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FMS Actual Paper 20071. A straight line is perpendicular to the straight line 2x + 3y = 5 and it passes through the point

Which of the following gives its equation?a. 2x 3y = 1 b. 2x + 3y = 2 c. 3x + 2y = 1 d. 3x 2y = 1

2. A straight line passes through the point (3, 2) and is perpendicular to the straight line x+ y = is perpendicular to the straight line x + y = 3. Find its equation.

a. x + y + 1 = 0 b. x y 1 = 0 c. x y + 1 = 0 d. x + y 1 = 0

3. The vertices of a triangle lie on points (0, 4), (3, 5) and (1, 1) in the X Y plane. Which

following is correct about this triangle?a. It is an isosceles right triangle. b. It is a right triangle.c. It is an equilateral triangle d. It is an obtuse triangle.

4. Find the length of the altitude of an equilateral triangle whose sides have a length of 3 3 un

a. 8.5 units b. 6.5 units c. 4.5 units d. 2.5 units

5. If a = log2, b = log 3 and c = log 7 then find the value of log67 in terms of a, b and c.

a.b

a c+b.

c

a b+c.

a

b c+d. None of these

6. If the real number x lies between 2 and 3, then which of the following expressions is valid?

a. (x 2) (x 3) = 0 b. (x 2) (x 3) < 0

c. x 2 x 3 > d. None of these

7. Solve for all values of x for which 26 x x 0+ a. 2 x 3 b. 2 x 3 c. 3 x 2 d. 3 x 2

8. Evaluate the expression

3 3 3 3

2 2 2 2

1 2 3 ... 12

1 2 3 ... 12

+ + +

+ + +

a.234

25b.

224

35c.

324

35d.

335

24

9. Evaluate

1001 i

1 i

+

a. 0 b. 1 c. 1 d.100

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10. Find the value of the expression

6 61 i 3 1 i 3

1 i 3 1 i 3

+ + +

a.0 b.2 c.128 d. None of these

11. Evaluate 3 4 5 6 7 8log 4log 5log 6log 7log 8log 9a.0 b.1 c.1 d. None of these

12. If the sum of the roots of the equation x2 + ax + 1 = 0 is equal to the sum of the squares oreciprocals, then which of the following is a possible value of a?a. 1 b. 2 c.1 d. None of these

13. If the straight lines ax by = k and cx dy = k1

are perpendicular to each other, then what relation between a, b, c & d?

a. ab + cd= 0 b. ab cd = 0 c. ac bd = 0 d. ac + bd = 0

14. The sum of the infinite series2 3x x

1 - x + ...2! 3!

+ is denoted by

a. sin x + cos x b. 1 + log (1 x) c. 1 log (1 + x) d. None of these

15. The value ofn 1

1

2n(2n 1)

= + is

a. 1 loge2 b. 1 + log

e2 c. log

e2 d. log

2e

16. If 2 +3x 2x2 < 0, then x is given by

a.1

x 22

< < b.1

x2

< c. x < 2 d.1

x or x 22

< >

17. If log(x 7) + log (x + 1) = 1 then which of the following is correct?a. x2 7x 6 e = 0 b. x2 7x 6 + e = 0c. x2 6x 7 e = 0 d. x2 6x 7 + e = 0

18. If the equations x2 + ax + b = 0 and x2 + bx + a = 0, have one root in common, then find the va

(a + b).a. 0 b. 1 c. 1 d. 2

19. Given the following three equations, find the value of x3 + y3 + z3 3xyz{Here, is a cube runity.}

2a b c x + + = ...(i)

2a b c y+ + = ...(ii)

2a b c z + + = ...(iii)a. 0 b. 1 c. 2 d. 1

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20. If 2 2 2 2 2 2logx logy logz

a b ab b c bc c a ac= =

+ + + + + +then, the value of (a b) (b c) (c a)x .y .z

is

a. 0 b. 1 c. abc d. (xyz)abc

21. Solve the equation for

1 1

3 3x, 2.x 2.x 5.

+ =

a.1

2,2

b.1

4,4

c.1

6,6

d.1

8,8

22. 3 .000064 simplifies to

a. 0.2 b. 0.02 c. 0.4 d. 0.04

23. Simplify the expression 6 4

(1 + i ) + (1 + i ).

a. 4 8i b. 4 8i c. 8 4i d. 8 + 4i

24. In a post graduate college, 5% of the students are married and 25% of the married studenfemales. Further, 60% of the students are neither married nor females. Which of the follo

statements are valid?I. There is 1 married female student for every 28 unmarried female students.II. There is 1 married male student for every 4 unmarried male students.

a. I b. II c. Both I and II d. None

25. An amount of Rs12500 was deposited for a period of 3 years at a compound interest rate ofWhat will be the amount of money, in rupees, at the end of 3 years?

a. 21600 b. 22600 c. 23600 d. None of these26. The market price of a machine depreciates at an annual compound rate of 10%. If the c

market price of the machine is Rs. 8748 then what was its market price 3 years ago?

a. Rs. 12500 b. Rs. 12000 c. Rs. 20000 d.Rs. 20500

27. A cylinder has a diameter of 8cm and a cuboid has a square base of side length 8cm. If both of

solids have a height of 14 cm then what is the difference in their volumes?a.196 cc b.1960 cc c.1920 cc d.195 cc

28. A metallic cuboid has dimensions of 9cm 10cm 11cm. How many spherical balls of radiucm, can be drawn from this cuboid?a. 2750 b. 5750 c. 8750 d. 3750

29. A cylinder of diameter 10 cm and a height of 20 cm is filled with water. If a sphere of diameter

is completely submerged inside the cylinder, what will be the increase in the level of water, cylinder?a. 3.33 cm b. 6.67 cm c. 8.33 cm d. cannot be determ

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30. Four brothers and three sisters sit in a single row, facing the photographers camera. If thesisters always sit together, how many different photographs, having all of them, can be elikea.840 b.126 c.120 d.720

31. From amongst the available 15 cricket players, of whom 5 are bowlers, a team of 11 is selected. What is the probability that the selected team will have at least 3 bowlers?

a.7

13b.

5

13c.

12

13d.

9

13

32. The imaginary part of the complex number(a ib)

(c id)

+ is given by

a. 2 2ac bd

c d

+

b. 2 2

ac bd

c d

+c. 2 2

ad bc

c d

d. 2 2

ad bc

c d

+

+

33. The area of a triangle is 21 sq. units. If two of its vertices lie on points (5, 3) and (4, 3), thethe locus of the third vertex.

a. 2x 3y = 15 b. 2x + 3y = 15 c. 3x + 2y = 15 d. 3x 2y = 15

34. The profit by selling an item was 25%. If the item was marked 40% above the selling price then

is the ratio of the marked price to the cost price of the item?

a.5

4b.

7

4c.

3

4d.

1

4

35. The per liter price of vehicular fuel has increased by 25%. If the transportation cost is still the sthen what is the ratio of the reduced fuel consumption to the previous fuel consumption?

a. 1:5 b. 1:4 c. 1:3 d. 1:6

36. The arithmetic mean of the kth and the lth terms of an A.P. is equal to the arithmetic mean of th

and the nth terms of the same A.P. Find the value of (m + n).a. l k b. k l c. l + k d. None of these

37. A very small ball lies at the point (3, 2) in the X Y plane. The ball is now shifted by 5 units towthe negative Y-axis. If Y-axis were a mirror, then at what point will the image of this ball, lie?

a. (3, 3) b. (3, 2) c. (2, 2) d. (2, 3)

38. In the X Y plane, three lines are concurrent. Their equations are

3x + 4y = 65x + 4y = 4zx + 4y = 5

Find the value of the constant z.a. 23 b. 25 c. 27 d. 29

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39. If the following three lines pass through the same point in the X Y plane, then find the va(a + b).3x 2y = 1

5x + 4y = 9ax + by = 3a. 0 b.1 c.2 d.3

40. If ax +by + c = 0 and dx + ey + f = 0 represent the same straight line then which of follownecessarily satisfied?

a. a = d, b = e and c = f b.a b c

d e f= =

c. ad + be + cf = 0 d. None of these

Directions for questions 41 to 45: Answer the questions on the basis of the information given beloThe following pie chart gives the percentage wise break up of the cost price of a machine. Study th

chart and answer the questions that follow.

Overhead Costs

(15%)

Other Costs

(28%)

Labour Cost (4%)

Marketing

Cost

(18%)

Packaging Cost

(35%)

41. If the "Labour Cost" of a single unit of machine is Rs.2500 then what is the per unit "Marketing

of the machine?a. Rs. 1125 b. Rs. 112500 c. Rs. 11250 d. none of these.

42. What is the angle subtended by the "Overheads Cost" at the centre of the circle, in the abo

chart?a. 15 b. 75 c. 54 d. 45

43. How much more is the per unit "Packaging Cost" with respect to the per unit "Marketing Coa. 94.44% b. 84.44% c. 104.44% d. none of these

44. If the per unit "Packaging Cost" cost of the machine is reduced by 10% then what will be the ch

in the per unit cost price of the machine?a. 2.5% b. 10% c. 1.5% d. 3.5%

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45. Which of the following is true?a. The sum of per unit "Other Costs" and the "Labour Cost" add up to the per unit "Pack

Cost"

b. The sum of per unit "Overhead Cost" and the "Marketing Cost" add up to the per unit "PackCost"

c. The sum of per unit "Other Cost" and the "Marketing Cost" add up to the per unit "Packa

Cost"d. none of these.

Directions for questions 46 to 50: Answer the questions on the basis of the information given beloThe following bar graph shows the annual comparisons of the "Targeted Production" with the "A

Production" for a manufacturing plant. Study the bar graph and answer the questions that follow.

300

425

350

600

500

275

450

325

675

625

1999-2000 2000 - 2001 2001 - 2002 2002 - 2003 2003 - 2004

Production

(in

units)

Target

Actual

46. What is the ratio of the "Targeted Production" to the "Actual Production" in the year 2000 - 2

a.11

12b.

17

18c.

15

16d.

19

20

47. What percent of the "Targeted production" was met by the "Actual Production", in the year 22003?

a. 112.5% b. 12.5% c. 125% d. 120.5%

48. Which of the following two consecutive years have followed the same trend of "Actual Produ

with respect to the "Targeted Production"?a. 19992000 and 20012002 b. 20002001 and 20022003c. 20012002 and 20002001 d. 20022003 and 20032004

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49. In which of the following years the "Actual Production" surpassed the "Targeted Production" bmaximum percentage?a. 1999-2000 b. 2000-2001 c. 2002-2003 d. 2003-2004

50. Which of the following statements is correct about the cumulative production of the plant froyear 1999 to the year 2004?

a. The cumulative "Actual Production" has missed the cumulative "Targeted Production" bthan 10%.

b. The cumulative "Actual Production" has surpassed the cumulative "Targeted Productio

more than 10%c. The cumulative "Actual Production" has missed the cumulative "Targeted Production" by

than 10%.d. The cumulative "Actual Production" has surpassed the cumulative "Targeted Productio

less than 10 %

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1. d Slope of the, line1 3

223

= =

Equation isy 1 3

x 1 2= or 3x 2y = 1

Hence (d) is the correct answer.

2. b Slope of the line( )

11

1= =

equation isy 2

1x 3

=

or x y = 1Hence (b).

3. d

A

BC

(1, 1)

(3, 5)(0, 4)

y

x

Slopes of lines AB, BC & AC are3 1

, and 52 3

.

The length of the sides AB, BC and AC are

52 units, 10 units and 26 units.

As. AC2 + BC2 < AB2; It is an obtuse triangle. Hence (d).

4. c A

B CD

ha

60

a 3 3 units=

2 2 2AB BD AD= +

or ( )2

2 a 3 3h a a 3 32 2 2

= = =

or h = 4.5 units. hence (c) is correct.

5. b76

log 7 log 7 clog

log 6 log 2 log 3 a b

= = =

+ +Hence, (b) is correct.

6. c If x lies between 2 and 3 then it is greater thanless than 3.

( )x 2 0 > and (x 3) < 0

( )( )x 2 x 3 0 < . Hence (b) is always co(a) is incorrect and (c) is correct for some valueonly.

7. a 26 x x 0+

2x x 6 0

or ( )( )x 2 x 3 0+

2 x 3 Hence (a) is correct.

8. a+ + +

+ + + +

3 3 3 3

2 2 2 2

1 2 3 ........12

1 2 3 ........ 12

( )

( )( )

212 12 1

2 234

12 12 1 12 2 1 25

6

+ = =

+ +

Hence (a) is correct.

9. b( )

( ) ( )

+ + + + = = = +

2 2

2 2

1 i1 i 1 i 2ii

1 i 1 11 i

( )+ = =

100 5021 i i 1

1 i

Hence (b) is correct.

10. b +

= +

6 61 i 3 1 i 3

2 2

( )

( ) ( )

( )

( ) ( )

+ = +

2

2 22 2

1 i 3 1 i 3

1 i 3 1 i 3

Answers and Explanations

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6 61 i 3 1 i 3

2 2

+= +

6 2 6= ( ) + ( )

{ is a cube root of unity}=( 3)2 + ( 3)4

= 1 + 1= 2.

11. 4 5 6 7 8 93 4 5 6 7 8log log log log log log

log4 log5 log6 log7 log8 log9

log3 log4 log5 log6 log7 log8=

29 33 3

log9log log 2

log3= = = = .

12. c Let roots are , . 2

2 2 2

1 1 ( ) 2( )

( )

+ + = + =

2

2

( a) 2 (1)a

(1)

=

2a a 2 0 + =

a 2 or 1. =

(c) is correct.

13. d Slope of line ax by = k isab

and the slop of line cx

dy = k1 isc

d

as the two lines are perpendicular to each other,

a c1

b d

=

ac bd =or ac + bd = 0Hence (d) is correct.

14. d The infinite series is denoted by ex.

15. a ( )

1 1 1

2n 2n 1 2n 2n 1

= + +

( )

=

= + + + + n 1

1 1 1 1.......

2n 2n 1 2.1 2.2 2.3

+ + + + + +

1 1 1 .......

2.1 1 2.2 1 2.3 1

= + + + 1 1 1 1 1 1

........2 3 4 5 6 7

= + + + 1 1 1 1 1 1

..........2 3 4 5 6 7

= + + +

1 1 1 1 1 1 ....... 1

2 3 4 5 6

= 2e log 1

= 2e1 log

e

2elog= Hence (a) is the correct answer.

16. d 2 + 3x 2x2 < 0

( )( )2x 1 x 2 0 + >

1x 2 or x

2 >