## W.B.C.S. Preliminary Question Paper Mathematics

1. In a group of cows and hens, the number of legs are 14 more than twice the number of heads. How many cows are there?
(A) 7
(B) 12
(C) 5
(D) 10
2. In a chess tournament each of six players will play every other player exactly once. How many matches will be played in the tournament?
(A) 12
(B) 15
(C) 30
(D) 72
3. The age of father is twice that of elder son.Ten years hence, the age of the father will be three times that of the younger son. If the difference of ages of the two sons is 15 years, find the age of the father.
(A) 50 years
(B) 5S years
(C) 60 years
(D) 70 years
4. The average of 4 consecutive odd numbers is 64. Greatest of them is
(A) 67
(B) 5
(C) 71
(D) 69
5. A fruit seller after purchasing a basket of mangoes saw that some fruits are rotten. He incurred a loss of 5% after selling the rest of the mangoes at & 2,280. How much money did he spend in purchasing a basket of mangoes?
(A) 3,000
(B) 4,000
(C) 2,400
(D) 2,500
6. What Is the percentage of a cloth that should be excluded from 40 metre cloth so that the remaining portion is 7 metre?
(A) 17:5
(B) 19
(C) 82:5
(D) 81
7. In a camp there was food for 190 day 4000 men. After 30 days 800 men left. Remaining men will spend the remaining food in how many days?
(A) 250 days
(B) 230 days
(C) 200 days
(D) 170days
1. The velocity ratio of the hour hand and minute hand of a clock is
(A) 1 : 12
(B) 12 : 1
(C) 24 : 1
(D) 1 : 24
1. Ratio of the rms speed and the most probable speed for molecules in an ideal gas is
(A) √3 : 2
(B) 1 : √3
(C) √3 : √2
(D) √2 : √3
1. Manoj can type 100 pages of a report in 10 hours and Bobby can do the same in 15 hours. They worked together for 5 hours. The remaining work was completed by Lucy in 2 hrs. If they received Rs. 2,400 for whole work, Lucy got
(A) Rs. 300
(B) Rs.250
(C) Rs. 200
(D) Rs. 400
1. The ratio of 6 inch to 4 feet will be
(A) 1 : 6
(B) 1 : 4
(C) 3 : 2
(D) 1 : 8
1. A ladder is kept against a wall. The top of the ladder touches the wall at a height of 270 cm from the ground. The base of the ladder is 54 cm away from the wall on the ground. Find the length of the ladder.
(A) √53682
(B) √68164
(C) √75816
(D) √82547
1. 480 students out of 1500 are enrolled in NCC. What percentage of students are not there in NCC ?
(A) 70%
(B) 68%
(C) 73%
(D) 64%
1. A building which is 64 feet high cast a shadow of length 96 feet. The height of telephone tower, which cast a shadow of length 180 feet, under similar condition is
(A) 80 feet
(B) 100 feet
(C) 120 feet
(D) 90 feet
1. Mohan takes 6 hours to do a job. Laltu takes 10 hours to do the same job. How long should it take if Mohan and Laltu work together the same job ? 1. Given set (8, 3, 2) then follows
(A) (168, 15, 6)
(B) (95, 24, 5)
(C) (63, 8, 3)
(D) (15, 6, 5)
1. Given set (7,77, 140) then follows
(A) (9, 88,180)
(B) (6, 66, 120)
(C) (8, 88, 166)
(D) (4, 10, 160)
1. A train is 150 m long. lt is running at a speed of 41 kmph. A man is running at 11 kmph in the same direction as the train. In what time will it pass the man ? 1. What is the missing number ?

32, 19, 8, ?
(A) 3
(B) 12
(C) 5
(D) 1

1. What is the missing number ?
1, 2, 10, 37, 101, ?
(A) 320
(B) 226
(C) 206
(D) 402
1. A caterpillar crawls up a pole 75 inches high, starting from the ground. Each day it crawls up 5 inches and each night it slides down 4 inches. When will it first reach the top of the pole ?
(A) The 70th day
(B) The 71st day
(C) The 72nd day
(D) The 75th day
2. The smallest composite number is
(A) 1
(B) 2
(C) 4
(D) 3
3. Let x1, x2, _, x100 be 100 numbers such that xi + xi+1 = 100 for all i. If x10 = 1, then the value of x1 is
(A) 100
(B) 99
(C) 101
(D) 1
4. What number should come next in the sequence 6, 11, 21, 36, 56, — ?
(A) 78
(B) 81
(C) 82
(D) 86
5. In writing the numbers from 10 to 100, how many times is the digit 7 used ?
(A) 20
(B) 19
(C) 10
(D) 11
6. Choose the two correct numbers in the '•‘ marked places of the multiplication below. (A) 6, 8  (B) 4, 8 (C) 8, 6 (D) 8, 4
7. Find the odd one out :
(A) 27
(B) 64
(C) 81
(D) 125
8. The speed of an ant is 75 cm/sec. The ant travels in a day is
(A) 64800 m/day
(B) 648000 m/day
(C) 648000 cm/day
(D) 64800000 cm/day
9. The sum of all the internal angles of a hexagon is
(A) 720°
(B) 360°
(C) 180°
(D) 600°
10. What comes next in the sequence 1, 3, 7, 15, 31, 63, — ?
(A) 127
(B) 125
(C) 121
(D) 129
11. What number should come next in the sequence 6, 18, 72, 360, 2160, — ?
(A) 12120
(B) 13120
(C) 14120
(D) 15120
1. Which of the following interchanges of numbers would make the given equation correct ?
8 x 20 ÷ 3 + 9 - 5 = 38
(A) 3, 8
(B) 8, 9
(C) 3,  5
(D) 3,  9
1. An arc of length 121 cm makes an angle 77° at the centre of a circle. The radius of the circle is
(A) 110 cm
(B) 100 cm
(C) 90 cm
(D) 70 cm
1. The arithmetic mean of the numbers 9, 12, 15, 18, 20, 22 is increased by 1, if 15 is replaced by
(A) 16
(B) 17
(C) 19
(D) 21
1. The percentage increase in the surface area of a cube when each side doubled is
(A) 25%
(B) 50%
(C) 150%
(D) 300%
1. Find the LCM of 4/3, 8/9 and  3/5.
(A) 20
(B) 24
(C) 1/24
(D) 1/20
1. At magnetic poles, the angle of dip is
(A) 45°
(B) 30°
(C) Zero
(D) 90°
1. If, + stands for division; x stands for addition; - stands for multiplication; ÷ stands for subtraction, which of the following equation is correct ?
(A) 36 + 6 - 3 x 5 ÷ 3 = 24
(B) 36 x 6 + 7 ÷ 2 - 6 = 20
(C) 36 ÷ 6 + 3 x 5 - 3 = 40
(D) 36 - 6 + 3 x 5 ÷ 3 = 74
2. What is the ratio of the perimeter of the shaded region to the circumference of the circle ? (A) 3/ 4
(B) 4+π/4π
(C) 2π/4+π  (D) 4+π/2π
3. Which of the following is the correct order ?
(A) 2 < 2.02 < 2.002 < 2.222
(B) 002 < 2.02 < 2.2 < 2.222
(C) 02 < 2.22 < 2.002 < 2.222
(D) None of the above
4. If per cent increase in radius of cylinder is 300. Then volume of the cylinder changes by how much percent ? [Keeping height of the cylinder constant]
(A) 1500%
(B) 600%
(C) - 600%
(D) None of the above
5. The difference of the ages of Rohit and Axar is 12 years. The ratio of their ages is 3 : 5 . The age of Axar is
(A) 32 years
(B) 24 years
(C) 28 years
(D) 30 years
6. P is greater than Q by 60% and greater than R by 30%. The ratio of Q and R is
(A) 1 : 2
(B) 2 : 1
(C) 13 : 16
(D) 16 : 13
7. A dishonest dealer defrauds his seller and buyer by using forged weights to the extent of 20%. His true gain percent is
(A) 20%
(B) 40%
(C) 44%
(D) 50%
8. In a mixture ratio of first and second liquid is 2 : 3 and in another mixture ratio of those two liquids is 5 : 4. Ratio in which the two mixture be mixed so that quantity of two liquids in the new mixture of two liquid in the new mixture be equal is
(A) 2 : 5
(B) 3 : 7
(C) 5 : 9
(D) 9 : 11
9. A clock fixed on the wall shows a time of 4.25. The time shown by its image on a plane mirror fixed to the opposite wall will be
(A) 8.35
(B) 7.25
(C) 7.35
(D) 8.25
1. If a * b = ab + b - a, what is the value of c such that c* (2*5) = 97 ?
(A) 8
(B) 7
(C) 3
(D) 91
1. If a ÷ b means 'a to be added to b' and a x b means 'a to be divided by b', then the value of (14 ÷ 7) ÷ (14 x 7) is
(A) No value
(B) 1
(C) 23
(D) 7
1. If ⊕ b = L.C.M. of a and b, a ⊗ b = G.C.M. of a and b, then (12 ⊗ 16) ⊕ (24 ⊗ 36) will be
(A) 4
(B) 2
(C) 12
(D) 16
1. The 6th term in the following series ab2 + bc2 + cd2 + de2 + ........
(A) ef2
(B) f2c
(C) fg2
(D) g2f
1. Due to rotten fish, a fish trader forces to sell in 10 % loss. If the purchase value is Rs. 250, the selling price will be
(A) Rs. 225
(B) Rs. 240
(C) Rs. 235
(D) Rs. 230
1. A man won Rs. 60,000 in a lottery. 35% of the money was taken by the Govt, as a tax. He actually receives
(A) Rs. 21,000
(B) Rs. 39,000
(C) Rs. 18,000
(D) Rs. 40,000
1. Due to some error in the weighting machine, Aahana's weight was shown 72 kg as against the actual value of 80 kg. The percentage error is
(A) 9%
(B) 8%
(C) 10%
(D) None of the above
1. A man starts from his office and goes 8 km East. Then he turns to the left and walks for 3 km. Again he turns left and walks for 8 km. At what distance is he from the starting point ?
(A) 5 km
(B) 4 km
(C) 6 km
(D) 3 km
1. 40% of A is 60% of B. A : B will be
(A) 2 : 3
(B) 3 : 2
(C) 7 : 8
(D) 8 : 7
1. Ratio of Bus and Train fare is 4 : 5. If Bus fare increases by 10% and Train fare increases by 20%, new ratio of Bus and Train fare will be
(A) 15 : 11
(B) 7 : 13
(C) 11 : 15
(D) 5 : 9
1. In an examination, 35% students fail in Math­ematics, 15% fail in English. If 10% fail in both, the pass percent is
(A) 60%
(B) 40%
(C) 35%
(D) 25%
1. A person, standing on a railway platform 120 meters long, notices that a train, which passed him in 5 seconds, passed completely through the station in 15 seconds. The length of the train is
(A) 50 m
(B) 60 m
(C) 100 m
(D) 55 m
1. A man deposited Rs. 3,000 in a Bank and Rs. 2,500 in a Post Office. Rate of interest of Bank is 1/2% more than that of Post Office. If he gets Rs. 235 as total interest at the end of the year, the rate of interest of Post Office is
(A) 2%
(B) 2  1/2%
(C) 4%
(D) 4  1/2%
1. The population of a district increases by 4% during the first year and decreases by 5% during the second year. If the present population of a district is 494000, two years ago it was
(A) 475000
(B) 500000
(C) 525000
(D) 600000
1. A box contains one red ball, one blue ball and one green ball. The ratio of the weight of the red and blue ball is 5 : 6 and that of blue and green ball is 5 : 4. If the blue ball weights 60g, the weight of the green ball is
(A) 48 g
(B) 50 g
(C) 40 g
(D) 55 g
1. The greatest number consisting of five digits which is a perfect square is —
(A) 99866
(B) 99856
(C) 99846
(D) 99876
1. A profit of 25% is made by selling an article for Rs. 30. If the article was sold for Rs. 33.60, the profit would have been
(A) 30%
(B) 35%
(C) 40%
(D) 45%
1. The incomes of A and B are in the ratio 3 : 2 and their expenditures are in the ratio 5 : 3. If each saves Rs. 1,000, then B's income is-
(A) Rs. 3,000
(B) Rs. 4,000
(C) Rs. 6,000
(D) Rs. 800
1. There are 100 questions in a question paper, each carrying 2 marks. But there is a negative marking. 1mark is deducted for each question answered incorrectly. A student answering all the questions got 80 marks. The number of questions correctly answered by him is-
(A) 70
(B) 60
(C) 80
(D) 75
1. What is the least number to be added to 1500 to make it a perfect square ?
(A) 12
(B) 15
(C) 21
(D) 25
1. If 17200 is divided by 18, the remainder is —
(A) 16
(B) 17
(C) 5
(D) 1
1. The next term in the sequence  4, 10, 22, 46, ... is —
(A) 66
(B) 76
(C) 56
(D) 94
1. The speeds of three cars are in the ratio 2 : 3 : 4. The ratio between the time taken by these cars to travel the same distance is -
(A) 2 : 3 : 4
(B) 4 : 3 : 6
(C) 3 : 4 : 6
(D) 6 : 4 : 3
1. How many 9's are sandwiched between 6 and 7 in 696996676979669779667 ?
(A) 2
(B) 3
(C) 4
(D) 5
1. A sum of money kept in a bank amounts to Rs. 1,240 in 4 years and Rs. 1,600 in 10 years at simple interest. Find the sum.
(A) Rs. 1,000
(B) Rs. 800
(C) Rs. 1,950
(D) Rs. 1,100
1. If 3 mangoes are sold for the cost price of Rs. 4, the profit is—
(A) 16 1/3 %
(B) 33  1/4 %
(C) 33  1/3 %
(D) 40  1/2 %
1. How many ways a captain and a vice-captain can be selected from a team of 11 players ?
(A) 99
(B) 110
(C) 98
(D) 22
1. A clock strikes once at 1 o' clock, twice at 2 o' clock, ......... twelve times at 12 o' clock. How many times will the bell strike in course of 2 days ?
(A) 78
(B) 264
(C) 312
(D) 144
1. A short day plant has a critical day length of 14 hours. It will flower when the day length is :
(A) 15 hours
(B) 18 hours
(C) 12 hours
(D) 16 hours
1. In a class of 60 where boys are twice that of girls, Ram ranked 17th from the top. If there are 9 boys ahead of Ram, how many girls are after him in the rank ?
(A) 26
(B) 13
(C) 12
(D) 33
1. Flight to Mumbai leaves every 5 hours. At the information counter I learnt that the flight took off 25 minutes before. If the time now is 10.45 a.m., what is the time for the next flight ?
(A) 2.20 a.m.
(B) 3.30 a.m.
(C) 3.55 P.m.
(D) 3.20 P.m.
1. What should come in the place of question mark in the following series ?
3, 8, 6, 14, ?, 20
(A) 11
(B) 10
(C) 8
(D) 9
1. Simantika sold two radios for Rs. 2000 each. On one she gains 16 % and on the other she losses 16 %. Find her gain or loss per cent in the whole transaction.
(A) 5.28
(B) 2.56
(C) 4.68
(D) 8.01
1. The difference between 78 % of a number and 59 % of the number is 323. What is 62% of that number ?
(A) 1054
(B) 1178
(C) 1159
(D) 1037
1. The population of a city increases at the rate of 15 % pa. If its population was 4000 at the end of 2009. Find its population at the end of 2011 .
(A) 5390
(B) 4780
(C) 5290
(D) 8256
1. How many iron rods each of length 14 m. and diameter 4 cm. can be made out of 0.88 m3 of iron ?
(A) 45
(B) 50
(C) 65
(D) 80
1. 879 x 439 + 879 x 321 = ?
(A) 668040
(B) 669040
(C) 667030
(D) 666040
1. 48 % of the first number is 60 % of the second number. What is the ratio of the first number to the second number ?
(A) 4 : 7
(B) 3 : 4
(C) 5 : 4
(D) 3 : 2
1. The product of two consecutive odd numbers is 6723. What is the greater number ?
(A) 89
(B) 85
(C) 91
(D) 83
1. 60 : 15 :: * : 1/4 , Find  *
(A) 1.1
(B) 2.1
(C) 1
(D) 0.1
1. What is the value of two-fifth of 60 % of 320 ?
(A) 76.6
(B) 38.4
(C) 76.8
(D) 37.4
1. The difference of the aqes of Riju and Rivu is 12 years. The ratio of their ages is 3 : 5. The age of Rivu is
(A) 32 years
(B) 24 years
(C) 28 years
(D) 30 years
1. Average of 5 numbers is 50. If every number is multiplied by 2, find the average.
(A) 52
(B) 48
(C) 100
(D) 25
1. A boat is rowed down stream at 35 Km./hr. and up stream at 17 km./hr. Find the speed of the stream.
(A) 4 km./hr.
(B) 9 km./hr.
(C) 6 km./hr.
(D) 7 km./hr.
1. In a row of boys, Syamantaka is 7th from the left and Venkat is 12th from the right. If they interchange their positions, Syamantaka becomes 22nd from the left. How many boys are there in the row ?
(A) 29
(B) 31
(C) 33
(D) 34

2. If the difference of the square of two natural numbers is 19, find the sum of the squares of these numbers.
(A) 220
(B) 169
(C) 189
(D) 181

3. A circular wire of radius 42 cm. is cut and bent in the form of an rectangle whose sides are in the ratio of 6 : 5. Find the smaller side of the rectangle.
(A) 120 cm.
(B) 144 cm.
(C) 177 cm.
(D) 110 cm.
1. Triangle ABC is rightangled at B. If AB = 24 mm. and BC = 7 mm. then AC = ?
(A) 31 mm
(B)21 mm
(C) 35mm
(D) 25mm

2. Every angle of a regular hexagon is
(A) 90°
(B) 120°
(C) 135°
(D) 145°
1. Find the value of K for which the lines
5x + 3y + 2 = 0 and 3x - Ky + 6 = 0 are perpendicular.
(A) 5
(B) 32
(C) 14
(D) 6
1. The half life period of an isotope is 2 hours. After 6 hours what fraction of the initial quantity of the isotope will be left behind ?
(A) 1/6
(B) 1/3
(C) 1/8
(D) 1/4
1. The value of (A) 2.0
(B) 1.75
(C) 1.0
(D) 2.5
1. The least integer multiplied by 112 to make the result a perfect square is —
(A) 2
(B) 7
(C) 3
(D) 11
1. The least integer multiplied by 112 to make the result a perfect square is —
(A) 2
(B) 7
(C) 3
(D) 11
1. A square lamina is made from three square laminae, whose sides are 2 cm, 3 cm, and 6 cm. The side of the new square lamina is —
(A) 11 cm
(B) 10 cm
(C) 7 ciri
(D) 9 cm
1. Two numbers are in the ratio 7 : 9 and their difference is 6. The numbers are —
(A) 49.55
(B) 91.97
(C) 21.27
(D) 42.54
1. A man sells an article at a loss of 10%. If he had sold it for Rs. 40 more he would have gained 10%. The cost price of the article is —
(A) Rs. 250
(B) Rs. 200
(C) Rs. 300
(D) Rs. 180
1. At every forty five minutes a train crosses the Maharaja Gate. Just 10 minutes ago one train crossed the gate and next will be crossing at 9.35 A. M. What is time now ?
(A) 9-15 A.M.
(B) 9-00 A.M.
(C) 9-05 A.M.
(D) 9-10 A.M.
1. The difference between two numbers is 15 and the difference between their square root is 1. The smaller number is —
(A) 81
(B) 49
(C) 36
(D) 25
1. 12 : 20 = * : 25, the missing term is —
(A) 16
(B) 24
(C) 18
(D) 15
1. Manish can type 500 words in 10 minutes and Rana can type 400 words in 10 minutes. In how many minutes they can together type 3600 words ?
(A) 60 minutes
(B) 45 minutes
(C) 40 minutes
(D) 38 minutes
1. The area of a sphere in sq.cm. is 3 times its volume in cu.cm. The diameter of the sphere is :
(A) 1 cm
(B) π cm
(C) 2 cm
(D) 3 cm
1. The value of A/625 + J & 25 + 0-0625 is :
(A) 27-75
(B) 25-25
(C) 27-25
(D) 25-75
1. A profit of 25% is made by selling an article for Rs. 30. If the article was sold for Rs 33.60, the profit would have been
(A) 30%
(B) 35%
(C) 40%
(D) 45%
1. Three times the first of three consecutive odd integers is 3 more than twice the third . What is the third integer ?
(A) 9
(B) 15
(C) 13
(D) 11
1. If a four digit number a381 is divisible by 11, what is the value of a ?
(A) 5
(B) 6
(C) 7
(D) 8
1. A sum of money is kept in a bank account to Rs. 1240 in 4 years and Rs. 1600 in 10 years at simple interest. Find the sum :
(A) Rs. 1000
(B) Rs. 800
(C) Rs. 1050
(D) Rs. 1100
1. A clock strikes once at 1 O'clock , twice at 2 O'clock ,....., twelve times at 12 O'clock . How many times will the bell be struck in course of 2 days ?
(A) 78
(B) 264
(C) 312
(D) 144
1. The salary of Anup is 30% more than that of Buran. Find by what percentage is the salary of Barun less than that of Anup
(A) 26.12%
(B) 21.23%
(C) 23.07%
(D) 27.03%
1. A captain and a vice-captain are to be chosen out of a team having 11 players. How many ways are there to do this ?
(A) 99
(B) 110
(C) 90
(D) 22
1. Define the following function : f(x, y) = (x+y) ÷ 2, g(x, y) = x2 - y2 and h(x, y) = (x - y) ÷ 2, Which of the followings has a value 0.25 for x = 0 and y = 0.5 ?
(A) f(x,y) g(x,y)
(B) g(x,y)
(C) f(x,y)
(D) f(x,y) + g(x,y)
1. A can do a piece of wark in 10 days and B can do the same work in 20 days . With the help of C , they finish the work in 5 days . How many days will it take for C alone to finish the worrk ?
(A) 10 days
(B) 15 days
(C) 20 days
(D) 5 days
1. The incomes of A and B are in ratio of 3 : 2 and their expenditure are in a ratio 5 : 3, If each saves Rs. 1000, then B's income is :
(A) Rs. 3000
(B) Rs. 4000
(C) Rs. 600
(D) Rs. 800
1. The speed of three cars are in ratio of 2 : 3 : 4. The ratio between the times taken by these cars to travel the same distance is :
(A) 2 : 3 : 4
(B) 4 : 3 : 6
(C) 3 : 4 : 6
(D) 6 : 4 : 3
1. A man walks 10 metres in front and 10 metres to the right. Then every time turning to his left, he walks 5, 15 and 15 metres respectively. How far is he now from his starting point ?
(A) 10 metres
(B) 5 metres
(C) 15 metres
(D) 20 metres
1. After drawing the salary, a man deposit 10% of the sum in a bank and then paid 4% of the remainder as house rent. If he draws Rs. 5000, the sum he paid as house rent is :
(A) Rs. 160
(B) Rs. 250
(C) Rs. 180
(D) Rs. 225
1. There are 100 question in the question paper each carrying 2 marks. But there is a negative marking; 1 mark is deducted from each question answered incorrectly. A student answering all the questions got 80 marks. The number of questions correctly answerd by him is :
(A) 70
(B) 60
(C) 80
(D) 75
1. If 3 mangoes are sold for cost price of Rs. 4, the profit is : 2. Ther next term in the sequence 4, 10, 22, 46, ... is
(A) 66
(B) 76
(C) 56
(D) 94
1. The expression of average speed is gaseous molecule is : Shopping Cart