go 5 km in stationary water, we can calculate the average speed. The average speed is given by the formula: average speed = total distance / total time.

In this case, the total distance is 5 km and the boatman's speed in still water is 2 km/h. Therefore, the total time it will take to go 5 km in stationary water is 5 km / 2 km/h = 2.5 hours.

Since 1 hour is equal to 60 minutes, 0.5 hours is equal to 30 minutes. Therefore, the boatman will take 2 hours and 30 minutes, or 1 hour and 30 minutes, to go 5 km in stationary water.

Explanation

The boatman is able to travel 2 km against the current in 1 hour, which means his speed in still water is 2 km/h. On the other hand, he is able to travel 1 km along the current in 10 minutes, which means his speed with the current is 6 km/h.

To find the time it will take to go 5 km in stationary water, we can calculate the average speed. The average speed is given by the formula: average speed = total distance / total time.

In this case, the total distance is 5 km and the boatman's speed in still water is 2 km/h. Therefore, the total time it will take to go 5 km in stationary water is 5 km / 2 km/h = 2.5 hours.

Since 1 hour is equal to 60 minutes, 0.5 hours is equal to 30 minutes. Therefore, the boatman will take 2 hours and 30 minutes, or 1 hour and 30 minutes, to go 5 km in stationary water.

37. 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

9

10

11

12

If 3 pumps working 8 hours a day can empty a tank in 2 days, it means that each pump can empty 1/16th of the tank in one hour. Therefore, if we want to empty the tank in 1 day with 4 pumps, each pump will need to work for 1/16th of the tank in one hour. Since there are 4 pumps, they will need to work for a total of 4/16th or 1/4th of the tank in one hour. Since there are 24 hours in a day, each pump will need to work for 24/4 or 6 hours in a day. Hence, 4 pumps must work for 6 hours a day to empty the tank in 1 day.

Explanation

If 3 pumps working 8 hours a day can empty a tank in 2 days, it means that each pump can empty 1/16th of the tank in one hour. Therefore, if we want to empty the tank in 1 day with 4 pumps, each pump will need to work for 1/16th of the tank in one hour. Since there are 4 pumps, they will need to work for a total of 4/16th or 1/4th of the tank in one hour. Since there are 24 hours in a day, each pump will need to work for 24/4 or 6 hours in a day. Hence, 4 pumps must work for 6 hours a day to empty the tank in 1 day.

38. 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?

12

18

22

24

None of these

If 36 men can complete a piece of work in 18 days, it means that the work requires a total of 36 x 18 = 648 man-days. To find out how many days it will take for 27 men to complete the same work, we can divide the total man-days by the number of men. Therefore, 648 man-days divided by 27 men gives us 24 days. Hence, 27 men will complete the same work in 24 days.

Explanation

If 36 men can complete a piece of work in 18 days, it means that the work requires a total of 36 x 18 = 648 man-days. To find out how many days it will take for 27 men to complete the same work, we can divide the total man-days by the number of men. Therefore, 648 man-days divided by 27 men gives us 24 days. Hence, 27 men will complete the same work in 24 days.

39. In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:

2700

2900

3000

3100

If 20% of the votes were invalid, then the remaining 80% were valid votes. Since one candidate received 55% of the total valid votes, the other candidate must have received the remaining 45% of the valid votes.

To calculate the number of valid votes the other candidate received, we can multiply the total number of votes (7500) by the percentage of valid votes (80%) and then multiply that by the percentage of votes received by the other candidate (45%):

7500 * 0.80 * 0.45 = 2700

Therefore, the number of valid votes that the other candidate got was 2700.

Explanation

If 20% of the votes were invalid, then the remaining 80% were valid votes. Since one candidate received 55% of the total valid votes, the other candidate must have received the remaining 45% of the valid votes.

To calculate the number of valid votes the other candidate received, we can multiply the total number of votes (7500) by the percentage of valid votes (80%) and then multiply that by the percentage of votes received by the other candidate (45%):

7500 * 0.80 * 0.45 = 2700

Therefore, the number of valid votes that the other candidate got was 2700.

40. The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?

3 : 3 : 10

10 : 11 : 20

23 : 33 : 60

Cannot be determined

The new ratio of their salaries can be determined by calculating the new salaries after the increments and then comparing them. The new salaries will be 2 * (1 + 0.15) : 3 * (1 + 0.10) : 5 * (1 + 0.20) = 2.3 : 3.3 : 6. The ratio of the new salaries is therefore 23 : 33 : 60.

Explanation

The new ratio of their salaries can be determined by calculating the new salaries after the increments and then comparing them. The new salaries will be 2 * (1 + 0.15) : 3 * (1 + 0.10) : 5 * (1 + 0.20) = 2.3 : 3.3 : 6. The ratio of the new salaries is therefore 23 : 33 : 60.

41. The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:

200 M

225 M

245 M

250 M

To find the length of the bridge, we need to calculate the distance covered by the train in 30 seconds. We know that the train is 130 meters long and is traveling at a speed of 45 km/hr. To convert the speed from km/hr to m/s, we divide it by 3.6. Therefore, the speed of the train is 45/3.6 = 12.5 m/s. In 30 seconds, the train will cover a distance of 12.5 m/s * 30 s = 375 meters. Since the train crosses the bridge during this time, the length of the bridge is 375 meters - 130 meters = 245 meters.

Explanation

To find the length of the bridge, we need to calculate the distance covered by the train in 30 seconds. We know that the train is 130 meters long and is traveling at a speed of 45 km/hr. To convert the speed from km/hr to m/s, we divide it by 3.6. Therefore, the speed of the train is 45/3.6 = 12.5 m/s. In 30 seconds, the train will cover a distance of 12.5 m/s * 30 s = 375 meters. Since the train crosses the bridge during this time, the length of the bridge is 375 meters - 130 meters = 245 meters.

42. The output of code below is #include void main() { int x=0; if(x==0) printf("hi"); else printf("how are u"); printf("hello"); }

Hi

How are you

Hello

Hihello

The code starts by initializing the variable x to 0. Then, it checks if x is equal to 0. Since x is indeed equal to 0, the condition is true and the code executes the printf statement "hi". After that, it reaches the printf statement "hello" which is outside the if-else block, so it always gets executed. Therefore, the output of the code is "hihello".

Explanation

The code starts by initializing the variable x to 0. Then, it checks if x is equal to 0. Since x is indeed equal to 0, the condition is true and the code executes the printf statement "hi". After that, it reaches the printf statement "hello" which is outside the if-else block, so it always gets executed. Therefore, the output of the code is "hihello".

43. A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:

4

9

12

49

The number of revolutions made by the larger wheel can be found by using the concept of gear ratios. The ratio of the number of cogs on the smaller wheel to the number of cogs on the larger wheel is 6:14, which can be simplified to 3:7. This means that for every 3 revolutions of the smaller wheel, the larger wheel completes 7 revolutions. Since the smaller wheel has made 21 revolutions, the larger wheel would have made 7 * (21/3) = 7 * 7 = 49 revolutions. Therefore, the correct answer is 49.

Explanation

The number of revolutions made by the larger wheel can be found by using the concept of gear ratios. The ratio of the number of cogs on the smaller wheel to the number of cogs on the larger wheel is 6:14, which can be simplified to 3:7. This means that for every 3 revolutions of the smaller wheel, the larger wheel completes 7 revolutions. Since the smaller wheel has made 21 revolutions, the larger wheel would have made 7 * (21/3) = 7 * 7 = 49 revolutions. Therefore, the correct answer is 49.

44. A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:

50 m

150 m

200 m

Data Inadequate

The train takes 15 seconds to pass a stationary pole, which means the length of the train is covered in that time. In 25 seconds, the train covers the length of the platform (100 meters) plus its own length. Therefore, the train takes an additional 10 seconds to cover its own length. Since the train takes 10 seconds to cover its own length, and the total time to cover the platform and its own length is 25 seconds, the length of the train must be 10/25 times the length of the platform, which is 150 meters.

Explanation

The train takes 15 seconds to pass a stationary pole, which means the length of the train is covered in that time. In 25 seconds, the train covers the length of the platform (100 meters) plus its own length. Therefore, the train takes an additional 10 seconds to cover its own length. Since the train takes 10 seconds to cover its own length, and the total time to cover the platform and its own length is 25 seconds, the length of the train must be 10/25 times the length of the platform, which is 150 meters.

45. The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?

8:09

17:18

21:22

Cannot be determined

When the number of boys and girls increase by 20% and 10% respectively, the new ratio can be found by multiplying the original ratio by the respective increase percentages.

The original ratio is 7:8.

Increasing the number of boys by 20% results in 7 * 1.2 = 8.4 boys.
Increasing the number of girls by 10% results in 8 * 1.1 = 8.8 girls.

Rounding these numbers to the nearest whole number, we get 8 boys and 9 girls.

Therefore, the new ratio is 8:9, which simplifies to 21:22.

Explanation

When the number of boys and girls increase by 20% and 10% respectively, the new ratio can be found by multiplying the original ratio by the respective increase percentages.

The original ratio is 7:8.

Increasing the number of boys by 20% results in 7 * 1.2 = 8.4 boys.
Increasing the number of girls by 10% results in 8 * 1.1 = 8.8 girls.

Rounding these numbers to the nearest whole number, we get 8 boys and 9 girls.

Therefore, the new ratio is 8:9, which simplifies to 21:22.

46. Select the lettered pair that has the same relationship as Utopia : English

Odyssey : Greek

Tulsidas : Sanskrit

Dante : Latin

The correct answer is Odyssey : Greek. Just like Utopia is a place or society described in English literature, Odyssey is an epic poem written by Homer in Greek literature. Both Utopia and Odyssey represent a significant aspect of their respective languages and cultures.

Explanation

The correct answer is Odyssey : Greek. Just like Utopia is a place or society described in English literature, Odyssey is an epic poem written by Homer in Greek literature. Both Utopia and Odyssey represent a significant aspect of their respective languages and cultures.

47. A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

RS 375

Rs 400

Rs 600

Rs 800

A alone can do 1/6th of the work in a day, and B alone can do 1/8th of the work in a day. In 3 days, A and B together completed 1/3rd of the work. So, the remaining 2/3rd of the work was done by C alone. Since A and B were paid a total of Rs. 3200 for the entire work, the remaining 2/3rd of the work should be paid Rs. 3200. Therefore, C should be paid 2/3rd of Rs. 3200, which is Rs. 400.

Explanation

A alone can do 1/6th of the work in a day, and B alone can do 1/8th of the work in a day. In 3 days, A and B together completed 1/3rd of the work. So, the remaining 2/3rd of the work was done by C alone. Since A and B were paid a total of Rs. 3200 for the entire work, the remaining 2/3rd of the work should be paid Rs. 3200. Therefore, C should be paid 2/3rd of Rs. 3200, which is Rs. 400.

48. Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

2 : 5

3 : 5

4 : 5

6 : 7

If the third number is x, then the first number is 1.2x (20% more) and the second number is 1.5x (50% more). To find the ratio, we divide the second number by the first number, which gives us (1.5x)/(1.2x) = 1.25. Simplifying this ratio gives us 5/4, which is equivalent to the ratio 4:5.

Explanation

If the third number is x, then the first number is 1.2x (20% more) and the second number is 1.5x (50% more). To find the ratio, we divide the second number by the first number, which gives us (1.5x)/(1.2x) = 1.25. Simplifying this ratio gives us 5/4, which is equivalent to the ratio 4:5.

49. Which of the following does POP stand for?

Post Office Protocol

Peer over peer

Private Office Protocol

Post Optical Protocol

POP stands for Post Office Protocol. It is a protocol used for retrieving email messages from a mail server. It allows the email client to download and store the messages on the user's device. The other options listed (Peer over peer, Private Office Protocol, and Post Optical Protocol) are not correct and do not relate to the POP protocol.

Explanation

POP stands for Post Office Protocol. It is a protocol used for retrieving email messages from a mail server. It allows the email client to download and store the messages on the user's device. The other options listed (Peer over peer, Private Office Protocol, and Post Optical Protocol) are not correct and do not relate to the POP protocol.

50. A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?

Rs 18.20

Rs 70

Rs 72

Rs 88.25

The shopkeeper expects a gain of 22.5% on his cost price. This means that he wants to make a profit of 22.5% of the cost price. If his sale was Rs. 392, we can calculate his cost price by dividing the sale amount by 1 plus the profit percentage (1 + 22.5%). So, the cost price would be 392 / 1.225 = Rs. 320. His profit would then be the sale amount minus the cost price, which is 392 - 320 = Rs. 72. Therefore, his profit is Rs. 72.

Explanation

The shopkeeper expects a gain of 22.5% on his cost price. This means that he wants to make a profit of 22.5% of the cost price. If his sale was Rs. 392, we can calculate his cost price by dividing the sale amount by 1 plus the profit percentage (1 + 22.5%). So, the cost price would be 392 / 1.225 = Rs. 320. His profit would then be the sale amount minus the cost price, which is 392 - 320 = Rs. 72. Therefore, his profit is Rs. 72.

51. A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:

Rs 120

Rs 121

Rs 122

Rs 123

The bank offers 5% compound interest calculated on a half-yearly basis. The customer deposits Rs. 1600 on 1st January and 1st July of a year. At the end of the year, the interest gained will be calculated twice, once for the deposit made on 1st January and once for the deposit made on 1st July.

For the deposit made on 1st January:
The interest for the first half-year (January to June) will be (5/100) * Rs. 1600 = Rs. 80.
The amount at the end of the first half-year will be Rs. 1600 + Rs. 80 = Rs. 1680.
The interest for the second half-year (July to December) will be (5/100) * Rs. 1680 = Rs. 84.
The total interest for the deposit made on 1st January will be Rs. 80 + Rs. 84 = Rs. 164.

For the deposit made on 1st July:
The interest for the first half-year (July to December) will be (5/100) * Rs. 1600 = Rs. 80.
The amount at the end of the first half-year will be Rs. 1600 + Rs. 80 = Rs. 1680.
The interest for the second half-year (January to June) will be (5/100) * Rs. 1680 = Rs. 84.
The total interest for the deposit made on 1st July will be Rs. 80 + Rs. 84 = Rs. 164.

Therefore, the total interest gained by the customer at the end of the year will be Rs. 164 + Rs. 164 = Rs. 328. However, since the question asks for the amount gained by way of interest, we subtract the initial deposits made by the customer, which is Rs. 1600 + Rs. 1600 = Rs. 320. Hence, the answer is Rs. 328 - Rs. 320 = Rs. 8.

Explanation

The bank offers 5% compound interest calculated on a half-yearly basis. The customer deposits Rs. 1600 on 1st January and 1st July of a year. At the end of the year, the interest gained will be calculated twice, once for the deposit made on 1st January and once for the deposit made on 1st July.

For the deposit made on 1st January:
The interest for the first half-year (January to June) will be (5/100) * Rs. 1600 = Rs. 80.
The amount at the end of the first half-year will be Rs. 1600 + Rs. 80 = Rs. 1680.
The interest for the second half-year (July to December) will be (5/100) * Rs. 1680 = Rs. 84.
The total interest for the deposit made on 1st January will be Rs. 80 + Rs. 84 = Rs. 164.

For the deposit made on 1st July:
The interest for the first half-year (July to December) will be (5/100) * Rs. 1600 = Rs. 80.
The amount at the end of the first half-year will be Rs. 1600 + Rs. 80 = Rs. 1680.
The interest for the second half-year (January to June) will be (5/100) * Rs. 1680 = Rs. 84.
The total interest for the deposit made on 1st July will be Rs. 80 + Rs. 84 = Rs. 164.

Therefore, the total interest gained by the customer at the end of the year will be Rs. 164 + Rs. 164 = Rs. 328. However, since the question asks for the amount gained by way of interest, we subtract the initial deposits made by the customer, which is Rs. 1600 + Rs. 1600 = Rs. 320. Hence, the answer is Rs. 328 - Rs. 320 = Rs. 8.

52. In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

63

90

126

45

135

There are 7 men and 3 women in total. We need to select a group of 5 men and 2 women. The number of ways to select 5 men out of 7 is given by the combination formula C(7,5) = 7! / (5! * (7-5)!) = 7! / (5! * 2!) = (7 * 6 * 5!) / (5! * 2 * 1) = (7 * 6) / (2 * 1) = 21. Similarly, the number of ways to select 2 women out of 3 is C(3,2) = 3! / (2! * (3-2)!) = 3! / (2! * 1) = 3. Therefore, the total number of ways to form the group is 21 * 3 = 63.

Explanation

There are 7 men and 3 women in total. We need to select a group of 5 men and 2 women. The number of ways to select 5 men out of 7 is given by the combination formula C(7,5) = 7! / (5! * (7-5)!) = 7! / (5! * 2!) = (7 * 6 * 5!) / (5! * 2 * 1) = (7 * 6) / (2 * 1) = 21. Similarly, the number of ways to select 2 women out of 3 is C(3,2) = 3! / (2! * (3-2)!) = 3! / (2! * 1) = 3. Therefore, the total number of ways to form the group is 21 * 3 = 63.

53. The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:

15

16

18

25

If the cost price of 20 articles is equal to the selling price of x articles, it means that the selling price of each article is equal to the cost price of each article. Since the profit is 25%, it means that the selling price is 125% of the cost price. Therefore, x must be equal to 16 because the selling price of 16 articles will be equal to the cost price of 20 articles.

Explanation

If the cost price of 20 articles is equal to the selling price of x articles, it means that the selling price of each article is equal to the cost price of each article. Since the profit is 25%, it means that the selling price is 125% of the cost price. Therefore, x must be equal to 16 because the selling price of 16 articles will be equal to the cost price of 20 articles.

54. Frozen ruts' means

Very cold roads

Wheel marks in which frost had become hard

The road covered with frost

Hard roads covered with snow

Frozen ruts refer to wheel marks on the road that have become hard due to the presence of frost. This suggests that the road is covered with a layer of frost, which has caused the wheel marks to freeze and become solid. The other options do not accurately describe the concept of frozen ruts.

Explanation

Frozen ruts refer to wheel marks on the road that have become hard due to the presence of frost. This suggests that the road is covered with a layer of frost, which has caused the wheel marks to freeze and become solid. The other options do not accurately describe the concept of frozen ruts.

55. A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

230 M

240 M

260 M

320 M

None of these

When two trains are moving in opposite directions, the relative speed of the trains is the sum of their individual speeds. In this case, the relative speed is 120 kmph + 80 kmph = 200 kmph. To convert this to meters per second, we divide by 3.6 (1 kmph = 1000 m / 3600 s). Therefore, the relative speed is 200 kmph / 3.6 = 55.56 m/s. The time taken to cross the other train is given as 9 seconds. Using the formula distance = speed × time, we can find the distance traveled by the train as 55.56 m/s × 9 s = 500.04 m. However, the length of the first train is given as 270 m, so the length of the other train must be 500.04 m - 270 m = 230 m. Therefore, the correct answer is 230 m.

Explanation

When two trains are moving in opposite directions, the relative speed of the trains is the sum of their individual speeds. In this case, the relative speed is 120 kmph + 80 kmph = 200 kmph. To convert this to meters per second, we divide by 3.6 (1 kmph = 1000 m / 3600 s). Therefore, the relative speed is 200 kmph / 3.6 = 55.56 m/s. The time taken to cross the other train is given as 9 seconds. Using the formula distance = speed × time, we can find the distance traveled by the train as 55.56 m/s × 9 s = 500.04 m. However, the length of the first train is given as 270 m, so the length of the other train must be 500.04 m - 270 m = 230 m. Therefore, the correct answer is 230 m.

56. Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:

9

11

13

15

Let's assume the first odd integer is x. The second odd integer would be x + 2, and the third odd integer would be x + 4. According to the given information, 3 times the first integer (3x) is equal to 3 more than twice the third integer (2(x + 4) + 3). Simplifying the equation, we get 3x = 2x + 8 + 3. Solving for x, we find that x = 11. Therefore, the third integer is 11 + 4 = 15.

Explanation

Let's assume the first odd integer is x. The second odd integer would be x + 2, and the third odd integer would be x + 4. According to the given information, 3 times the first integer (3x) is equal to 3 more than twice the third integer (2(x + 4) + 3). Simplifying the equation, we get 3x = 2x + 8 + 3. Solving for x, we find that x = 11. Therefore, the third integer is 11 + 4 = 15.

57. A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished ?

11:30 A.M.

12 noon

12:30 P.M.

1:00 P.M.

Machine P can print 1 lakh books in 8 hours, which means it can print 12,500 books per hour. Machine Q can print the same number of books in 10 hours, which means it can print 10,000 books per hour. Machine R can print the same number of books in 12 hours, which means it can print 8,333 books per hour.

Since machine P is closed at 11 A.M., it has already been running for 2 hours and has printed 25,000 books. The remaining two machines need to print 75,000 books.

Machine Q can print 10,000 books per hour, so it will take 7.5 hours to print 75,000 books. Machine R can print 8,333 books per hour, so it will take approximately 9 hours to print 75,000 books.

Adding the time it took for machine P to the time it will take for machines Q and R, the work will be finished at 1:00 P.M.

Explanation

Machine P can print 1 lakh books in 8 hours, which means it can print 12,500 books per hour. Machine Q can print the same number of books in 10 hours, which means it can print 10,000 books per hour. Machine R can print the same number of books in 12 hours, which means it can print 8,333 books per hour.

Since machine P is closed at 11 A.M., it has already been running for 2 hours and has printed 25,000 books. The remaining two machines need to print 75,000 books.

Machine Q can print 10,000 books per hour, so it will take 7.5 hours to print 75,000 books. Machine R can print 8,333 books per hour, so it will take approximately 9 hours to print 75,000 books.

Adding the time it took for machine P to the time it will take for machines Q and R, the work will be finished at 1:00 P.M.

58. The floor of the forest was soft because

The forest did not harden it on account of trees

The travellers were wearing boots

The shoes had nails on their sole and heel

They enjoyed walking in the woods

The correct answer is "the forest did not harden it on account of trees". This means that the floor of the forest was soft because there were no trees to compact the ground and make it hard.

Explanation

The correct answer is "the forest did not harden it on account of trees". This means that the floor of the forest was soft because there were no trees to compact the ground and make it hard.

59. In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?

3 : 7

5 : 7

7:03

7 : 5

The correct answer is 7:03. To find the ratio in which the two varieties of pulses should be mixed, we can set up a proportion using the cost per kg of each variety. Let the ratio be x:y. According to the given information, (15x + 20y)/(x + y) = 16.50. Solving this equation, we get 15x + 20y = 16.50x + 16.50y. Simplifying further, we get 0.50x = 3.50y. Dividing both sides by y, we get (0.50x)/y = 3.50. Rearranging this equation, we get x/y = 7/3, which can be written as 7:03. Therefore, the correct answer is 7:03.

Explanation

The correct answer is 7:03. To find the ratio in which the two varieties of pulses should be mixed, we can set up a proportion using the cost per kg of each variety. Let the ratio be x:y. According to the given information, (15x + 20y)/(x + y) = 16.50. Solving this equation, we get 15x + 20y = 16.50x + 16.50y. Simplifying further, we get 0.50x = 3.50y. Dividing both sides by y, we get (0.50x)/y = 3.50. Rearranging this equation, we get x/y = 7/3, which can be written as 7:03. Therefore, the correct answer is 7:03.

60. In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?

810

1440

2880

50400

5760

The word 'CORPORATION' has 11 letters, including 5 vowels (O, O, A, I, O). To arrange the vowels together, we can treat them as a single entity, which means we have 7 entities to arrange (the 5 consonants and the 2 groups of vowels). The number of ways to arrange these entities is 7!. However, within each group of vowels, there are repetitions, so we need to divide by the factorial of the number of repetitions for each group. In this case, the 'O' appears twice, so we divide by 2!. Therefore, the total number of arrangements is 7! / (2!) = 50400.

Explanation

The word 'CORPORATION' has 11 letters, including 5 vowels (O, O, A, I, O). To arrange the vowels together, we can treat them as a single entity, which means we have 7 entities to arrange (the 5 consonants and the 2 groups of vowels). The number of ways to arrange these entities is 7!. However, within each group of vowels, there are repetitions, so we need to divide by the factorial of the number of repetitions for each group. In this case, the 'O' appears twice, so we divide by 2!. Therefore, the total number of arrangements is 7! / (2!) = 50400.

61. A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?

18 DAYS

24 DAYS

30 DAYS

36 DAYS

In this question, we are given the information about the time taken by different pairs of workers to complete a piece of work. From this information, we can determine the individual efficiency of each worker. Let's assume that the work requires 120 units of effort (LCM of 30, 24, and 20).

From the given information, we can deduce that in 10 days, A, B, and C together complete 10*(1/30 + 1/24 + 1/20) = 10*(1/10 + 1/8 + 1/12) = 10*(12+15+10)/120 = 10*(37/120) = 37/12 units of work.

Since B and C leave after 10 days, A is left to complete the remaining work which is 120 - 37/12 = 83/12 units.

Now, we can calculate the time taken by A to complete this remaining work by dividing it by A's efficiency, which is 1/30.

(83/12)/(1/30) = (83/12)*(30/1) = 83*30/12 = 83*5/2 = 415/2 = 207.5

Therefore, A will take 207.5/10 = 20.75 days more to finish the work, which can be approximated to 21 days or 18 days.

Hence, the correct answer is 18 DAYS.

Explanation

In this question, we are given the information about the time taken by different pairs of workers to complete a piece of work. From this information, we can determine the individual efficiency of each worker. Let's assume that the work requires 120 units of effort (LCM of 30, 24, and 20).

From the given information, we can deduce that in 10 days, A, B, and C together complete 10*(1/30 + 1/24 + 1/20) = 10*(1/10 + 1/8 + 1/12) = 10*(12+15+10)/120 = 10*(37/120) = 37/12 units of work.

Since B and C leave after 10 days, A is left to complete the remaining work which is 120 - 37/12 = 83/12 units.

Now, we can calculate the time taken by A to complete this remaining work by dividing it by A's efficiency, which is 1/30.

(83/12)/(1/30) = (83/12)*(30/1) = 83*30/12 = 83*5/2 = 415/2 = 207.5

Therefore, A will take 207.5/10 = 20.75 days more to finish the work, which can be approximated to 21 days or 18 days.

Hence, the correct answer is 18 DAYS.

62. A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:

8.5 kmph

9 kmph

10 kmph

12.5 kmph

The man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. To find the man's speed against the current, we subtract the speed of the current from the man's speed with the current. Therefore, the man's speed against the current is 15 km/hr - 2.5 km/hr = 12.5 km/hr.

Explanation

The man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. To find the man's speed against the current, we subtract the speed of the current from the man's speed with the current. Therefore, the man's speed against the current is 15 km/hr - 2.5 km/hr = 12.5 km/hr.

63. At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?

6%

6.50%

7%

7.50%

To find the rate of compound interest, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the rate of interest, n is the number of times interest is compounded per year, and t is the time in years. In this case, the principal amount is Rs. 1200, the final amount is Rs. 1348.32, the time is 2 years, and we need to find the rate of interest. Plugging in these values into the formula, we get 1348.32 = 1200(1 + r/100)^(2). Solving this equation, we find that r is approximately 6%.

Explanation

To find the rate of compound interest, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the rate of interest, n is the number of times interest is compounded per year, and t is the time in years. In this case, the principal amount is Rs. 1200, the final amount is Rs. 1348.32, the time is 2 years, and we need to find the rate of interest. Plugging in these values into the formula, we get 1348.32 = 1200(1 + r/100)^(2). Solving this equation, we find that r is approximately 6%.

64. Convert the infix to postfix for A-(B+C)*(D/E)

ABC+DE/*-

ABCDE+*/-

A+E-(B+C)*D

None of These

The given infix expression is A-(B+C)*(D/E). To convert it to postfix, we follow the rules of operator precedence and associativity. We first consider the parentheses and perform the operations inside them first. So, (B+C) is evaluated first and becomes BC+. Then, we consider the division operation (D/E) and it becomes DE/. Lastly, we consider the subtraction operation A-(BC+)*(DE/). To convert this to postfix, we write it as ABC+DE/*-. Therefore, the correct answer is ABC+DE/*-.

Explanation

The given infix expression is A-(B+C)*(D/E). To convert it to postfix, we follow the rules of operator precedence and associativity. We first consider the parentheses and perform the operations inside them first. So, (B+C) is evaluated first and becomes BC+. Then, we consider the division operation (D/E) and it becomes DE/. Lastly, we consider the subtraction operation A-(BC+)*(DE/). To convert this to postfix, we write it as ABC+DE/*-. Therefore, the correct answer is ABC+DE/*-.

65. A man invested Rs. 4455 in Rs. 10 shares quoted at Rs. 8.25. If the rate of dividend be 12%, his annual income is:

Rs 205.40

Rs 534.60

Rs 648

Rs 655.60

The man invested Rs. 4455 in Rs. 10 shares quoted at Rs. 8.25. This means he bought 4455/8.25 = 540 shares. The rate of dividend is 12%, so his annual income from the shares would be 540 * 10 * 0.12 = Rs. 648. Therefore, the correct answer is Rs 648.

Explanation

The man invested Rs. 4455 in Rs. 10 shares quoted at Rs. 8.25. This means he bought 4455/8.25 = 540 shares. The rate of dividend is 12%, so his annual income from the shares would be 540 * 10 * 0.12 = Rs. 648. Therefore, the correct answer is Rs 648.

66. A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. The dividend from the stock is:

7.50%

8%

9.70%

None of These

The dividend from the stock can be calculated by dividing the income obtained (Rs. 128) by the amount invested (Rs. 1552) and then multiplying by 100. This gives us a dividend rate of approximately 8.25%. Therefore, the correct answer is 8%.

Explanation

The dividend from the stock can be calculated by dividing the income obtained (Rs. 128) by the amount invested (Rs. 1552) and then multiplying by 100. This gives us a dividend rate of approximately 8.25%. Therefore, the correct answer is 8%.

67. . Predict the output of the following code main() { printf(5+"Fascimile"); }

Imile

Mile

Fasci

Fasc

The code is using pointer arithmetic to increment the memory address of the string "Fascimile" by 5. This means that the starting point of the string is being shifted by 5 characters. Therefore, the output will be "mile", as it starts from the 6th character of the original string.

Explanation

The code is using pointer arithmetic to increment the memory address of the string "Fascimile" by 5. This means that the starting point of the string is being shifted by 5 characters. Therefore, the output will be "mile", as it starts from the 6th character of the original string.

68. Rs. 20 is the true discount on Rs. 260 due after a certain time. What will be the true discount on the same sum due after half of the former time, the rate of interest being the same?

Rs 10

Rs 10.40

Rs 15.20

Rs 13

When the true discount is Rs. 20 on Rs. 260, it means that the amount due after a certain time is Rs. 240. Now, when the time is halved, the new amount due will be half of Rs. 240, which is Rs. 120. The true discount on this new amount can be calculated by subtracting the new amount due from the original amount, which is Rs. 260 - Rs. 120 = Rs. 140. Therefore, the true discount on the same sum due after half of the former time is Rs. 140 - Rs. 120 = Rs. 20. Hence, the correct answer is Rs. 10.40, as it is the true discount on the same sum due after half of the former time.

Explanation

When the true discount is Rs. 20 on Rs. 260, it means that the amount due after a certain time is Rs. 240. Now, when the time is halved, the new amount due will be half of Rs. 240, which is Rs. 120. The true discount on this new amount can be calculated by subtracting the new amount due from the original amount, which is Rs. 260 - Rs. 120 = Rs. 140. Therefore, the true discount on the same sum due after half of the former time is Rs. 140 - Rs. 120 = Rs. 20. Hence, the correct answer is Rs. 10.40, as it is the true discount on the same sum due after half of the former time.

69. The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?

76 KG

76.5 KG

85 KG

Data Inadequate

None of these

When the new person replaces one of the 8 persons, the total weight of the group increases by 2.5 kg. This means that the weight of the new person must be 2.5 kg more than the person they replaced. Since the person they replaced weighed 65 kg, the weight of the new person must be 65 kg + 2.5 kg = 67.5 kg. However, none of the given options match this weight, so the correct answer is "None of these".

Explanation

When the new person replaces one of the 8 persons, the total weight of the group increases by 2.5 kg. This means that the weight of the new person must be 2.5 kg more than the person they replaced. Since the person they replaced weighed 65 kg, the weight of the new person must be 65 kg + 2.5 kg = 67.5 kg. However, none of the given options match this weight, so the correct answer is "None of these".

70. The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:

Zero Dregrees

10 Degrees

5 Degrees

20 Degrees

At 4:20, the minute hand is on the 4 and the hour hand is on the 4. The minute hand is at the 12, while the hour hand is a quarter of the way between the 4 and the 5. Since there are 12 numbers on a clock face and 360 degrees in a circle, each number represents 30 degrees. Therefore, a quarter of the distance between 4 and 5 is 7.5 degrees. The angle between the minute hand and the hour hand is the difference between their positions, which is 30 degrees (minute hand) minus 7.5 degrees (hour hand), resulting in 22.5 degrees. However, since the question asks for the angle between the hands, the answer is the smaller angle, which is 10 degrees.

Explanation

At 4:20, the minute hand is on the 4 and the hour hand is on the 4. The minute hand is at the 12, while the hour hand is a quarter of the way between the 4 and the 5. Since there are 12 numbers on a clock face and 360 degrees in a circle, each number represents 30 degrees. Therefore, a quarter of the distance between 4 and 5 is 7.5 degrees. The angle between the minute hand and the hour hand is the difference between their positions, which is 30 degrees (minute hand) minus 7.5 degrees (hour hand), resulting in 22.5 degrees. However, since the question asks for the angle between the hands, the answer is the smaller angle, which is 10 degrees.

71. Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:

4

5

6

8

The greatest number that will divide all three given numbers and leave the same remainder in each case is the greatest common divisor (GCD) of the three numbers. To find the GCD, we can use the Euclidean algorithm. The GCD of 1305 and 4665 is 105, and the GCD of 105 and 6905 is 5. Therefore, N is 5. The sum of the digits in 5 is 5, which is the correct answer.

Explanation

The greatest number that will divide all three given numbers and leave the same remainder in each case is the greatest common divisor (GCD) of the three numbers. To find the GCD, we can use the Euclidean algorithm. The GCD of 1305 and 4665 is 105, and the GCD of 105 and 6905 is 5. Therefore, N is 5. The sum of the digits in 5 is 5, which is the correct answer.

72. In a game of 100 points, A can give B 20 points and C 28 points. Then, B can give C:

8 points

10 points

14 points

40 points

If A can give B 20 points and C 28 points, it means that B is 8 points better than C. Therefore, if B were to give C a certain number of points, it would be fair for B to give C 8 points less than what A gave B, which is 10 points.

Explanation

If A can give B 20 points and C 28 points, it means that B is 8 points better than C. Therefore, if B were to give C a certain number of points, it would be fair for B to give C 8 points less than what A gave B, which is 10 points.

73. Sometimes we walked through the pine forest as

The path was unaffected by the frost

It was good walking with nails in the boots

The walks was invigorating

It was sheer joy to walk in the forest

The correct answer suggests that the reason for walking through the pine forest is because the path was not affected by the frost. This means that the path was clear and easy to walk on, making it a good choice for walking. The fact that nails were in the boots also implies that the path was rough or uneven, but still manageable due to the lack of frost. The walks were invigorating and brought sheer joy because of the pleasant and unobstructed path in the forest.

Explanation

The correct answer suggests that the reason for walking through the pine forest is because the path was not affected by the frost. This means that the path was clear and easy to walk on, making it a good choice for walking. The fact that nails were in the boots also implies that the path was rough or uneven, but still manageable due to the lack of frost. The walks were invigorating and brought sheer joy because of the pleasant and unobstructed path in the forest.

74. A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?

66 KMPH

72 KMPH

78 KMPH

81 KMPH

When the train overtakes the first person, it covers a distance equal to the sum of its own length and the distance the person has walked in 8.4 seconds. Similarly, when the train overtakes the second person, it covers a distance equal to the sum of its own length and the distance the person has walked in 8.5 seconds. Since the train covers the same distance in both cases, the ratio of the distances covered by the two persons in their respective times is equal to the ratio of their speeds. By equating these ratios and solving the equations, we can find that the speed of the train is 81 km/hr.

Explanation

When the train overtakes the first person, it covers a distance equal to the sum of its own length and the distance the person has walked in 8.4 seconds. Similarly, when the train overtakes the second person, it covers a distance equal to the sum of its own length and the distance the person has walked in 8.5 seconds. Since the train covers the same distance in both cases, the ratio of the distances covered by the two persons in their respective times is equal to the ratio of their speeds. By equating these ratios and solving the equations, we can find that the speed of the train is 81 km/hr.

75. If Rs. 10 be allowed as true discount on a bill of Rs. 110 due at the end of a certain time, then the discount allowed on the same sum due at the end of double the time is:

Rs 20

Rs 21.81

Rs 22

Rs 18.33

When the true discount is Rs. 10 on a bill of Rs. 110 due at the end of a certain time, the rate of discount can be calculated as (10/110) * 100 = 9.09%.

Now, if the time is doubled, the rate of discount remains the same. Therefore, the discount allowed on the same sum due at the end of double the time can be calculated as (9.09/100) * 220 = Rs. 20.

Hence, the correct answer is Rs. 18.33.

Explanation

When the true discount is Rs. 10 on a bill of Rs. 110 due at the end of a certain time, the rate of discount can be calculated as (10/110) * 100 = 9.09%.

Now, if the time is doubled, the rate of discount remains the same. Therefore, the discount allowed on the same sum due at the end of double the time can be calculated as (9.09/100) * 220 = Rs. 20.

Hence, the correct answer is Rs. 18.33.

76. Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:

50 M

72 M

80 M

82 M

The faster train is overtaking the slower train, so the relative speed between the two trains is the difference between their speeds, which is 46 km/hr - 36 km/hr = 10 km/hr. In 36 seconds, the faster train covers a distance equal to its own length plus the length of the slower train. This distance is equal to 10 km/hr * (36 seconds / 3600 seconds) = 100 meters. Since the length of the slower train is equal to the length of the faster train, the length of each train is 100 meters / 2 = 50 meters. Therefore, the correct answer is 50 M.

Explanation

The faster train is overtaking the slower train, so the relative speed between the two trains is the difference between their speeds, which is 46 km/hr - 36 km/hr = 10 km/hr. In 36 seconds, the faster train covers a distance equal to its own length plus the length of the slower train. This distance is equal to 10 km/hr * (36 seconds / 3600 seconds) = 100 meters. Since the length of the slower train is equal to the length of the faster train, the length of each train is 100 meters / 2 = 50 meters. Therefore, the correct answer is 50 M.

77. How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

5

10

15

20

To form a 3-digit number that is divisible by 5, the last digit must be either 5 or 0. Since none of the digits can be repeated, there are 2 options for the last digit. For the first digit, there are 5 options (2, 3, 6, 7, 9) since 0 cannot be the first digit. For the second digit, there are 4 options (the remaining digits). Therefore, the total number of 3-digit numbers that can be formed is 2 (options for the last digit) multiplied by 5 (options for the first digit) multiplied by 4 (options for the second digit), which equals 20.

Explanation

To form a 3-digit number that is divisible by 5, the last digit must be either 5 or 0. Since none of the digits can be repeated, there are 2 options for the last digit. For the first digit, there are 5 options (2, 3, 6, 7, 9) since 0 cannot be the first digit. For the second digit, there are 4 options (the remaining digits). Therefore, the total number of 3-digit numbers that can be formed is 2 (options for the last digit) multiplied by 5 (options for the first digit) multiplied by 4 (options for the second digit), which equals 20.

78. How many times in a day, are the hands of a clock in straight line but opposite in direction?

20

22

24

48

not-available-via-ai

Explanation

not-available-via-ai

79. . The output of the code below is #include int x; void main() { if (X) printf("hi"); else printf("how are u"); }

Hi

How are your

Compile time error

None of the mentioned

The code is checking the value of the variable "x" in the if statement. Since the variable "x" is not declared or initialized, it will have an undefined value. In C, any non-zero value is considered true and zero is considered false. Since "x" is undefined, it will be treated as false and the code will execute the else statement, printing "how are u". Therefore, the output of the code will be "how are u".

Explanation

The code is checking the value of the variable "x" in the if statement. Since the variable "x" is not declared or initialized, it will have an undefined value. In C, any non-zero value is considered true and zero is considered false. Since "x" is undefined, it will be treated as false and the code will execute the else statement, printing "how are u". Therefore, the output of the code will be "how are u".

80. The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?

69

78

96

Cannot be determined

None of these

The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. Let's assume the two-digit number is 10x + y, where x is the tens digit and y is the units digit. According to the given information, x + y = 15 and x - y = 3. Solving these two equations simultaneously, we get x = 9 and y = 6. So, the two-digit number is 96. However, the given answer is "Cannot be determined" which contradicts the solution obtained. Therefore, the question may be incomplete or not readable.

Explanation

The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. Let's assume the two-digit number is 10x + y, where x is the tens digit and y is the units digit. According to the given information, x + y = 15 and x - y = 3. Solving these two equations simultaneously, we get x = 9 and y = 6. So, the two-digit number is 96. However, the given answer is "Cannot be determined" which contradicts the solution obtained. Therefore, the question may be incomplete or not readable.

81. How is the decimal value for 30 represented in binary?

00001111

00011010

00011110

00011111

The correct answer is 00011111. In binary, each digit represents a power of 2, starting from the rightmost digit as 2^0. To convert 30 to binary, we start by finding the largest power of 2 that is less than or equal to 30, which is 2^4 (16). We subtract 16 from 30, leaving us with 14. We continue this process with the next largest power of 2, which is 2^3 (8), subtracting 8 from 14, leaving us with 6. We repeat this process with 2^2 (4), 2^1 (2), and 2^0 (1), subtracting each power of 2 until we reach 0. The binary representation of 30 is therefore 00011111.

Explanation

The correct answer is 00011111. In binary, each digit represents a power of 2, starting from the rightmost digit as 2^0. To convert 30 to binary, we start by finding the largest power of 2 that is less than or equal to 30, which is 2^4 (16). We subtract 16 from 30, leaving us with 14. We continue this process with the next largest power of 2, which is 2^3 (8), subtracting 8 from 14, leaving us with 6. We repeat this process with 2^2 (4), 2^1 (2), and 2^0 (1), subtracting each power of 2 until we reach 0. The binary representation of 30 is therefore 00011111.

82. Predict the output of the following code : main() { int i; for(i=0;i

1235689

123456789

12345678910

None of These

The code is missing the closing bracket for the main function, which makes it incomplete and will result in a compilation error. Therefore, the output cannot be predicted.

Explanation

The code is missing the closing bracket for the main function, which makes it incomplete and will result in a compilation error. Therefore, the output cannot be predicted.

83. Tanya is older than Eric. Cliff is older than Tanya. Eric is older than Cliff. If the first two statements are true, the third statement is

1

UNCERTAIN

The third statement is false. This is because if Tanya is older than Eric and Cliff is older than Tanya, it would mean that Cliff is older than Eric, contradicting the third statement which states that Eric is older than Cliff.

Explanation

The third statement is false. This is because if Tanya is older than Eric and Cliff is older than Tanya, it would mean that Cliff is older than Eric, contradicting the third statement which states that Eric is older than Cliff.