Model Question Paper
Combined Defence Services (I) Exam, 2014
Q1. What is the number of integral solutions of the equations HCF (a, b) = 5 and a + b = 65 ?
(a) None
(b) Infinitely many
(c) Less than 65
(d) Exactly one
Q2. The difference of two consecutive cubes
(a) is odd or even
(b) is never divisible by 2
(c) is always even
(d) None of the above
Q3. The product of four consecutive natural numbers plus one is
(a) a non-square
(b) always sum of two square numbers
(c) a square
(d) None of the above
Q4. For any integers 'a’ and ‘b’ with HCF (a, b) = 1, what is HCF (a + b, a - b) equal to ?
(a) It is always 1
(b) It is always 2
(c) Either 1 or 2
(d) None of the above
Q5. The expression 2x3 + x2 - 2x - 1 is divisible by
(a) x + 2
(b) 2x + 1
(c) x - 2
(d) 2x - 1
Q6.A positive number, when increased by 10, equals 200 times its reciprocal. What is that number ?
(a) 100
(b) 10
(c) 20
(d) 200
Q7. x3 + 6x2 + 11x + 6 is divisible by
(a) (x + 1) only
(b) (x + 2) only
(c) (x + 3) only
(d) All of the above
Q8. The present age of Ravi's father is four times Ravi's present age. Five years back he was seven times as old as Ravi was at that time. What is the present age of Ravi's father ?
(a) 84 years
(b) 70 years
(c) 40 years
(d) 35 years
Q9.The average age of male employees in a firm is 52 years and that of female employees is 42 years. The mean age of all employees is 50 years. The percentage of male and female employees are respectively
(a) 80% and 20%
(b) 20% and 80%
(c) 50% and 50%
(d) 52% and 48%
Q10. 15 men complete a work in 16 days. If 24 men are employed, then the time required to complete that work will be
(a) 7 days
(b) 8 days
(c) 10 days
(c) 12 days
Q11.A train takes 9 seconds to cross a pole. If the speed of the train is 48 km/hr, the length of the train is
(a) 150 m
(b) 120 m
(c) 90 m
(d) 80 m
Q12.Ravi's brother is 3 years elder to him. His father was 28 years of age when his sister was born while his mother was 26 years of age when he was born. If his sister was 4 years of age when his brother was born, the ages of Ravi's father and mother respectively when his brother was born were
(a) 32 years and 23 years
(b) 32 years and 29 years
(c) 35 years and 29 years
(d) 35 years and 33 years
Q13.In solving a problem, one student makes a mistake in the coefficient of the first degree term and obtains - 9 and - 1 for the roots. Another student makes a mistake in the constant term of the equation and obtains 8 and 2 for the roots. The correct equation was
(a) x2 + 10x + 9 = 0
(b) x2 - 10x + 16 = 0
(c) x2 + 10x + 9 = 0
(d) None of the above
Q14.If m and n are the roots of the equation ax2 + bx + c = 0, then the equation whose roots are (m2 + 1)/m and (n2 + 1)/n is
(a) acx2 + (ab + bc) x + b2 + (a - c)2 =0
(b) acx2 + (ab - bc) x + b2 + (a - c)2 =0
(c) acx2 + (ab - bc) x + b2 - (a - c)2 = 0
(d) acx2 + (ab + bc) x + b2 - (a - c)2 =0
Q15. The value of x2 - 4x + 11 can never be less than
(a) 7
(b) 8
(c) 11
(d) 22
Q16.What should be added to the expression x (x + a) (x + 2a) (x + 3a) so that the sum may be a perfect square ?
(a) 9a2
(b) 4a2
(c) a4
(d) None of the above
Q17.If the roots of the equation Ax2 + Bx + C = 0 are -1 and 1, then which one of the following is correct ?
(a) A and C are both zero
(b) A and B are both positive
(c) A and C are both negative
(d) A and C are of opposite sign
Q18.A water pipe is cut into two pieces. The longer piece is 70% of the length of the pipe. By how much percentage is the longer piece longer than the shorter piece ?
(a) 140%
(b) 400/3%
(c) 40%
(d) None of the above
Q19.The sum of two positive numbers x and y is 2.5 times their difference. If the product of the numbers is 84, then what is the sum of the two numbers ?
(a) 26
(b) 24
(c) 22
(d) 20
Q20.If n is a whole number greater than 1, then n2 (n2 - 1) is always divisible by
(a) 12
(b) 24
(c) 48
(d) 60
Q21.What is the remainder when 41000 is divided by 7?
(a) 1
(b) 2
(c) 4
(d) None of the above
Q22. On a 20% discount sale, an article costs Rs. 596. What was the original price of the article ?
(a) Rs. 720
(b) Rs. 735
(c) Rs. 745
(d) Rs. 775
Q23.Two chairs and one table cost Rs. 700 and 1 chair and 2 tables cost Rs. 800. If the cost of m tables and m chairs is 30,000, then what is m equal to ?
(a) 60
(b) 55
(c) 50
(d) 45
Q24. Consider the following statements :
1. No integer of the form 4k + 3, where k is an integer, can be expressed as the sum of two squares.
2. Square of an odd integer can be expressed in the form 8k +1, where k is an integer.
Which of the above statements is/are correct?
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d Neither 1 nor 2
Q25. For any integer n, what is HCF (22n + 7, 33n + 10) equal to ?
(a) n
(b)1
(c)11
(d) None of the above
Q26.In a fire range, 4 shooters are firing at their respective targets. The first, the second, the third and the fourth shooter hit the target once every 5 s, 6 s, 7 s and 8 s respectively. If all of them hit their target at 9:00 am, when will they hit their target together again
(a) 9: 04 am
(b) 9:08 am
(c)9:14 am
(d)None of the above
Q27. If A : B = 2 : 3, B : C = 5 : 7 and C : D = 3 : 10, then what is A : D equal to ?
(a) 1:7
(b)2:7
(c) 1:5
(d) 5:1
Q28Out of 105 students taking an examination for English and Mathematics, 80 students pass in English, 75 students pass in Mathematics and 10 students fail in both the subjects. How many students pass in only one subject ?
(a) 26
(b) 30
(c) 35
(d) 45
Q29.The dimensions of a field are 15 m by 12 m. A pit 8 m long, 2.5 m wide and 2 m deep is dug in one corner of the field and the earth removed is evenly spread over the remaining area of the field. The level of the field is raised by
(a) 15 cm
(b) 20 cm
(c) 25 cm
(d) 200/9 cm
Q30The sides of a right-angled triangle are equal to three consecutive numbers expressed in centimeters. What can be the area of such a triangle ?
(a) 6 cm2
(b) 8 cm2
(c) 10 cm2
(d) 12 cm2
Q31. How many circular plates of diameter d can be taken out of a square plate of side 2d with minimum loss of material ?
(a) 8
(b) 6
(c) 4
(d) 2
Q32. What is the diameter of the largest circle lying on the surface of a sphere of surface area 616 square cm ?
(a) 14 cm
(b) 10.5 cm
(c) 7 cm
(d) 3.5 cm
Q33. What is sin 25° sin 35° sec 65° sec 55° equal to?
(a) -1
(b) 0
(c) 1/2
(d) 1
Q34. The value of cos 25° - sin 25° is
(a) positive but less than 1
(b) positive but greater than 1
(c) negative
(d) 0
Q35. In a right-angled triangle ABC, right-angled at B, if cos A = 4/5, then what is sin C equal to?
(a) 3/5
(b 4/5
(c) 3/4
(d) 2/5
Q36. A square is inscribed in a circle of diameter 2a and another square is circumscribing the circle. The difference between the areas of the outer and inner squares is
(a) a2
(b) 2a2
(c) 3a2
(d) 4a2
Q37. A cone of radius r cm and height h cm is divided into two parts by drawing a plane through the middle point of its height and parallel to the base. What is the ratio of the volume of the original cone to the volume of the smaller cone ?
(a) 4 : 1
(b) 8 : 1
(c) 2 : 1
(d) 6 : 1
Q38. Which one of the following is a Pythagorean triple in which one side differs from the hypotenuse by two units ?
(a) (2n + 1, 4n, 2n2 + 2n)
(b) (2n, 4n, _n2+1)
(c) (2n2, 2n, 2n + 1)
(d) (2n, n2-1, n2 + 1)
where n is a positive real number.
Q39. A cube has each edge 2 cm and a cuboid is 1 cm long, 2 cm wide and 3 cm high. The paint in a certain container is sufficient to paint an area equal to 54 cm2 .
Which one of the following is correct ?
(a) Both cube and cuboid can be painted
(b) Only cube can be painted
(c) Only cuboid can be painted
(d) Neither cube nor cuboid can be painted
Q40. ABC is a triangle right-angled at A where AB = 6 cm and AC = 8 cm. 'Semicircles are drawn (outside the triangle) on AB, AC and BC as diameters which enclose areas x, y and z square units respectively. What is x + y - z equal to ?
(a) 48 cm2
(b) 32 cm2
(c) 0
(d) None of the above
Q41. The area of a rectangle lies between 40 cm2 and 45 cm2. If one of the sides is 5 cm, then its diagonal lies between
(a) 8 cm and 10 cm
(b) 9 cm and 11 cm
(c) 10 cm and 12 cm
(d) 11 cm and 13 cm
Q42. A cylinder is surmounted by a cone at one end, a hemisphere at the other end. The common radius is 3.5 cm, the height of the cylinder is 6.5 cm and the total height of the structure is 12.8 cm. The volume V of the structure lies between
(a) 370 cm3 and 380 cm3
(b) 380 cm3 and 390 cm3
(c) 390 cm3 and 400 cm3
(d) None of the above
Question Paper
SSC Matric Level Posts Exam (held on 26/03/2017)
Answer key of Qs, Published in issue 13-19 Jan, 2018
1. B
2. A
3. A
4. C
5. B
6. B
7. C
8. C
9. A
10. B
11. B
12. C
13. B
14. B
15. D
16. A
17. B
18. D
19. C
20. A
21. C
22. B
23. A
24. D
25. C
26. C
27. B
28. A
29. A
30. C
31. B
32. C
33. D
34. D
35. A
36. B
37. A
38. D
39. C
40. C