SBI Clerk Quantitative Aptitude Questions and Answers | Download in PDF

SBI Clerk Quantitative Aptitude Questions and Answers | Download in PDF

SBI Clerk Aptitude Questions and Answers

State Bank of India (SBI) is the largest organization in the banking sector across India. However, the higher authorities of SBI has been released the notification in order to select clerks. Therefore, for the sake of competitors, we have provided SBI Clerk Quantitative Aptitude Questions and Answers in this article. So, applicants can download SBI Clerk Quantitative Aptitude Questions and Answers in the form of PDF.

As of now, the bank examination is a heavy competitive examination in India. It seems very difficult to clear the examination. To make it easy we are providing SBI Clerk Quantitative Aptitude Questions and Answers with clear explanation. Therefore, candidates can practice SBI Clerk Quantitative Aptitude Questions and Answers and secure maximum marks in the examination.

SBI Clerk Quantitative Aptitude Questions and Answers

Quantitative Aptitude is one of the important section in State Bank of India (SBI) Clerk Examination, especially for the mains examination. The Number of questions asked in SBI Clerk examination is 50 and the maximum marks also 50 only. Therefore, for the sake of applicants, we have listed the sample questions and  with the explanation for the competitors’ practice

1. Arun went to buy an Android mobile, the shopkeeper told him to pay 20% tax if he asked the bill. Arun manages to get the discount of 5% on the actual sale price of the mobile and he paid the shopkeeper Rs. 8550 without tax. Besides he manages to avoid to pay 20% tax on the already discounted price, what is the amount of discount?

A.2685
B.2636
C.2250
D.2675
E.2690

Answer – C.2250
Explanation :
CP = 100, SP (with tax) =120
New SP = 100 – 5 = 95
Discount = 120 – 95 = 25
Discount = 25/95 * 8550 = 2250

2. Cost Price of two mobiles is the same. One is sold at a profit of 20% and the other for Rs. 5200 more than the first. If the net profit is 40%. Find the cost price of each mobile?
A. Rs. 13000
B. Rs. 12000
C. Rs. 16000
D. Rs. 12500
E. None of these

Answer – A. Rs. 13000
Explanation:
CP of each mobile be Rs.x then
(2 x 1.20 xx) + 5200 = 2 x 1.4 x N
⇒ 0.4 x = 5200
∴ N = 13000

3. Rahul sells his laptop to Ravi at a loss of 20% who subsequently sells it to Suresh at a profit of 25%. Suresh after finding some defect in the laptop returns it to Ravi but could recover only Rs.4.50 for every Rs. 5 he had paid. Find the amount of Suresh’s loss if Rahul had paid Rs.50,000 for the laptop?
A. Rs.6000
B. Rs.7000
C. Rs.2000
D. Rs.5000
E. None of these

Answer – D. Rs. 5000
Explanation :
0.50/5 * 50,000 = 5000

4. A reduction of 20% in the price of sugar enables a housewife to purchase 6 kg more for Rs. 240. What is the original price per kg of sugar?
A. Rs.10 per Kg
B. Rs.8 per Kg
C. Rs.6 per Kg
D. Rs.5 per Kg
E. None of these

Answer – A. Rs.10 per Kg
Explanation:
Reduction in price = 1/5 = 20%
Increase in Quantity = 25%
25% = 6 Kg.
original amount of Sugar = 6*4 = 24Kg.
Original price of the sugar = 240/24 = Rs. 10 per kg.

5. A Bike is available at 40% discount at showroom “A” and the same is available at only a 25% discount at showroom “B”. Mr. Arun has just sufficient amount of Rs. 60,000 to purchase it at showroom “A”. What is the amount that Mr. Arun has less than the required amount to purchase it at that showroom “B”?
A. Rs. 70000
B. Rs. 50000
C. Rs. 10000
D. Rs. 15000
E. None of these

Answer – D. Rs. 15000
Explanation :
Let the market price be x.
Cost price (CP) = 40 % discount on MP = 0.6y = 60000
⇒ y= Rs.100000 MP
SP at Show Room “A” = Rs. 60000
SP at Show Room “B” = 100000 X 0.75 = 75000; Difference = 15000

6. Arun can do a piece of work in 40 days, but Bala can do the same work in 5 days less, than Arun, when working alone. Arun and Bala both started the work together but Bala left after some days and Arun finished the remaining work in 30 days with half of his efficiency but he did the work with Bala with his complete efficiency. For how many days they had worked together?
A. 25/3 days
B. 31/3 days
C. 35/3 days
D. 38/3 days
E. None of these

Answer – C. 35/3 days
Explanation :
1 day work of Arun and Bala = 1/40 + 1/35 = 15/280
Arun finished the remaining work in 30 days = 30 * 1/40 * 2 = 3/8
Remaining work was done by Arun and Bala = 5/8
Worked together = (5/8)/(15/280) = 35/3 days.

7. Kiran can do a work in 20 days, while Karan can do the same work in 25 days. They started the work jointly. A few days later Suman also joined them and thus all of them completed the whole work in 10 days. All of them were paid total Rs.1000. What is the share of Suman?
A. 200
B. 400
C. 100
D. 300
E. 500

Answer – C. 100
Explanation :
The efficiency of Kiran = 5%
The efficiency of Karan = 4%
They will complete only 90% of the work = [(5+4)*10] =90
Remaining work was done by Suman = 10%.
Share of Suman = 10/100 * 1000 = 100

8. 7 Indian and 4 American finish a job in 6 days. 7 African and 3 American finish the same job in 8 days. The efficiency of each person of a particular nationality is the same but different from others. One Indian One American and One African will complete the work in:
A. 10 days
B. 12 days
C. 24 days
D. 36 days
E. None of these

Answer – C. 24 days
Explanation :
7I + 4Am = 1/6
7Af + 4Am = 1/8
7I + 7Af + 7Am = 7/24
1I + 1Af + 1Am = 1/24
Therefore, One Indian One American and One African will complete the work in – 24 days.

9. Chitra is twice efficient as Arun. Bala takes thrice as many days as Chitra. Arun takes 12 days to finish the work alone. If they work in pairs(i.e Arun-Bala, Bala-Chitra, Chitra-Arun) starting with Arun – Bala on the first day, Bala – Chitra on the second day and Chitra – Arun on the third day and so on, then how many days are required to finish the work?
A. 26/9 days
B. 46/9 days
C. 16/9 days
D. 56/9 days
E. None of these

Answer – B. 9 days
Explanation :
No of days taken by Arun = 12 days
No of days(Arun:Bala:Chitra) = 2:3:1
1 day work of (Arun+Bala) = 5/36
1 day work of (Bala+Chitra) = 8/36
1 day work of (Chitra+Arun) = 9/36
5 days of total work – 35/36
1/36 is done by Arun-Chitra
Number of days taken by Arun-Chitra for the rest of the work = (1/36)/(9/36) = 1/9
Total time taken to complete the work = 5 + 1/9 = 46/9 days

10. Work is done by 30 workers not all of them have the same capacity to work. Every day exactly 2 workers, do the work with no pair of workers working together twice. Even after all possible pairs have worked once, all the workers together work for six more days to finish the work. Find the number of days in which all the workers together will finish the work?
A. 22 days
B. 20 days
C. 24 days
D. 35 days
E. 32 days

Answer – D. 35 days
Explanation :
30 workers work in pairs, with no same pair of workers working together twice
29[1/w1 + 1/w2 ….. + 1/w30] + 6[1/w1 + 1/w2 ….. + 1/w30] = 1
[1/w1 + 1/w2 ….. + 1/w30] = 1/35
35 days.

11. The distance of the School and house of Suresh is 80km. One day he was late by 1 hour than the normal time to leave for the college, so he increased his speed by 4km/h and thus he reached to college at the normal time. What is the changed speed of Suresh?
A. 28 kmph
B. 25 kmph
C. 20 kmph
D. 24 kmph

Answer – C. 20 kmph
Explanation :
80/x – 80/(x+4) = 1
x(x+20) – 16(x+20) = 0
x = 16kmph
Increased speed = 20 kmph

12. Anita goes to College at 20 km/h and reaches college 4 minutes late. Next time she goes at 25 km/h and reaches the college 2 minutes earlier than the scheduled time. What is the distance of her school?
A. 16 km
B. 12 km
C. 15 km
D. 10 km

Answer – D. 10 km
Explanation:
20*25/(25-20)*6/60=10.

13. Two places R and S are 800 km apart from each other. Two persons start from R towards S at an interval of 2 hours. Whereas A leaves R for S before B. The speeds of A and B are 40 kmph and 60 kmph respectively. B overtakes A at M, which is on the way from R to S. What is the ratio of time taken by A and B to meet at M?
A. 1:3
B. 1:2
C. 1:4
D. 3:2
E. None of these

Answer – D. 3:2
Explanation :
Time is taken by B to reach M = 4h
Time is taken by A to reach M = 6h
Ratio = 6:4 = 3:2

14. Two places R and S are 800 km apart from each other. Two persons start from R towards S at an interval of 2 hours. Whereas A leaves R for S before B. The speeds of A and B are 40 kmph and 60 kmph respectively. B overtakes A at M, which is on the way from R to S. What is the extra time taken by A to reach S?
A. 6hrs 20 minutes
B. 6hrs 40 minutes
C. 6hrs 30 minutes
D. 6hrs 10 minutes

Answer – B. 6hrs 40 minutes
Explanation :
Time is taken by A to reach at Q = 800/40 = 20 hours
Time is taken by B to reach at Q = 800/60 = 13 hours and 20 min
A takes 6hr 40 minutes extra time to reach Q.

15. In school, the number of boys and girls are in the ratio of 4:7. If the number of boys is increased by 25% and the number of girls is increased by 15%. What will be the new ratio of a number of boys to that of girls?
a) 100:131
b) 100:151
c) 100:161
d) 100:181
e) None of these

Answer – c) 100:161
Explanation :
Boys = 4x and girls = 7x
Ratio = 4x*125/100 : 7x*115/100 = 100:161

16. When 40% percent of a number is added to another number the second number increases to its 20%. What is the ratio between the first and second number?
a) 2:1
b) 1:2
c) 2:3
d) 3:4
e) None of these

Answer – b) 1:2
Explanation :
(40/100)*a + b = (120/100)*b
a:b = 1:2

17. An amount of money is to be distributed among P, Q and R in the ratio of 5:4:7 respectively. If the total share of P and R is 3 times the share of Q, what is definitely Q’s share?
a) 2000
b) 4000
c) 6000
d) data inadequate
e) None of these

Answer – d) data inadequate
Explanation :
A total sum not given

18. Two candles of the same height are lighted at the same time. The first is consumed in 6 hours and second in 4 hours. Assuming that each candle burns at a constant rate, in how many hours after being light, the ratio between the first and second candles becomes 2:1?
a) 1 hour
b) 2 hour
c) 3 hour
d) 4 hour
e) None of these

Answer – c) 3 hour
Explanation :
Let the height of both candles is ‘h’ and let after t times the ratio between the height be 2:1
h – t*h/6 : h – t*h/4 = 2:1
t = 3

19. An employer reduces the number of his employees in the ratio of 7:4 and increases their wages in the ratio 3:5. State whether his bill of total wages increases or decreases and in what ratio.
a) increases 20:21
b) decreases 21:20
c) increases 21:22
d) decreases 22:21
e) None of these

Answer – b) decreases 21:20
Explanation :
Let initial employees be 7x and then 4x similarly initial wages be 3y and then 5y
so total wage = 21xy initially and then 20xy
so wages decreases and ratio = 21:20

20. Veena bought a watch costing Rs. 1404 including sales tax at 8%. She asked the shopkeeper to reduce the price of the watch so that she can save the amount equal to the tax. The reduction in the price of the watch is?
A. Rs.108
B. Rs.104
C. Rs.112
D. Rs.120
E. None of these

Answer – B. Rs.104
Explanation:
1.08x = 1404
x = 1300
The reduction of the price of the watch = 104

21. A Sales Executive gets a commission on total sales at 8%. If the sale is exceeded Rs.10,000 he gets an additional commission as a bonus of 4% on the excess of sales over Rs.10,000. If he gets the total commission of Rs.950, then the bonus he received is?
A. 40
B. 50
C. 36
D. 48
E. None of these

Answer – B. 50
Explanation:
Commission up to 10000 = 10000 * 8/100 = 800
Ratio = 2x:x ; Commission = 2x, Bonus = x ;
Bonus = 950 – 800 * 1/3 = 150 * 1/3 = 50

22. In college, there are 1800 students. Last day except for 4% of the boys all the students were present in the college. Today except for  5% of the girls all the students are present in the college, but in both the days number of students present in the college, were the same. The number of girls in the college is?
A. 1000
B. 400
C. 800
D. 600
E. 1200

Answer – C. 800
Explanation:
From Options;
let Number of girls = 800
Number of boys = 1000
96% of 1000 + 800 = 95% of 800 + 1000 [satisfies the condition; Check the condition with other options also]

23. In a library 60% of the books are in Hindi, 60% of the remaining books are in English rest of the books are in Malayalam. If there are 4800 books in English, then the total number of books in Malayalam are?
A. 3400
B. 3500
C. 3100
D. 3200
E.None of these

Answer – D. 3200
Explanation:
Let there are X books in the library.
Hindi books = 60% of X = 60X /100 = 0.6X
Remaining Books = X – 0.6X = 0.4X
English books = 40% of reaming books = 60% of 0.4X = 0.24X.
Malayalam Books = X-0.6X -0.24X = 0.16X
Given,
0.24X = 4800
X = 4800/0.24 = 20000
Malayalam Books = 0.16X = 0.16*20000 = 3200.

24. 80% of a small number is 4 less than 40% of a larger number. The larger number is 125 greater than the smaller one. The sum of these two numbers is
A. 325
B. 345
C. 355
D. 365
E. None of these

Answer – C. 355
Explanation:
smaller number = x; larger number = y
0.8x + 4 = 0.4y
4y – 8x = 40
y – x = 125
x = 115; y = 240
x + y = 355

25. 4, 4, 6, 12, 30, ?
1. 97
2. 92
3. 95
4. 98
5. 90

Answer – 5. 90
Explanation :
4 * 1 = 4
4 * 1.5 = 6
6 * 2 = 12
12 * 2.5 = 30
30 * 3 = 90

26. 10 5 5 10 40 ?
1.350
2.320
3.360
4.370
5.380

Answer – 2.320
Explanation :
10 * 0.5 = 5
5 * 1 = 5
5 * 2 = 10
10 * 4 = 40
40 * 8 = 320

27. 3, 5, ?, 27, 92, 349
1. 12
2. 18
3. 15
4. 10
5. 11

Answer – 4. 10
Explanation :
3 + 1² + 1 = 5
5 + 2² + 1= 10
10 + 4² + 1= 27

28. 1, 2, 6, 17, ?, 157.5
1. 40.5
2. 42.5
3. 49.5
4. 51.5
5. 50.5

Answer – 3. 49.5
Explanation :
1 * 1 + 1 = 2
2* 1.5 + 3 = 6
6 * 2 + 5 = 17
17 * 2.5 + 7 = 49.5
49.5 * 3 + 9 =157.5

29. 7, ?, 19, 45, 95, 177
1.8
2.5
3.6
4.7
5.9

Answer – 5. 9
Explanation :
7 + 1² + 1= 9
9 + 3² + 1= 19
19 + 5² + 1= 45……..

30. 9, 8, 15, ?, 175, 874
1.42
2.24
3.38
4.44
5.14

Answer – 4.44
Explanation :
9*1 – 1 = 8
8*2 – 1 = 15
15*3 – 1 = 44

30. A deer and a rabbit can complete a full round on a circular track in 9 minutes and 5 minutes respectively. P, Q, R and S are the four consecutive points on the circular track which are equidistant from each other. P is opposite to R and Q is opposite to S. After how many minutes will they meet together for the first time at the starting point, when both have started simultaneously from the same point in same direction?
1.15 minutes
2.25 minutes
3.35 minutes
4.45 minutes
5.None of these

Answer – 4.45 minutes
Explanation :
Time taken by a deer to complete one round = 9 minutes
Time taken by a rabbit to complete one round = 5 minutesThey meet together for the first time at the starting point = LCM of 9 and 5 = 45 minutes.
31. A cylindrical cistern whose diameter is 14 cm is partly filled with water. If a rectangular block of iron 22 cm in length, 14 cm in breadth and 7 cm in thickness is wholly immersed in water, by how many centimeter will the water level rise?
1. 10 cm
2. 14 cm
3. 12 cm
4. 15 cm
5. None of these
Answer – 2. 14 cm
Explanation :
Volume of the block = 22 * 14 * 7
Radius of the cistern = 14/2 = 7
Volume of the Cylinder = 22/7 * R2* h
22/7 * R2* h = 22/7 * 7 * 7 * h
22/7 * 7 * 7 * h = 22 * 14 * 7 => h = 14
32. A well with 28 m inside diameter is dug out 18 m deep. The earth taken out of it has been evenly spread all around it to a width of 21 m to form an embankment. Find the height of the embankment.

1.3 m
2.8 m
3.9 m
4.6 m
5.None of these

Answer – 1.3 m
Explanation :
22/7[(R2) – (r2)] * h = 22/7(7*7*18)
[(352) – (72)]h = 14 * 14 * 18
(42*28)h = 14*14*18
h = 3 m
33. A park is in the form of a square one of whose sides is 50 m. The area of the park excluding the circular lawn in the center of the park is 1884 m². The radius of the circular lawn is?
1. 21 m
2. 31 m
3. 41 m
4. 14 m
5. None of these

Answer – 4. 14m
Explanation :
Area of park = 50 x 50 = 2500 m²
Area of circular lawn = Area of park – area of park excluding circular lawn
= 2500 – 1884
= 616
Area of circular lawn = (22/7) x r² = 616 m²
⇒ r² = (616 x 7) / 22
= 28 x 7
= 2 x 2 x 7 x 7
∴ r = 14 m
34. Bharat borrowed Rs.180,000 on a condition that he had to pay 7.5% interest every year. He also agreed to pay the principal in equal annual installments over 21 years. After a certain number of years, however, the rate of interest has been reduced to 7%. It is also known that at the end of the agreed period, he will have paid in all Rs.2,70,900 in interest. For how many years does he pay at the reduced interest rate?

A. 10 years
B. 12 years
C. 13 years
D. 14 years
E. None of the Above

Answer – D. 14 years
Explanation:
x = interest paid at 7.5%
(21-x) years interest paid at 7%
((180000*x*7.5)/100) + ((180000*7*(21-x))/100) = 270900
x = 7
21 – 7 = 14 years he paid at the reduced interest rate.
35. Ankita borrows Rs.7000 at simple Interest from a lender. At the end of 3 years, she again borrows Rs.3000 and settled that amount after paying Rs.4615 as interest after 8 years from the time she made the first borrowing. what is the rate of interest?

A. 5.5%
B. 9.5%
C. 7.5%
D. 6.5%
E. None of the Above

Answer – D. 6.5%
Explanation:
SI for Rs.7000 for 8 years= (7000*r*8)/100
Again borrowed=3000
SI = (3000*r*5)/100
Total interest= [(7000*r*8)/100] + [(3000*r*5)/100] = 4615
560r + 150r = 4615
710r = 4615
r = 6.5%
36. Hari borrowed some money for one year at 6% per annum simple interest and after 18 months, he again borrowed the same money at a Simple Interest of 24% per annum. In both cases, he paid Rs.4704. Which of the following could be the amount that was borrowed by Hari in each case if interest is paid half-yearly?

A. 4000
B. 3000
C. 4400
D. 4200
E. None of the Above

Answer – D. 4200
Explanation:
12% for 6 months
x = Borrowed money
Take x =100%
112% of x = 4704
x = 4200

37. The difference between the total simple interest and the total compound interest compounded annually at the same rate of interest on a sum of money at the end of two years is Rs. 350. What is definitely the rate of interest percent per annum?
A.9,300
B.7600
C.12000
D.Data inadequate
E.None of these

Answer – D.Data inadequate
Explanation :
Difference = Pr2/(100)2
= (350×100×100)/(P×r2)
P is not given

38. Aswin invested an amount of Rs.9000 in a fixed deposit scheme for 2 years at CI rate 6% pa. How much amount will Aswin get on maturity of the fixed amount?
A.Rs.11,230
B.Rs.10,250
C.Rs.10,112
D.Data inadequate
E.None of these

Answer – C.Rs.10,112
Explanation :
Amount = 9000*106/100*106/100
= 9000*53/50*53/50
= 10,112

39. A sum of money invested for 7years in Scheme 1 which offers SI at a rate of 8% pa. The amount received from Scheme 1 after 7 years invested for 2 years in Scheme 2 which offers CI rate of 10% pa. If the interest received from Scheme B was Rs.1638. What was the sum invested in Scheme 1?
A.Rs.7500
B.Rs.5000
C.Rs.8200
D.Rs.9000
E.None of these

Answer – B.Rs.5000
Explanation :
SI =>Amount = x*8*7/100 + x = 56x+100x/100 = 156x/100 = 39x/25
CI=> 39x/25[(1+10/100)2 – 1] 1638 = 39x/25[121/100 – 1] = 39x/100[21/100] X = 1638*100*25/21*39 = 5000

40. Rs.5200 was partly invested in Scheme A at 10% pa CI for 2 years and Partly invested in Scheme B at 10% pa SI for 4 years. Both the schemes earn equal interests. How much was invested in Scheme A ?
A.Rs.1790
B.Rs.2200
C.Rs.3410
D.Rs.2670
E.None of these

Answer – C.Rs.3410
Explanation :
Amount invested in Scheme B = X
Amount invested in Scheme A = 5200 – x
X*10*4/100 = (5200-x)*21/100……………………[(1-10/100)2-1] = 21/100
40x/100 = (5200-x)*21/100
2x/5 = (5200-x)*21/100
200x = 5200*21*5 – x*5*21
200x = 546000 – 105x
305x = 546000
X = 1790
Scheme A = 5200 – 1790 = 3410

41. An alloy contains iron, copper, and zinc in the ratio of 3:4:2. Another alloy contains copper, zinc, and tin in the ratio of 10:5:3. If equal quantities of both alloys are melted, then the weight of tin per kg in the new alloy
a) 1/8 kg
b) 1/10 kg
c) 1/12 kg
d) 1/14 kg
e) None of these

Answer – c) 1/12 kg
Explanation :
I:C:Z = 3:4:2 (in first alloy) and C:Z:T = 10:5:3
Equal quantities are taken. So, I:C:Z = 6:8:4 in first alloy and C:Z:T = 10:5:3
I = 6
C = 8 + 10 = 18
Z = 4+5 = 9
T = 3
So weight of tin = 3/36 = 1/12

42. 8 liters are drawn from a flask containing milk and then filled with water. The operation is performed 3 more times. The ratio of the quantity of milk left and the total solution is 81/625. How much milk the flask initially holds?
a) 10ltr
b) 20ltr
c) 30ltr
d) 40ltr
e) None of these

Answer – b) 20ltr
Explanation :
let initial quantity be Q, and final quantity be F
F = Q*(1 – 8/Q)^4
81/625 = (1-8/Q)^4
3/5 = 1 – 8/Q
Q = 20

43. A 40-liter mixture contains milk and water in the ratio of 3:2. 20 liters of the mixture is drawn off and filled with pure milk. This operation is repeated one more time. At the end what is the ratio of milk and water in the resulting mixture?
a) 5:1
b) 6:1
c) 8:1
d) 9:1
e) None of these

Answer – d) 9:1
Explanation :
milk = 40*3/5 = 24 and water = 16 litres initially
milk = 24 – 20*3/5 + 20 = 32 – 20*4/5 + 20 = 36
water = 16 – 20*2/5 = 8 – 20*1/5 = 4

44. In how many different ways can the letter of the word ELEPHANT be arranged so that vowels always occur together?
a) 2060
b) 2160
c) 2260
d) 2360
e) None of these

Answer – b) 2160
Explanation :
Vowels = E, E, and A. They can be arranged in 3!/2! Ways
so total ways = 6!*(3!/2!) = 2160

45. There are 4 bananas, 7 apples and 6 mangoes in a fruit basket. In how many ways can a person make a selection of fruits from the basket.
a) 269
b) 280
c) 279
d) 256
e) None of these

Answer – c) 279
Explanation :
Zero or more bananas can be selected in 4 + 1 = 5 ways (0 orange, 1 orange, 2 orange, 3 orange, and 4 orange) similarly, apples can be selected in 7 +1 = 8 ways and mangoes in 6 +1 = 7 ways
so total number of ways = 5*8*7 = 280
but we included a case of 0 orange, 0 apples, and 0 mangoes, so we have to subtract this, so 280 – 1 = 279 ways

46. There are 15 points in a plane out of which 6 are collinear. Find the number of lines that can be formed from 15 points.
a) 105
b) 90
c) 91
d) 95
e) None of these

Answer – c) 91
Explanation :
From 15 points the number of lines formed = 15c2
6 points are collinear, number of lines formed by these = 6c2
So total lines = 15c2 – 6c2 + 1 = 91

47. In how many ways 4 Indians, 5 Africans and 7 Japanese be seated in a row so that all person of same nationality sits together
a) 4! 5! 7! 3!
b) 4! 5! 7! 5!
c) 4! 6! 7! 3!
d) can’t be determined
e) None of these

Answer – a) 4! 5! 7! 3!
Explanation :
4 Indians can be seated together in 4! Ways, similarly for Africans and Japanese in 5! and 7! respectively. So total ways = 4! 5! 7! 3!

48. A box contain 4 white, 3 blue and 2 black marbles. If 2 marbles are picked up at random. What is the probability that both of them are black ?
A.20
B.1/36
C.1/22
D.36
E.None of these

Answer – B.1/36
Explanation :
P = 2C2/9C2 = 1/36

49. An urn contains 6 maroon, 3 pink and 4 white balls. If three balls are drawn What is the probability that all are pink or white?
A.11/328
B.7/212
C.5/286
D.9/127
E.None of these

Answer – C.5/286
Explanation :
P =3C3/13C3 + 4C3/13C3
= 1/286 + 4/286 = 5/286

50. From a pack of 52 cards 3 cards are drawn one by one without replacements. Find the probability that both of them are king ?
A.132/1338
B.32/2340
C.1/5525
D.4/2755
E.None of these

Answer – C.1/5525
Explanation :
4/52*3/51*2/50 = 24/132600 = 4/22100 = 1/5525

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