Education and Career Forum

I need the last two to three year papers of FMS part time MBA exam. Please guide. thanks

dear,
its better for you to contact with your seniors and ask for the same.they not only provides you the papers but also guide you about the tips to attempt the answers.if not possible then take the help of sample papers given at the end of your books.

hi friend,

I didnt get your question correctly, you are wanting paper of MBA or MBA entrance?
However I am attaching last year's papers for this perpose and also pasting the link where you can get info about parttime course MBA in FMS.:
http://www.fms.edu/programmes/parttime_ps.php

The Faculty of Management Studies is affiliated to the University of Delhi. The part time Master of Business Administration course is split into six semesters which the candidates are required to complete in maximum of 5 years on securing admission. Question papers are available in the following link:-
http://www.onestopmba.com/downloads/fms.asp

Originally Posted by drgs

I need the last two to three year papers of FMS part time MBA exam. Please guide. thanks

FMS / ACTUAL PAPER 2007 Page 1
FMS Actual Paper – 2007 (Memory Based Questions)
1. A straight line is perpendicular to the straight line 2x + 3y = 5 and it passes through the point (1, 1).
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 = 3 and
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 of the
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 units.
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 6 + x - x2 ³ 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
25
b.
224
35
c.
324
35
d.
335
24
9. Evaluate
100 1 i
1 i
æ + ö
çè - ÷ø
a. 0 b. 1 c. –1 d.100
Page 2 FMS / ACTUAL PAPER 2007
10. Find the value of the expression
6 6
1 i3 1 i 3
1 i3 1 i 3
æ + ö æ - ö çç ÷÷ + çç ÷÷ è - ø è + ø
a.0 b.2 c.128 d. None of these
11. Evaluate log3 4×log45×log56×log67×log78×log89
a.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 of their
reciprocals, 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 is the
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 series
x2 x3
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 of
n 1
1
2n(2n 1)
¥
= + å is
a. 1 – loge2 b. 1 + loge2 c. loge2 d. log2e
16. If 2 +3x – 2x2 < 0, then x is given by
a.
1
x 2
2
- < < b.
1
x
2
<- c. x < 2 d.
1
x orx 2
2
<- >
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 = 0
c. 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 value of
(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, w is a cube root of
unity.}
aw2 + b + cw = x ...(i)
a + bw+ cw2 = y ...(ii)
aw + bw2 + c = z ...(iii)
a. 0 b. 1 c. 2 d. –1
FMS / ACTUAL PAPER 2007 Page 3
20. If 2 2 2 2 2 2
logx logy logz
a b ab b c bc c a ac
= =
+ + + + + +
then, the value of x(a-b) .y(b-c) .z(c-a) is
a. 0 b. 1 c. abc d. (xyz)abc
21. Solve the equation for
1 1
x, 2.x3 2.x 3 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 (1 + i )6 + (1 + i )4 .
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 students ae
females. Further, 60% of the students are neither married nor females. Which of the following
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 of 20%.
What will be the amount of money, in rupees, at the end of 3 years?
a. 21600 b. 22600 c. 23600 d. None of these
26. The market price of a machine depreciates at an annual compound rate of 10%. If the current
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 these
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 radius 0.3
cm, 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 10 cm
is completely submerged inside the cylinder, what will be the increase in the level of water, in the
cylinder?
a. 3.33 cm b. 6.67 cm c. 8.33 cm d. cannot be determined
Page 4 FMS / ACTUAL PAPER 2007
30. Four brothers and three sisters sit in a single row, facing the photographer’s camera. If the three
sisters always sit together, how many different photographs, having all of them, can be eliked?
a.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 to be
selected. What is the probability that the selected team will have at least 3 bowlers?
a.
7
13
b.
5
13
c.
12
13
d.
9
13
32. The imaginary part of the complex number
(a ib)
(c id)
+
- is given by
a. 2 2
ac 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), then find
the 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 what
is the ratio of the marked price to the cost price of the item?
a.
5
4
b.
7
4
c.
3
4
d.
1
4
35. The per liter price of vehicular fuel has increased by 25%. If the transportation cost is still the same,
then 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 the mth
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 towards
the 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 = 6
5x + 4y = 4
zx + 4y = 5
Find the value of the constant z.
a. 23 b. 25 c. 27 d. 29
FMS / ACTUAL PAPER 2007 Page 5
39. If the following three lines pass through the same point in the X – Y plane, then find the value of
(a + b).
3x – 2y = 1
5x + 4y = 9
ax + by = 3
a. 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 following is
necessarily 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 below.
The following pie chart gives the percentage wise break up of the cost price of a machine. Study the pie
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 Cost"
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 above pie
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 Cost"?
a. 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 change
in the per unit cost price of the machine?
a. –2.5% b. –10% c. –1.5% d. –3.5%
Page 6 FMS / ACTUAL PAPER 2007
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 "Packaging
Cost"
b. The sum of per unit "Overhead Cost" and the "Marketing Cost" add up to the per unit "Packaging
Cost"
c. The sum of per unit "Other Cost" and the "Marketing Cost" add up to the per unit "Packaging
Cost"
d. none of these.
Directions for questions 46 to 50: Answer the questions on the basis of the information given below.
The following bar graph shows the annual comparisons of the "Targeted Production" with the "Actual
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 - 2001?
a.
11
12
b.
17
18
c.
15
16
d.
19
20
47. What percent of the "Targeted production" was met by the "Actual Production", in the year 2002 -
2003?
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 Production"
with respect to the "Targeted Production"?
a. 1999–2000 and 2001–2002 b. 2000–2001 and 2002–2003
c. 2001–2002 and 2000–2001 d. 2002–2003 and 2003–2004
FMS / ACTUAL PAPER 2007 Page 7
49. In which of the following years the "Actual Production" surpassed the "Targeted Production" by the
maximum 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 from the
year 1999 to the year 2004?
a. The cumulative "Actual Production" has missed the cumulative "Targeted Production" by less
than 10%.
b. The cumulative "Actual Production" has surpassed the cumulative "Targeted Production" by
more than 10%
c. The cumulative "Actual Production" has missed the cumulative "Targeted Production" by more
than 10%.
d. The cumulative "Actual Production" has surpassed the cumulative "Targeted Production" by
less than 10 %
FMS ACTUAL PAPER 2007 Page 1
1. d Slope of the, line
–1 3
–2 2
3
= =
Equation is
y –1 3
x –1 2
= or 3x – 2y = 1
Hence (d) is the correct answer.
2. b Slope of the line ( )
–1
1
–1
= =
equation is
y –2
1
x –3
=
or x – y = 1
Hence (b).
3. d
A
C B
(–1, –1)
(0, 4) (3, 5)
y
x
Slopes of lines AB, BC & AC are
3 1
, and5
2 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 D C
h
a
60°
a = 3 3 units
AB2 = BD2 + AD2
or ( ) 2
2 a 3 3
h a – a 3 3
2 2 2
= æ ö = = ´ çè ÷ø
or h = 4.5 units. hence (c) is correct.
5. b
76
log7 log 7 c
log
log6 log2 log3 a b
= = =
+ +
Hence, (b) is correct.
6. c If x lies between 2 and 3 then it is greater than 2 and
less than 3.
Þ(x – 2) > 0 and (x – 3) < 0
Þ(x – 2)(x – 3) < 0 . Hence (b) is always correct.
(a) is incorrect and (c) is correct for some values of x,
only.
7. a 6 + x – x2 ³ 0
Þ x2 – x – 6 £ 0
or (x + 2)(x – 3) £ 0
Þ –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
( )
( )( )
2
12 12 1
2 234
12 12 1 12 2 1 25
6
ïì + ïü
í ý
= îï ïþ =
+ ´ +
Hence (a) is correct.
9. b ( )
( ) ( )
+ ° + ° + ° + ° = = =°
° ° +
2 2
2 2
1 i 1 i 1 i 2i
i
1– i 1 – i 1 1
æçè + °° ö÷ø = (° ) =
100 50 1 i 2
i 1
1–i
Hence (b) is correct.
10. b
æ + ö æ ö = çç ÷÷ + çç ÷÷ è ø è ø
6 6
–1 i3 –1– i 3
2 2
( )
( ) ( )
( )
( ) ( )
æ + ö æ ö = ç ÷ + ç ÷ ç ÷ ç ÷
èç ø÷ èç ø÷
2
2 2 2 2
1 i 3 1– i 3
1 – i3 1 – i 3
Answers and Explanations
Page 2 FMS ACTUAL PAPER 2007
6 6
–1 i3 –1– i 3
2 2
æ + ö æ ö = çç ÷÷ + çç ÷÷ è ø è ø
= (w)6 + (w2 )6
{wis a cube root of unity}
=(w3)2 + (w3)4
= 1 + 1
= 2.
11. 4 5 6 7 8 9
log3´ log4´log5´ log6´ log7´ log8
log4 log5 log6 log7 log8 log9
log3 log4 log5 log6 log7 log8
= ´ ´ ´ ´ ´
9 32
3 3
log9log log 2
log3
= = = =.
12. c Let roots are a,b.
2
2 2 2
1 1 ( ) 2
( )
( )
a + b = + = a + b - ab
a b ab
2
2
( a) 2 (1)
a
(1)
Þ - = - - ´
Þ a2 + a - 2 = 0
Þ a = -2 or 1.
Þ (c) is correct.
13. d Slope of line ax – by = k is
a
b
and the slop of line cx –
dy = k1 is
–c
d
as the two lines are perpendicular to each other,
a c
–1
b d
æ ö ´ æ ö = çè ÷ø çè ÷ø
Þac = –bd
or ac + bd = 0
Hence (d) is correct.
14. d The infinite series is denoted by e–x.
15. a ( )
1 1 1
–
2n 2n 1 2n 2n 1
= æ ö + èç ø÷ +
( )
¥
=
= æ + + + ¥ö + èç ø÷ å
n 1
1 1 1 1
.......
2n 2n 1 2.1 2.2 2.3
æ + + + ¥ö çè + + + ÷ø
1 1 1
– .......
2.1 1 2.2 1 2.3 1
= æ ö + æ ö + æ ö + ¥ çè ÷ø çè ÷ø çè ÷ø
1 1 1 1 1 1
– – – ........
2 3 4 5 6 7
= é + + + ¥ù êë úû
1 1 1 1 1 1
–– – – – ..........
2 3 4 5 6 7
= éæ + + + ¥ö ù êçè ÷ø ú ë û
1 1 1 1 1
– 1– – – ....... –1
2 3 4 5 6
= é ù êë úû
2e
– log –1
= 2e
1– log
e
2
= loge Hence (a) is the correct answer.
16. d 2 + 3x – 2x2 < 0
Þ(2x +1)(x – 2) > 0
–1
x 2 orx
2
Þ > <
Option (d) is correct.
17. c log (x – 7) + log (x +1) = 1
Þlog éë(x – 7)(x + 1)ùû = 1 = loge e
Þ(x – 7)(x +1) = e
Þ x2 – 6x – 7 – e = 0
Option (e) is correct.
18. c Let x2 + ax + b = 0 has roots (a,b)
and x2 + bx + a = 0 has roots (a,g)
a is a root of the equation;
(x2 + ax + b) – (x2 + bx + a) = 0
or, (a – b) x = (a –b)
Þ a = 1
From the first equation,
a + b = bÞ1+ b = –a & a.b = bÞ1.b = bÞb = b
Hence a + b = –1.
Option (c) is correct.
19. a aw2 + b + cw = x
a + bw + cw2 = y
aw+ bw2 + c = z
Adding the three equations,
a(1+ w + w2) + b(1+ w + w2 ) + c(1+ w + w2 ) = x + y + z
or x + y + z = 0
Þ x3 + y3 + z3 - 3xyz = 0
Option (a) is correct.
FMS ACTUAL PAPER 2007 Page 3
20. b Let 2 2 2 2 2 2 1
logx logy logz
k
a b ab b c bc c a ac
= = =
+ + + + + +
and x(a–b) .y (b – c) . z(c–a) = k2
(a – b)log x + (b – c)log y + (c – a)log z = log k2
Þ {( )( 2 + 2 + )+ ( )( 2 + 2 + )
1 k a –b a b ab b –c b c bc
= ( )( 2 + 2 + )}
c – a c a ac logK2
Þ log K2g = 0
ÞK2 = 1
Hence, (b) is the answer.
21. d
1 –1
2x3 + 2x 3 = 5
1
Let x3 = t
2 2
2t 5 or 2t – 5t 2 0
t
Þ + = + =
1
3 1
t x 2 or
2
Þ = =
1
x 8 or
8
Þ =
Hence, (d).
22. a ( )1
–6 2 1
0.000064 64 10
3
é ù
= ê ´ ú ê ú
êë úû
( )
1
1 3
–3 2 2 8 10
é ù
êé ù ú
= êê ´ ú ú
êë û ú
êë úû
( ) ( )´
= ´ = ´ = ´
1 1
–3 –1 3 –1 8 10 3 2 10 3 2 10
= 0.2
Hence (a).
23. a (1 + i)6 + (1 + i)4 = (1 + i)4 [(1 + i)2 + 1]
= (12 + i2 + 2i)2 [12 + i + 2i + 1]
= [4 (i)2] [1 + 2i]
= (–4) (1 + 2i)
= (–4 – 8i)
24. a Let N = total number of students
Number of married students
N
20
=
Number of unmarried students
19
N
20
=
Number of married female students
N
80
=
Number of unmaried male students
12
N
20
=
Number of unmaried female students
7
N
20
=
Þ = ´ = Number of married female student N 20 1
.
Number of un-married female student 80 7N 28
= ´ = Number of married male students 3N 20 1
& .
number of un-married male students 80 12N 16
Þ Only (I) is valid .
Þ Option (a) is correct
26. b Final price, A = 8748 Rs.
Time = n = 3 years
depreciation rate = r = –10%
Let the price, 3 years ago be, P
Then,
r n
A P 1
100
æ ö = +
èç÷ø
or 8748 =
10 3
P 1–
100
æ ö
çè ÷ø
ÞP = 12,000
Hence (b) is correct.
27. c Volume of cylinder = p´r2h
22 ( )2 ( )
8 14
7
= ´ ´
= 2816 cc.
Volume of cuboid = a2 × h
= (8)2 × (14)
= 896 cc.
The difference is 1920 cc.
Hence (c) is correct.
28. c Let the number of balls be N,
= = ´ ´ =
´ ´ æ ö çè ÷ø
3
9 10 11
N 8750
4 22 3
3 7 10
Hence (c) is correct.
Page 4 FMS ACTUAL PAPER 2007
29. b Let the increase in the level of water, inside the cylinder
beDh,then
( ) ( ) ( ) 2 3
cylinder sphare
4
r h r
3
p´ ´ D = ´p
( )420
h 5 cm
3 3
Þ D = ´ = or Dh = 6.67 cm
Hence, (b) is correct.
30. d Taking the three sisters as a single entity, we have to
arrange 5 entities & then we have to arrange 3 three
sisters, internally. Hence, total number of different
photographs, that can be taken = (5!) × (3!) = 720.
Hence, (d) is correct.
31. c P(atleast 3 bowlers)
= P(3 bowlers) + P(4 bowlers) + P(5 bowlers)
5 10 5 10 5 10
3 8 4 7 5 6
15 15 15
11 11 11
C × C C × C C × C
= + +
C C C
10 45 5 120 1 210
1365 1365 1365
= ´ + ´ = ´ 252 12
.
273 13
= =
Þ Option (c) is corrects.
32. d
+ = + +
- - +
a ib (a ib)(c id)
c id (c id)(c id)
2
2 2
ac iad ibc (i) bd
c d
= + + +
+
= - + +
2 + 2
(ac bd) i(ad bc)
c d
= +
2 + 2
ad bc
Imaginary part
c d
Þ(d) is the correct answer.
33. a Let the co-ordinates of the third vertex be (h, k). Then,
5 3 1
1–
4 –3 1 21 2h – 3k 15
2
h k 1
= Þ =
Þ Locus of the third vortex is 2x – 3y = 15.
option (a) is correct.
34. b Let the cost price = Rs. 100,
then, selling price = Rs. 125
æ ö Þ = +
èç÷ø
40
Marked price 125 1
100
Þ
Marked Pr ice 175
Cost Pr ice 100
= = 1.75
Option (b) is correct.
35. b (Fuel Consumption) × (Fuel Price) = (Transportation
Cost) = constant
Current Fuel Consumption Pr evious Fuel Pr ice
Pr evious Fuel Consumption Current Fuel Pr ice
=
=
100
125
Þ
reduced Fuel consumption (125 100)
Pr evious Fuel consumption 100
-
=
=
25 1
100 4
=
option (b) is correct.
36. Let the first term and the common difference of the AP
are a & d.
a (k 1)d a (l 1)d a (m 1)d a (n 1)d
2 2
ëé + - ûù + ëé + - ûù ëé + - ûù + ëé + - ûù =
Þ (k – 1) + (l – 1) = (m – 1) + (n – 1)
Þ (m + n) = (l + k)
option (c) is correct.
37.
A
C’ B
y
x
(3, 2)
(–3, –3) (3, –3)
The ball first lied at point A (3, 2).
It was shifted by 5 units to point B (3, – 3).
Its reflection is at point C (– 3, – 3).
Option (a) is correct.
38. As the three lines are concurrent,
3 4 6
5 4 4 0 z 29
z 4 5
-
- = Þ =
-
Hence (d) is correct.
39. 3 2 1
5 4 9 0
a b 3
- -
- =
-
Þ 3(– 12 + 9b) + 2(– 15 + 9a) – 1 (5b – 4a) = 0
Þ 22 (a + b) = 66
Þ (a + b) = 3
Þ Option (d) is correct
FMS ACTUAL PAPER 2007 Page 5
40. b For two lines ax + by + c = 0 and dx + ey + f = 0 to be
concurrent, the necessary and sufficient conditions
is
a b c
d e f
= =
option (b) is correct.
41. c Labour cost =
4
100
× (Total cost)
Marketing Cost =
18
100
× (Total cost)
Þ Marketing Cost =
18
100
×
100
4
æ ö
çè ÷ø × 2500
= Rs. 11,250
Option (c) is correct.
42. b Contribution of the Overhead Cost = 15%
Þ angle subtended =
15
100
× (360°) = 54°
Þ option (b) is correct.
43. a
Packaging cost 35
1.944
Marketing cost 18
= =
Þ Packaging cost is 94%, more than the Marketing
cost.
44. d Let the total cost of manufacturing one unit = Rs. 100
Þ Packaging cost = Rs. 35
Þ new packaging cost = 35
10
1
100
æ ö -
èç÷ø
= Rs. 31.50
Þ new total cost = [100 – (35)] + 31.50
= Rs. 96.5
96.5 100
change 3.5
100
= - = -
Hence (d) is correct.
45. a,b,c
Other Cost =
28
100
× (Total cost)
Labour Cost =
4
100
× (Total cost)
Overhead Cost =
15
100
× (Total cost)
Marketing cost =
18
100
× (Total cost)
none of (a), (b) or (c) is correct.
46. b
TargetedPr oduction 425 17
Actual Pr oduction 450 18
= =
Option (b) is correct.
47. a Actual Production = 675 units.
Targeted Production = 600 units
the required percentage =
675 600
600
-
× 100 = 112.5%
option (a) is correct.
48. d From the bar graph, it is clear that in the years 2002 -
2003 and 2003 - 2004 the actual production was more
than the targeted production. Hence (d) is correct.
49. d In 2000 - 2001,
ActualPr oduction 450
1.058
Targeted Pr oduction 425
= =
In 2002 - 2003,
ActualPr oduction 675
1.125
Targeted Pr oduction 600
= =
and, In 2003 - 2004,
ActualPr oduction 625
1.25
Targeted Pr oduction 500
= =
Þ (d) is correct.
50. d Cumulative Targeted Production
= (300 + 425 + 350 + 600 + 500) = 2175 units
Cumulative Actual Production
= (275 + 450 + 325 + 375 + 625) = 2350 units
Cumulative ActualPr oduction 2350
1.08
Cumulative Targeted Pr oduction 2175
Þ = =
Þ (d) option is correct.
all the best

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