Prepare for bank exams with these sample question papers. SBI PO, SBI Clerk, SBI Specialist Officer Bank exam sample question papers for the year 2016. Prepare for the bank exams with these bank exam papers.

1. The street of a city are arranged like the lines of a chessboard , there are m street running north and south and n east and west. Find the no. ways in which a man can travel from N.W to the S.E corner, going by the shortest possible distance.

2. How many different arrangement can be made out of the letters in the ex-pression a^3b^2c^4 when written at full length?

3. How many 7-digit numbers exist which are divisible by 9 and whose last but one digit is 5?

4. You continue flipping a coin until the number of heads equals the number of tails. I then award you prize money equal to the number of flips you conducted .How much are you willing to pay me to play this game?

5. Consider those points in 3-space whose three coordinates are all nonnegative integers, not greater than n. Determine the number of straight lines that pass through n of these points.

6 Four figures are to be inserted into a six-page essay, in a given order. One page may contain at most two figures. How many different ways are there to assign page numbers to the figures under these restrictions?

7. How many (unordered) pairs can be formed from positive integers such that, in each pair, the two numbers are coprime and add up to 285?

8. ( 1+ x) ^ n – nx is divisible by

A. x B. x.x C. x.x.x. D. None of these

9. The root of the equation (3-x)^4 + (2-x)^4 = (5-2x)^4 are

a. ALL REAL B. all imaginary C. two real and 2 imaginary D. None of these

10. The greatest integer less than or equal to ( root(2)+1)^6 is

A. 196 B.197 C.198 D.199.

11. How many hundred-digit natural numbers can be formed such that only even digits are used and any two consecutive digits differ by 2?

12. If x1 , x2, x3 are the root of x^3-1=0 , then

A. x1+x2+x3 not equal to 0 B. x1.x2.x3 not equal to 1 C.(x1+x2+x3)^2 = 0 D. None of these

13. How many different ways are there to arrange the numbers 1,2,...,n in a single row such that every number, except the number which occurs first, is preceded by at least one of its original neighbours?

14. There are N people in one room. How big does N have to be until the probability that at least two people in the room have the same birthday is greater than 50 percent? (Same birthday means same month and day, but not necessarily same year.)

15. A 25 meter long wound cable is cut into 2 and 3 meter long pieces. How many different ways can this be done if also the order of pieces of different lengths is taken into account?

16. You are presented with a ladder. At each stage, you may choose to advance either one rung or two rungs. How many different paths are there to climb to any particular rung; i.e. how many unique ways can you climb to rung "n"? After you've solved that, generalize. At each stage, you can advance any number of rungs from 1 to K. How many ways are there to climb to rung "n"?

17. Find the no. of rational number m/n where m ,n are relatively prime positive no. satisfying m<n and mn = 25!..?

18. The master of a college and his wife has decided to throw a party and invited N guest and their spouses. On the night of the party, all guests turned up with their spouse, and they all had a great time. When the party was concluding, the master requested all his guests (including his wife, but not himself) to write down the number of persons they shook hands with, and to put the numbers in a box. When the box was opened, he was surprised to find all integers from 0 to 2N inclusive. Assuming that a person never shake hands with their own spouse and that no one lied, how many hands did the master shake?

19. A rectangle OACB with 2 axes as sides, the origin O as a vertex is drawn in which length OA is 4 time the width OB . A circle is drawn passing through the point B and C touching OA at its min-point, thus dividing the rectangle into 3 parts. Find the ratio of areas of these 3 parts. ?

20. A rod is broken into 3 parts ; the 2 break point are chosen at random.Find the probability that the 3 parts can be joined at the ends to form a triangle.?

21. The distance between town A and B is 1000 k.m. A load containing 10000 kg of jaggery is to be transferred from A to B. A camel is the only source of transport. However, the camel is unique. It can maximum carry a load of 1000 kgs. Further, for it is a voracious eater, and for every k.m. it travels, it eats a kilo of the jaggery which it is carrying. What is the maximum amount of jaggery that can be transferred from A to B ?

22. The ticket office at a train station sells tickets to 200 destinations. One day, 3800 passengers buy tickets. Then minimum no of destinations receive the same number of passengers is

A.6 B.5 C.7 D.9

23. A hexagon with sides of length 2, 7, 2, 11, 7, 11 is inscribed in a circle. Find the radius of the circle.

24.On the sides of an acute triangle ABC are constructed externally a square, a regular n-gon and a regular m-gon (m, n > 5) whose centers form an equilateral triangle. Prove that m = n = 6, and find the angles of ABC.

25. The area of triangle formed by the point (p,2-2p) , (1-p,2p) and (-4-p,6-2p) is 70 units. How many integral values of p are possible.?

A. 2 B. 3 C. 4 D. None of these

1. The street of a city are arranged like the lines of a chessboard , there are m street running north and south and n east and west. Find the no. ways in which a man can travel from N.W to the S.E corner, going by the shortest possible distance.

2. How many different arrangement can be made out of the letters in the ex-pression a^3b^2c^4 when written at full length?

3. How many 7-digit numbers exist which are divisible by 9 and whose last but one digit is 5?

4. You continue flipping a coin until the number of heads equals the number of tails. I then award you prize money equal to the number of flips you conducted .How much are you willing to pay me to play this game?

5. Consider those points in 3-space whose three coordinates are all nonnegative integers, not greater than n. Determine the number of straight lines that pass through n of these points.

6 Four figures are to be inserted into a six-page essay, in a given order. One page may contain at most two figures. How many different ways are there to assign page numbers to the figures under these restrictions?

7. How many (unordered) pairs can be formed from positive integers such that, in each pair, the two numbers are coprime and add up to 285?

8. ( 1+ x) ^ n – nx is divisible by

A. x B. x.x C. x.x.x. D. None of these

9. The root of the equation (3-x)^4 + (2-x)^4 = (5-2x)^4 are

a. ALL REAL B. all imaginary C. two real and 2 imaginary D. None of these

10. The greatest integer less than or equal to ( root(2)+1)^6 is

A. 196 B.197 C.198 D.199.

11. How many hundred-digit natural numbers can be formed such that only even digits are used and any two consecutive digits differ by 2?

12. If x1 , x2, x3 are the root of x^3-1=0 , then

A. x1+x2+x3 not equal to 0 B. x1.x2.x3 not equal to 1 C.(x1+x2+x3)^2 = 0 D. None of these

13. How many different ways are there to arrange the numbers 1,2,...,n in a single row such that every number, except the number which occurs first, is preceded by at least one of its original neighbours?

14. There are N people in one room. How big does N have to be until the probability that at least two people in the room have the same birthday is greater than 50 percent? (Same birthday means same month and day, but not necessarily same year.)

15. A 25 meter long wound cable is cut into 2 and 3 meter long pieces. How many different ways can this be done if also the order of pieces of different lengths is taken into account?

16. You are presented with a ladder. At each stage, you may choose to advance either one rung or two rungs. How many different paths are there to climb to any particular rung; i.e. how many unique ways can you climb to rung "n"? After you've solved that, generalize. At each stage, you can advance any number of rungs from 1 to K. How many ways are there to climb to rung "n"?

17. Find the no. of rational number m/n where m ,n are relatively prime positive no. satisfying m<n and mn = 25!..?

18. The master of a college and his wife has decided to throw a party and invited N guest and their spouses. On the night of the party, all guests turned up with their spouse, and they all had a great time. When the party was concluding, the master requested all his guests (including his wife, but not himself) to write down the number of persons they shook hands with, and to put the numbers in a box. When the box was opened, he was surprised to find all integers from 0 to 2N inclusive. Assuming that a person never shake hands with their own spouse and that no one lied, how many hands did the master shake?

19. A rectangle OACB with 2 axes as sides, the origin O as a vertex is drawn in which length OA is 4 time the width OB . A circle is drawn passing through the point B and C touching OA at its min-point, thus dividing the rectangle into 3 parts. Find the ratio of areas of these 3 parts. ?

20. A rod is broken into 3 parts ; the 2 break point are chosen at random.Find the probability that the 3 parts can be joined at the ends to form a triangle.?

21. The distance between town A and B is 1000 k.m. A load containing 10000 kg of jaggery is to be transferred from A to B. A camel is the only source of transport. However, the camel is unique. It can maximum carry a load of 1000 kgs. Further, for it is a voracious eater, and for every k.m. it travels, it eats a kilo of the jaggery which it is carrying. What is the maximum amount of jaggery that can be transferred from A to B ?

22. The ticket office at a train station sells tickets to 200 destinations. One day, 3800 passengers buy tickets. Then minimum no of destinations receive the same number of passengers is

A.6 B.5 C.7 D.9

23. A hexagon with sides of length 2, 7, 2, 11, 7, 11 is inscribed in a circle. Find the radius of the circle.

24.On the sides of an acute triangle ABC are constructed externally a square, a regular n-gon and a regular m-gon (m, n > 5) whose centers form an equilateral triangle. Prove that m = n = 6, and find the angles of ABC.

25. The area of triangle formed by the point (p,2-2p) , (1-p,2p) and (-4-p,6-2p) is 70 units. How many integral values of p are possible.?

A. 2 B. 3 C. 4 D. None of these

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