SSB Question Paper - Elementary Mathematics
1. What is the last digit in the expansion of 34798
2. What is the sum of the digits of the least number which, when divided by 52, leaves 33 as remainder; when divided by 78, leaves 59 and when divided by 117, leaves 98 as remainder?
3. If f (x) ang(x) are d t wo polynomas with integral coefficients which vansa , th en wase factor of HCF of f (x) and g(x) ? .
(b) x - 2
4. The ratio between the ages of A and B is 2 : 5. After 8 years, their ages will be in the ratio 1:2. What is the difference between' their present ages?
(a) 20 years
(b) 22 years
(c) 24 years
(d) 25 years
5. A mixture contains milk and water in the ratio 5 : 1. On adding 5 litres of water, the ratio ofi milk and water becomes 5 : 2. What is the quantity of milk in the original mixture?
(a) 5 litres
(b) 25 litres
(c) 27.5 litres
(d) 32.5 litres
6. A person spends 30% of monthly salary on rent, 25% on food, 20% on children's education and 12% on electricity, and the balance of Rs 1,040 on the remaining items. What is the monthly salary of the person?
(a) Rs 8,000
(b) Rs 9,000
(c) Rs 9,600
(d) Rs 10,600
7. A father and his son start at a point A with speeds of 12 kmph and 18 kmph respectively, and reachanother point B. If his son starts 60 minutes after his father at A and reaches B 60 minutes before his ather, what is the distance between A and B?
(a) 90 km
(b) 72 km
(c) 36 km
(d) None of the above
8. Two trains of lengths 100 in And 150 m are traveling in opposite directions at speeds of 75 kmph and 50 Icrnph respectively. What is the time taken by them to cross each other?
(a) 7-4 s
(b) 7.2 s
(c). 7 s
9. If the 14th term of an arithmeticseries is 6 and 6th term is . 14, then what is the 95th term?
(a) - 75
(d) -- 80
10. If k is any even positive integer, then (k 2 + 2k) is
(a) divisible by 24
(b) divisible by 8 but may not be divisible by 24
(c) divisible by 4 but may not be divisible by 8
(d) divisible by 2 but may not be divisible by 4
11. If salary of X is 20% more than salary of Y, then by how much percentage is salary of Y less than X?
(b) 2 0
12. Which one of the following is a non-terminating and repeatingdecimal?
13. A can do a piece of work in 24 days. If B is 60% more efficient than A, then how many days does B require to do the same work?
14. A sum of money tent on simple interest trebles itself in 15 years and 6 months. In how many years will it be doubled?
(a) 6 years and 3 months
(b) 7 years and 9 months
(c) 8 years and 3 months
(d) 9 years and 6 months
15. On selling an article for Rs 240, a trader loses 4%. In order to gain 10%, he must sell the article for
(a) Rs 275
(b) Rs 280
(c) Rs 285
(d) Rs 300
16. In a class, the number of boys is more than the number of girls by 12% of the total strength. What is the ratio of number of boys to that of girls?
(a) 11 : 14
(b) 14 :11
(c) 28 :25
(d) 25 28
17. Three numbers are in the ratio 3 : 2 : 5 and the sum of their squares is 1862. What are the three numbers?
(a) 18, 12, 30
(b) 24, 16, 40
(c) 15, 10, 25
(d) 21, 14, 35
18. The product of a rational number and an irrational number is
(a) a natural number
(b) an irrational number
(c) a composite number
(d) a rational number
19. If sin 0 + cos 0 = 1, then what is the value of sin 0 cos 0 ?
20. The shadow of a tower is 15 m when the Sun's altitude is 30°. What is the length of the shadow when the Sun's altitude is X60° ?
(a) 3 m
(b) 4 m
(c) 5 m
(d) 6 m
21. In a triangle, if sum of two angles is equal to the third angle (considering the interior angles only), then the triangle is
22. Let PAB be a secant to a circle intersecting at points A and B, and PC is a tangent. Which one of the following is correct?
(a)The area of rectangle with PA,PB as sides is equal to the area of square with PC as side
(b) The area of rectangle with PA,PC as sides is equal to the area of square with PB as side
(c) The area of rectangle with PC4 PB as sides is equal to the area of square with PA as side
(d) The perimeter of rectangle with PA, PB as sides is equal to the perimeter of square with PC as side
23. What is the radius of the circle inscribed in a triangle having side lengths 35 cm,. 44 cm and 75 cm?
(a) 3 cm
(b) 4 cm
(c) 5 cm
(d) 6 cm
24. A rectangular area of 6 square metres is to be painted on a 3 m x 4 m board leaving a border of uniform width on all sides. What should be the width of the border?
(a) 0.25 m
(b) 0.5 m
(c) 1 m
(d) 3 m
25. A solid cylinder of height 9 m has its curved surface area equal to one-third of the total surface area. What is the radius of the base?
(a) 9 m
(b) 18 m
(c) 27 m
(d) 30 m
26. The diameters of 'two circles are 18 cm and 8 cm! The distance between their centres is 13 cm. What is the number of common tangents?
(d) None of the above
27. If the height of a cone'is increased by 50%, then what is the percentage increase in the volume of the cone?
28. A wheel of a bicycle has inner diameter 50 cm and thickness 10 cm. What is the speed of the bicycle if it makes 10 revolutions in 5 seconds?
(a) 5.5 m/s
(b) 4.4 m/s
(c) 3-3 m/s
(d) 2.2 m/s
29. A wire of length 36 cm is bent in the form of a semicircle. What is theradius of the semicircle?
(a) 9 cm
(b) 8 cm
(c) 7 cm
(d) 6 cm
30. In order to fix an electric pole along a roadside, a pit with dimensions 50 cm x 50 cm is dug with the help of a spade. The pit is prepared by removing earth by 250 strokes of spade. If one stroke of spade removes 500 cm3 of earth, then what is the depth of the pit?
(a) 2 m
(b) 1 m
(c) 0.75 in
(d) 0-5 in