## MAT Mock Test Series 5 | MAT Online Test Series 5 | MAT Sample Papers

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MAT Online Test Series 5, MAT Free Online Test Series 5. MAT Free Mock Test Exam 2019. MAT Exam Free Online Quiz 2019, MAT Full Online Mock Test **Series 5th** in English. MAT Free Mock Test Series in English. MAT Free Mock Test **Series 5.** MAT English Language Online Test in English **Series 5th**. Take MAT Online Quiz. The MAT Full online mock test paper is free for all students. MAT Question and Answers in English and Hindi **Series 5**. Here we are providing** MAT Full Mock Test Paper in English. MAT **Mock Test **Series 5th** 2019. Now Test your self for MAT Exam by using below quiz…

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- Question 1 of 50
##### 1. Question

8/15 / 1 1/3 * 3 ?/4 = 1.5

Correct8/15 * 3/4 * 3 ?/4 = 1.5

=> 3 ?/4 = 3/2 * 5/2 = 15/4 = 3 3/4

=> ? = 3.Incorrect8/15 * 3/4 * 3 ?/4 = 1.5

=> 3 ?/4 = 3/2 * 5/2 = 15/4 = 3 3/4

=> ? = 3. - Question 2 of 50
##### 2. Question

In finding the HCF of two numbers, the last divisor was 41 and the successive quotients, starting from the first, where 2, 4 and 2. The numbers are?

CorrectIncorrect - Question 3 of 50
##### 3. Question

A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?

CorrectHere, five seniors out of 12 seniors can be selected in ¹²C₅ ways. Also, five juniors out of ten juniors can be selected ¹⁰C₅ ways. Hence the total number of different ways of selection = ¹²C₅ * ¹⁰C₅ = ¹²C₇ * ¹⁰C₅

= ¹²C₅ = ¹²C₇IncorrectHere, five seniors out of 12 seniors can be selected in ¹²C₅ ways. Also, five juniors out of ten juniors can be selected ¹⁰C₅ ways. Hence the total number of different ways of selection = ¹²C₅ * ¹⁰C₅ = ¹²C₇ * ¹⁰C₅

= ¹²C₅ = ¹²C₇ - Question 4 of 50
##### 4. Question

The radius of the base of cone is 3 cm and height is 4 cm. Find the volume of the cone?

Correct1/3 * π * 3 * 3 * 4 = 12 π

Incorrect1/3 * π * 3 * 3 * 4 = 12 π

- Question 5 of 50
##### 5. Question

The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8500. If his salary for the month of May is Rs.6500, find his salary for the month of January?

CorrectSum of the salaries of the person for the months of January, February, March and April = 4 * 8000 = 32000 —-(1)

Sum of the salaries of the person for the months of February, March, April and May = 4 * 8500 = 34000 —-(2)

(2)-(1) i.e. May – Jan = 2000

Salary of May is Rs.6500

Salary of January = Rs.4500IncorrectSum of the salaries of the person for the months of January, February, March and April = 4 * 8000 = 32000 —-(1)

Sum of the salaries of the person for the months of February, March, April and May = 4 * 8500 = 34000 —-(2)

(2)-(1) i.e. May – Jan = 2000

Salary of May is Rs.6500

Salary of January = Rs.4500 - Question 6 of 50
##### 6. Question

A sum of money place at compound interest doubles itself in 4 years. In how many years will it amount to eight times itself?

Correct100 —- 200 —- 4

400 —- 4

800 —- 4

——

12 yearsIncorrect100 —- 200 —- 4

400 —- 4

800 —- 4

——

12 years - Question 7 of 50
##### 7. Question

The height of two right circular cones are in the ratio 1:2 and their perimeters of their bases are in the ratio 3:4, the ratio of their volume is?

CorrectIncorrect - Question 8 of 50
##### 8. Question

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?

CorrectOriginally, let the number of boys and girls in the college be 7x and 8x respectively.

Their increased number is (120% of 7x) and (110% of 8x).

i.e., (120/100 * 7x) and (110/100 * 8x)

i.e., 42x/5 and 44x/5

Required ratio = 42x/5 : 44x/5 = 21:22IncorrectOriginally, let the number of boys and girls in the college be 7x and 8x respectively.

Their increased number is (120% of 7x) and (110% of 8x).

i.e., (120/100 * 7x) and (110/100 * 8x)

i.e., 42x/5 and 44x/5

Required ratio = 42x/5 : 44x/5 = 21:22 - Question 9 of 50
##### 9. Question

A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?

CorrectArea = (l + b – d) d

(80 + 60 – 10)10 => 1300 m^{2}

1300 * 3 = Rs.3900IncorrectArea = (l + b – d) d

(80 + 60 – 10)10 => 1300 m^{2}

1300 * 3 = Rs.3900 - Question 10 of 50
##### 10. Question

A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?

CorrectTwo balls can be picked from nine balls in ⁹C₂ ways.

We select one white ball and one red ball from five white balls and four red balls. This can be done ⁵C₁ . ⁴C₁ ways.

The required probability = (5 * 4)/⁹C₂ = 20/36 = 5/9IncorrectTwo balls can be picked from nine balls in ⁹C₂ ways.

We select one white ball and one red ball from five white balls and four red balls. This can be done ⁵C₁ . ⁴C₁ ways.

The required probability = (5 * 4)/⁹C₂ = 20/36 = 5/9 - Question 11 of 50
##### 11. Question

8.008 + 0.8 + 80.8 + 800.8 + 0.08 = ?

Correct8.008 + 0.8 + 80.8 + 800.8 + 0.08

= 8 + 0.008 + 0.8 + 80 + 0.8 + 800 + 0.8 + 0.08

= 8 + 80 + 800 + 0.008 + 0.08 + 0.8 + 0.8 + 0.8

= 888 + 2.488 = 890.488Incorrect8.008 + 0.8 + 80.8 + 800.8 + 0.08

= 8 + 0.008 + 0.8 + 80 + 0.8 + 800 + 0.8 + 0.08

= 8 + 80 + 800 + 0.008 + 0.08 + 0.8 + 0.8 + 0.8

= 888 + 2.488 = 890.488 - Question 12 of 50
##### 12. Question

There is food for 760 men for 22 days. How many more men should join after two days so that the same food may last for 19 days more?

Correct760 —- 22

760 —- 20

x —– 19

x*19 = 760*20

x = 800

760

——-

40Incorrect760 —- 22

760 —- 20

x —– 19

x*19 = 760*20

x = 800

760

——-

40 - Question 13 of 50
##### 13. Question

A man on tour travels first 160 km at 64 km/he and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is?

CorrectTotal time taken = (160/64 + 160/8) = 9/2 hrs.

Average speed = 320 * 2/9 = 71.11 km/hr.IncorrectTotal time taken = (160/64 + 160/8) = 9/2 hrs.

Average speed = 320 * 2/9 = 71.11 km/hr. - Question 14 of 50
##### 14. Question

Rahim bought 65 books for Rs.1150 from one shop and 50 books for Rs.920 from another. What is the average price he paid per book ?

CorrectAverage price per book = (1150 + 920) / (65 + 50) = 2070 / 115 = Rs.18

IncorrectAverage price per book = (1150 + 920) / (65 + 50) = 2070 / 115 = Rs.18

- Question 15 of 50
##### 15. Question

The radius of a cylindrical vessel is 7cm and height is 3cm. Find the whole surface of the cylinder?

Correctr = 7 h = 3

2πr(h + r) = 2 * 22/7 * 7(10) = 440Incorrectr = 7 h = 3

2πr(h + r) = 2 * 22/7 * 7(10) = 440 - Question 16 of 50
##### 16. Question

Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 27 seconds. Find the length of the faster train?

CorrectRelative speed = (72 – 36) * 5/18 = 2 * 5 = 10 mps.

Distance covered in 27 sec = 27 * 10 = 270 m.

The length of the faster train = 270 m.IncorrectRelative speed = (72 – 36) * 5/18 = 2 * 5 = 10 mps.

Distance covered in 27 sec = 27 * 10 = 270 m.

The length of the faster train = 270 m. - Question 17 of 50
##### 17. Question

The ratio of numbers is 3:4 and their H.C.F is 4. Their L.C.M is:

CorrectLet the numbers be 3x and 4x.

Then their H.C.F = x. So, x = 4.

So, the numbers are 12 and 16.

L.C.M of 12 and 16 = 48.IncorrectLet the numbers be 3x and 4x.

Then their H.C.F = x. So, x = 4.

So, the numbers are 12 and 16.

L.C.M of 12 and 16 = 48. - Question 18 of 50
##### 18. Question

Two persons A and B can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 3 days?

CorrectA’s one day’s work = 1/30

B’s one day’s work = 1/45

(A + B)’s one day’s work = 1/30 + 1/45 = 1/18

The part of the work completed in 3 days = 3 (1/18) = 1/6.IncorrectA’s one day’s work = 1/30

B’s one day’s work = 1/45

(A + B)’s one day’s work = 1/30 + 1/45 = 1/18

The part of the work completed in 3 days = 3 (1/18) = 1/6. - Question 19 of 50
##### 19. Question

There are some rabbits and peacocks in a zoo. The total number of their heads is 60 and total number of their legs is 192. Find the number of total rabbits?

CorrectLet the number of rabbits and peacocks be ‘r’ and ‘p’ respectively. As each animal has only one head, so r + p = 60 — (1)

Each rabbit has 4 legs and each peacock has 2 legs. Total number of legs of rabbits and peacocks, 4r + 2p = 192 — (2)

Multiplying equation (1) by 2 and subtracting it from equation (2), we get

=> 2r = 72 => r = 36.IncorrectLet the number of rabbits and peacocks be ‘r’ and ‘p’ respectively. As each animal has only one head, so r + p = 60 — (1)

Each rabbit has 4 legs and each peacock has 2 legs. Total number of legs of rabbits and peacocks, 4r + 2p = 192 — (2)

Multiplying equation (1) by 2 and subtracting it from equation (2), we get

=> 2r = 72 => r = 36. - Question 20 of 50
##### 20. Question

A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?

CorrectM = 15

S = 5

DS = 15 + 5 = 20IncorrectM = 15

S = 5

DS = 15 + 5 = 20 - Question 21 of 50
##### 21. Question

The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?

CorrectArea of the four walls = 2h(l + b)

Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) – (6 * 3) – 3(4 * 3) = 906 sq.ft.

Total cost = 906 * 5 = Rs. 4530IncorrectArea of the four walls = 2h(l + b)

Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) – (6 * 3) – 3(4 * 3) = 906 sq.ft.

Total cost = 906 * 5 = Rs. 4530 - Question 22 of 50
##### 22. Question

An automobile financier claims to be lending money at S.I., but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes?

CorrectLet the sum be Rs. 100. Then,

S.I. for first 6 months = (100 * 10 *1) / (100 * 2) = Rs. 5

S.I. for last 6 months = (105 * 10 * 1) / (100 * 2) = Rs. 5.25

So, amount at the end of 1 year = (100 + 5 + 5.25) = Rs. 110.25

Effective rate = (110.25 – 100) = 10.25%.IncorrectLet the sum be Rs. 100. Then,

S.I. for first 6 months = (100 * 10 *1) / (100 * 2) = Rs. 5

S.I. for last 6 months = (105 * 10 * 1) / (100 * 2) = Rs. 5.25

So, amount at the end of 1 year = (100 + 5 + 5.25) = Rs. 110.25

Effective rate = (110.25 – 100) = 10.25%. - Question 23 of 50
##### 23. Question

The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.1045.What was his original salary?

CorrectX * (110/100) * (95/100) = 1045

X * (11/10) * (1/100) = 11

X = 1000IncorrectX * (110/100) * (95/100) = 1045

X * (11/10) * (1/100) = 11

X = 1000 - Question 24 of 50
##### 24. Question

A sum amount to Rs.1344 in two years at simple interest. What will be the compound interest on the same sum at the same rate of interest for the same period?

CorrectIncorrect - Question 25 of 50
##### 25. Question

Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hr and 40 km/hr respectively. By the time they meet, the first train has traveled 100 km more than the second. The distance between P and Q is?

CorrectAt the time of meeting, let the distance traveled by the second train be x km. Then, distance covered by the first train is (x + 100) km.

x/40 = (x + 100)/50

50x = 40x + 4000 => x = 400

So, distance between P and Q = (x + x + 100)km = 900 km.IncorrectAt the time of meeting, let the distance traveled by the second train be x km. Then, distance covered by the first train is (x + 100) km.

x/40 = (x + 100)/50

50x = 40x + 4000 => x = 400

So, distance between P and Q = (x + x + 100)km = 900 km. - Question 26 of 50
##### 26. Question

The diagonals of a rhombus are 15 cm and 20 cm. Find its area?

Correct1/2 * 15 * 20 = 150

Incorrect1/2 * 15 * 20 = 150

- Question 27 of 50
##### 27. Question

One train is traveling 45 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is?

Correct45 * 5/18 = 10

25:20 => 5:4Incorrect45 * 5/18 = 10

25:20 => 5:4 - Question 28 of 50
##### 28. Question

The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers?

CorrectLet the numbers be a and b. Then,

a + b = 12 and ab = 35.

(a + b)/ab = 12/35

= (1/b + 1/a) = 12/35

Sum of reciprocals of given numbers = 12/35.IncorrectLet the numbers be a and b. Then,

a + b = 12 and ab = 35.

(a + b)/ab = 12/35

= (1/b + 1/a) = 12/35

Sum of reciprocals of given numbers = 12/35. - Question 29 of 50
##### 29. Question

Sixty men can stitch 200 shirts in 30 days working 8 hours a day. In how many days can 45 men stitch 300 shirts working 6 hours a day?

CorrectWe have M

_{1}D_{1}H_{1}/ W_{1}= M_{2}D_{2}H_{2}/ W_{2}(Variation rule)

(60 * 30 * 8)/ 200 = (45 * D_{2}* 6) / 300

D_{2}= (60 * 30 * 8 * 300) / (200 * 45 * 6) => D_{2}= 80.IncorrectWe have M

_{1}D_{1}H_{1}/ W_{1}= M_{2}D_{2}H_{2}/ W_{2}(Variation rule)

(60 * 30 * 8)/ 200 = (45 * D_{2}* 6) / 300

D_{2}= (60 * 30 * 8 * 300) / (200 * 45 * 6) => D_{2}= 80. - Question 30 of 50
##### 30. Question

Mahesh marks an article 15% above the cost price of Rs. 540. What must be his discount percentage if he sells it at Rs. 496.80?

CorrectCP = Rs. 540, MP = 540 + 15% of 540 = Rs. 621

SP = Rs. 496.80, Discount = 621 – 496.80 = 124.20

Discount % = 124.2/621 * 100 = 20%IncorrectCP = Rs. 540, MP = 540 + 15% of 540 = Rs. 621

SP = Rs. 496.80, Discount = 621 – 496.80 = 124.20

Discount % = 124.2/621 * 100 = 20% - Question 31 of 50
##### 31. Question

A candidate who gets 30% of the marks fails by 50 marks. But another candidate who gets 45% marks gets 25 marks more than necessary for passing. Find the number of marks for passing?

Correct30% ———— 50

45% ———— 25

———————-

15% ————- 75

30% ————– ?

150 + 50 = 200 MarksIncorrect30% ———— 50

45% ———— 25

———————-

15% ————- 75

30% ————– ?

150 + 50 = 200 Marks - Question 32 of 50
##### 32. Question

Excluding stoppages, the speed of a bus is 54 km/hr and including stoppages, it is 45 km/hr. For how many minutes does the bus stop per hour?

CorrectDue to stoppages, it covers 9 km less.

Time taken to cover 9 km = 9/54 * 60 = 10 min.IncorrectDue to stoppages, it covers 9 km less.

Time taken to cover 9 km = 9/54 * 60 = 10 min. - Question 33 of 50
##### 33. Question

If a: b = 3:4, b:c = 7:9, c:d = 5:7, find a:d?

Correcta/d = (3/4)*(7/9)*(5/7) => 5/12

Incorrecta/d = (3/4)*(7/9)*(5/7) => 5/12

- Question 34 of 50
##### 34. Question

What is the least number, which is perfect square but contains 2700 as its factor?

Correct900 * 3 * 3 = 8100

Incorrect900 * 3 * 3 = 8100

- Question 35 of 50
##### 35. Question

If the L.C.M of two numbers is 750 and their product is 18750, find the H.C.F of the numbers.

CorrectH.C.F = (Product of the numbers) / (Their L.C.M) = 18750/750 = 25.

IncorrectH.C.F = (Product of the numbers) / (Their L.C.M) = 18750/750 = 25.

- Question 36 of 50
##### 36. Question

In a hostel there were 100 students. To accommodate 20 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?

Correct100x + 400 = 12(x – 5)

x = 50

100 * 50 + 400 = 5400Incorrect100x + 400 = 12(x – 5)

x = 50

100 * 50 + 400 = 5400 - Question 37 of 50
##### 37. Question

The weights of three boys are in the ratio 4 : 5 : 6. If the sum of the weights of the heaviest and the lightest boy is 45 kg more than the weight of the third boy, what is the weight of the lightest boy?

CorrectLet the weights of the three boys be 4k, 5k and 6k respectively.

4k + 6k = 5k + 45

=> 5k = 45 => k = 9

Therefore the weight of the lightest boy

= 4k = 4(9) = 36 kg.IncorrectLet the weights of the three boys be 4k, 5k and 6k respectively.

4k + 6k = 5k + 45

=> 5k = 45 => k = 9

Therefore the weight of the lightest boy

= 4k = 4(9) = 36 kg. - Question 38 of 50
##### 38. Question

A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.

CorrectRequired probability = 1 – 1/126 = 125/126

IncorrectRequired probability = 1 – 1/126 = 125/126

- Question 39 of 50
##### 39. Question

A man said to his son, “I was two-third of your present age when you were born”. If the present age of the man is 48 years, find the present age of the son?

CorrectPresent age of the son be P, he was born P years ago.

The age of the man was: (48 – P).

His age when the son was born should be equal to 2/3 of P.

(48 – P) = 2/3 P

5P = 144 => P = 28.8IncorrectPresent age of the son be P, he was born P years ago.

The age of the man was: (48 – P).

His age when the son was born should be equal to 2/3 of P.

(48 – P) = 2/3 P

5P = 144 => P = 28.8 - Question 40 of 50
##### 40. Question

The speed of a car is 90 km in the first hour and 60 km in the second hour. What is the average speed of the car?

CorrectS = (90 + 60)/2 = 75 kmph

IncorrectS = (90 + 60)/2 = 75 kmph

- Question 41 of 50
##### 41. Question

If Rs.450 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?

Correct90 = (450*4*R)/100

R = 5%

I = (450*6*5)/100 = 135

450 + 135 = 585Incorrect90 = (450*4*R)/100

R = 5%

I = (450*6*5)/100 = 135

450 + 135 = 585 - Question 42 of 50
##### 42. Question

3 men, 4 women and 6 children can complete a work in 7 days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days?

CorrectLet 1 woman’s 1 day work = x.

Then, 1 man’s 1 day work = x/2 and 1 child’s 1 day work x/4.

So, (3x/2 + 4x + + 6x/4) = 1/7

28x/4 = 1/7 => x = 1/49

1 woman alone can complete the work in 49 days.

So, to complete the work in 7 days, number of women required = 49/7 = 7.IncorrectLet 1 woman’s 1 day work = x.

Then, 1 man’s 1 day work = x/2 and 1 child’s 1 day work x/4.

So, (3x/2 + 4x + + 6x/4) = 1/7

28x/4 = 1/7 => x = 1/49

1 woman alone can complete the work in 49 days.

So, to complete the work in 7 days, number of women required = 49/7 = 7. - Question 43 of 50
##### 43. Question

Convert the 13/36 m/s into kilometers per hour?

Correct13/36 m/s = 13/36 * 18/5 = 13/10 = 1.3 kmph.

Incorrect13/36 m/s = 13/36 * 18/5 = 13/10 = 1.3 kmph.

- Question 44 of 50
##### 44. Question

A and B can do a work in 12 days and 36 days respectively. If they work on alternate days beginning with B, in how many days will the work be completed?

CorrectThe work done in the first two days = 1/12 + 1/36 = 1/9

so, 9 such two days are required to finish the work.

i.e., 18 days are required to finish the work.IncorrectThe work done in the first two days = 1/12 + 1/36 = 1/9

so, 9 such two days are required to finish the work.

i.e., 18 days are required to finish the work. - Question 45 of 50
##### 45. Question

The volumes of two cubes are in the ratio 27: 125, what shall be the ratio of their surface areas?

Correcta

_{1}^{3}: a_{2}^{3}= 27 : 125

a_{1}: a_{2 }= 3 : 5

6 a_{1}^{2 }: 6 a_{2}^{2}

a_{1}^{2}: a_{2}^{2}= 9 : 25Incorrecta

_{1}^{3}: a_{2}^{3}= 27 : 125

a_{1}: a_{2 }= 3 : 5

6 a_{1}^{2 }: 6 a_{2}^{2}

a_{1}^{2}: a_{2}^{2}= 9 : 25 - Question 46 of 50
##### 46. Question

A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it?

Correct5/30 + 20/x = 1

x = 24

1/30 + 1/24 = 3/40

40/3 = 13 1/3 daysIncorrect5/30 + 20/x = 1

x = 24

1/30 + 1/24 = 3/40

40/3 = 13 1/3 days - Question 47 of 50
##### 47. Question

Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?

CorrectThey are moving in opposite directions, relative speed is equal to the sum of their speeds.

Relative speed = (54 + 72)*5/18 = 7*5 = 35 mps.

The time required = d/s = 100/35 = 20/7 sec.IncorrectThey are moving in opposite directions, relative speed is equal to the sum of their speeds.

Relative speed = (54 + 72)*5/18 = 7*5 = 35 mps.

The time required = d/s = 100/35 = 20/7 sec. - Question 48 of 50
##### 48. Question

The sum of four consecutive even numbers is 36. Find the sum of the squares of these numbers?

CorrectLet the four numbers be x, x + 2, x + 4 and x + 6.

=> x + x + 2 + x + 4 + x + 6 = 36

=> 4x + 12 = 36 => x = 6

The numbers are 6, 8, 10 and 12.

Sum of their squares = 6^{2}+ 8^{2}+ 10^{2}+ 12^{2}= 36 + 64 + 100 + 144 = 344.IncorrectLet the four numbers be x, x + 2, x + 4 and x + 6.

=> x + x + 2 + x + 4 + x + 6 = 36

=> 4x + 12 = 36 => x = 6

The numbers are 6, 8, 10 and 12.

Sum of their squares = 6^{2}+ 8^{2}+ 10^{2}+ 12^{2}= 36 + 64 + 100 + 144 = 344. - Question 49 of 50
##### 49. Question

A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?

CorrectGiven that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 * 2)/(15 * 14) = 1/35

Probability that both are yellow = ²C₂/¹⁵C₂ = (2 * 1)/(15 * 14) = 1/105

Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵C₂ = (2 * 3 * 2)/(15 * 14) = 2/35

Required probability = 1/35 + 1/105 + 2/35

= 3/35 + 1/105 = 1/35(3 + 1/3)

= 10/(3 * 35) = 2/21IncorrectGiven that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 * 2)/(15 * 14) = 1/35

Probability that both are yellow = ²C₂/¹⁵C₂ = (2 * 1)/(15 * 14) = 1/105

Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵C₂ = (2 * 3 * 2)/(15 * 14) = 2/35

Required probability = 1/35 + 1/105 + 2/35

= 3/35 + 1/105 = 1/35(3 + 1/3)

= 10/(3 * 35) = 2/21 - Question 50 of 50
##### 50. Question

Mohit sold an article for Rs. 18000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?

CorrectLet the CP be Rs. x.

Had he offered 10% discount, profit = 8%

Profit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x = 18000 – 10/100(18000) = 18000 – 1800 = Rs. 16200

=> 1.08x = 16200

=> x = 15000IncorrectLet the CP be Rs. x.

Had he offered 10% discount, profit = 8%

Profit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x = 18000 – 10/100(18000) = 18000 – 1800 = Rs. 16200

=> 1.08x = 16200

=> x = 15000