FMS Sample Papers 2007 Verbal, Quant, Data Interpretation for FMS 2011 MBA

Question

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?

Possible Answers

Selected	Possible Answer
	A. 2x â€“ 3y = 1
	B. 2x + 3y = 2
	C. 3x + 2y = 1
	D. 3x â€“ 2y = 1

Question

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.

Possible Answers

Selected	Possible Answer
	A. x + y + 1 = 0
	B. x â€“ y â€“ 1 = 0
	C. x â€“ y + 1 = 0
	D. x + y â€“ 1 = 0

Question

The vertices of a triangle lie on points (0, 4), (3, 5) and (â€“1, â€“1) in the X â€“ Y plane. Which of the following is correct about this triangle?

Possible Answers

Selected	Possible Answer
	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.

Question

Find the length of the altitude of an equilateral triangle whose sides have a length of $3 \sqrt{3}$ units.

Possible Answers

Selected	Possible Answer
	A. 8.5 units
	B. 6.5 units
	C. 4.5 units
	D. 2.5 units

Question

If a = log2, b = log 3 and c = log 7 then find the value of $\log_67$ in terms of a, b and c.

Possible Answers

Selected	Possible Answer
	A. $\cfrac{b}{a+c}$
	B. $\cfrac{c}{a+b}$
	C. $\cfrac{a}{b+c}$
	D. None of these

Question

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

Possible Answers

Selected	Possible Answer
	A. (x â€“ 2) (x â€“ 3) = 0
	B. (x â€“ 2) (x â€“ 3) < 0
	C. \| x – 2 \| > \| x – 3 \|
	D. None of these

Question

Solve for all values of x for which $6 + x - x^2 \geq 0$

Possible Answers

Selected	Possible Answer
	A. $-2 \leq x \leq 3$
	B. $2 \leq x \leq 3$
	C. $-3 \leq x \leq 2$
	D. $-3 \leq x \leq - 2$

Question

Evaluate the expression $\cfrac{1^3 + 2^3 +3^3 ... +12^3}{1^2 + 2^2 +3^2 ... +12^2}$

Possible Answers

Selected	Possible Answer
	A. $\cfrac{234}{25}$
	B. $\cfrac{224}{35}$
	C. $\cfrac{324}{35}$
	D. $\cfrac{335}{24}$

Question

Evaluate $\bigg( \cfrac{1+i}{1-i}\bigg)^{100}$

Possible Answers

Selected	Possible Answer
	A. 0
	B. 1
	C. -1
	D. 100

Question

Find the value of the expression $\bigg( \cfrac{1 + i \sqrt{3}}{1 - i \sqrt{3}} \bigg)^6$ $\bigg( \cfrac{1 - i \sqrt{3}}{1+ i \sqrt{3}} \bigg)^6$

Possible Answers

Selected	Possible Answer
	A. 0
	B. 2
	C. 128
	D. None of these

Question

Evaluate log_34Ã—log_45Ã—log_56Ã—log_67Ã—log_78Ã—log_89

Possible Answers

Selected	Possible Answer
	A. 0
	B. 1
	C. -1
	D. 2

Question

If the sum of the roots of the equation x^2 + 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?

Possible Answers

Selected	Possible Answer
	A. -1
	B. 2
	C. 1
	D. None of these

Question

If the straight lines ax â€“ by = k and cx â€“ dy = k1 are perpendicular to each other, then what is the relation between a, b, c & d?

Possible Answers

Selected	Possible Answer
	A. ab + cd= 0
	B. ab â€“ cd = 0
	C. ac â€“ bd = 0
	D. ac + bd = 0

Question

The sum of the infinite series $1 - x + \cfrac{x^2}{2!} - \cfrac{x^3}{3!} + ... \infty$ is denoted by

Possible Answers

Selected	Possible Answer
	A. sin x + cos x
	B. 1 + log (1 â€“ x)
	C. 1 â€“ log (1 + x)
	D. None of these

Question

The value of $\sum_{n=1}^\infty \cfrac{1}{2n(2n+1)}$ is

Possible Answers

Selected	Possible Answer
	A.
	B.
	C.
	D.

Question

If 2 +3x - 2x^2 < 0 , then x is given by

Possible Answers

Selected	Possible Answer
	A. $-\cfrac{1}{2} < x < 2$
	B. $x < - \cfrac{1}{2}$
	C.
	D. $x < - \cfrac{1}{2}$ or

Question

If log(x – 7) + log (x + 1) = 1 then which of the following is correct?

Possible Answers

Selected	Possible Answer
	A.
	B.
	C.
	D.

Question

If the equations x^2 + ax + b = 0 and x^2 + bx + a = 0 , have one root in common, then find the value of (a + b) .

Possible Answers

Selected	Possible Answer
	A. 0
	B. 1
	C. -1
	D. 2

Question

Given the following three equations, find the value of x^3 + y^3 + z^3 - 3xyz {Here, $\omega .$ is a cube root of unity.}

$a\omega^2+b+c\omega=x$ .. .. .. (i)
$a+b\omega+c\omega^2=y$ .. .. .. (ii)
$a\omega+b\omega2+c=z$ .. .. .. (iii)

Possible Answers

Selected	Possible Answer
	A. 0
	B. 1
	C. 2
	D. -1

Question

If $\cfrac{log x}{a^2 + b^2 + ab} =$ $\cfrac{log y}{b^2 + c^2 +bc}$ $= \cfrac{log z}{c^2 + a^2 + ac}$ then, the value of $x^{(a-b)} . y^{(b-c)}. ^{(c-a)}$ is

Possible Answers

Selected	Possible Answer
	A. 0
	B. 1
	C. abc
	D. $(xyz)^{abc}$

Question

Solve the equation for $x, 2. x^{\frac{1}{3}} + 2. x^{-1}{3} = 5.$

Possible Answers

Selected	Possible Answer
	A. 2, 1/2
	B. 4, 1/4
	C. 6, 1/6
	D. 8, 1/8

Question

$\sqrt[3]{\sqrt{.000064}}$ simplifies to

Possible Answers

Selected	Possible Answer
	A. 0.2
	B. 0.02
	C. 0.4
	D. 0.04

Question

Simplify the expression (1 + i)^6 + (1 + i)^4 .

Possible Answers

Selected	Possible Answer
	A. -4-8i
	B. 4 â€“ 8i
	C. 8 â€“ 4i
	D. 8 + 4i

Question

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.

Possible Answers

Selected	Possible Answer
	A. I
	B. II
	C. Both I and II
	D. None

Question

An amount of $12500 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?

Possible Answers

Selected	Possible Answer
	A. 21600
	B. 22600
	C. 23600
	D. None of these

Question

The market price of a machine depreciates at an annual compound rate of 10%. If the current market price of the machine is $8748 then what was its market price 3 years ago?

Possible Answers

Selected	Possible Answer
	A. $12500
	B. $12000
	C. $20000
	D. $20500

Question

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?

Possible Answers

Selected	Possible Answer
	A. 196 cc
	B. 1960 cc
	C. 1920 cc
	D. 195 cc

Question

A metallic cuboid has dimensions of 9cm Ã— 10cm Ã— 11cm. How many spherical balls of radius 0.3 cm, can be drawn from this cuboid?

Possible Answers

Selected	Possible Answer
	A. 2750
	B. 5750
	C. 8750
	D. 3750

Question

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?

Possible Answers

Selected	Possible Answer
	A. 3.33 cm
	B. 6.67 cm
	C. 8.33 cm
	D. cannot be determined

Question

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?

Possible Answers

Selected	Possible Answer
	A. 840
	B. 126
	C. 120
	D. 720

Question

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?

Possible Answers

Selected	Possible Answer
	A. 7/13
	B. 5/13
	C. 12/13
	D. 9/13

Question

The imaginary part of the complex number (a + ib)/ (c-id) is given by

Possible Answers

Selected	Possible Answer
	A. $\cfrac{ac+bd}{c^2 - d^2}$
	B. $\cfrac{ac - bd}{c^2 + d^2}$
	C. $\cfrac{ad - bc}{c^2 - d^2}$
	D. $\cfrac{ad+bc}{c^2 + d^2}$

Question

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

Possible Answers

Selected	Possible Answer
	A. 2x – 3y = 15
	B. 2x + 3y = 15
	C. 3x + 2y = 15
	D. 3x – 2y = 15

Question

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?

Possible Answers

Selected	Possible Answer
	A. 5/4
	B. 7/4
	C. 3/4
	D. 1/4

Question

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?

Possible Answers

Selected	Possible Answer
	A. 1:5
	B. 1:4
	C. 1:3
	D. 1:6

Question

The arithmetic mean of the $k^{th}$ and the $l^{th}$ terms of an A.P. is equal to the arithmetic mean of the $m^{th}$ and the $n^{th}$ terms of the same A.P. Find the value of (m + n).

Possible Answers

Selected	Possible Answer
	A. l – k
	B. k – l
	C. l + k
	D. None of these

Question

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?

Possible Answers

Selected	Possible Answer
	A. (-3, -3)
	B. (-3, -2)
	C. (-2, -2)
	D. (-2, -3)

Question

In the X â€“ 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.

Possible Answers

Selected	Possible Answer
	A. 23
	B. 25
	C. 27
	D. 29

Question

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

Possible Answers

Selected	Possible Answer
	A. 0
	B. 1
	C. 2
	D. 3

Question

If ax +by + c = 0 and dx + ey + f = 0 represent the same straight line then which of following is necessarily satisfied?

Possible Answers

Selected	Possible Answer
	A. a = d, b = e and c = f
	B. $\cfrac{a}{d} = \cfrac{b}{e} = \cfrac{c}{f}$
	C. ad + be + cf = 0
	D. None of these

Question

Directions for next five questions

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.

If the “Labour Cost” of a single unit of machine is Rs.2500 then what is the per unit “Marketing Cost” of the machine?

Possible Answers

Selected	Possible Answer
	A. $1125
	B. $112500
	C. $11250
	D. None of these.

Question

What is the angle subtended by the “Overheads Cost” at the centre of the circle, in the above pie chart?

Possible Answers

Selected	Possible Answer
	A. $15^{\circ}$
	B. $75^{\circ}$
	C. $54^{\circ}$
	D. $45^{\circ}$

Question

How much more is the per unit “Packaging Cost” with respect to the per unit “Marketing Cost”?

Possible Answers

Selected	Possible Answer
	A. 94.44%
	B. 84.44%
	C. 104.44%
	D. None of these

Question

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?

Possible Answers

Selected	Possible Answer
	A. -2.5%
	B. -10%
	C. -1.5%
	D. -3.5%

Question

Which of the following is true?

Possible Answers

Selected	Possible Answer
	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.

Question

Directions for next 5 questions
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.

What is the ratio of the “Targeted Production” to the “Actual Production” in the year 2000 – 2001?

Possible Answers

Selected	Possible Answer
	A. 11/12
	B. 17/18
	C. 15/16
	D. 19/20

Question

What percent of the “Targeted production” was met by the “Actual Production”, in the year 2002 -2003?

Possible Answers

Selected	Possible Answer
	A. 112.5%
	B. 12.5%
	C. 125%
	D. 120.5%

Question

Which of the following two consecutive years have followed the same trend of “Actual Production” with respect to the “Targeted Production”?

Possible Answers

Selected	Possible Answer
	A. 1999â€“2000 and 2001â€“2002
	B. 2000â€“2001 and 2002â€“2003
	C. 2001â€“2002 and 2000â€“2001
	D. 2002â€“2003 and 2003â€“2004

Question

In which of the following years the “Actual Production” surpassed the “Targeted Production” by the maximum percentage?

Possible Answers

Selected	Possible Answer
	A. 1999-2000
	B. 2000-2001
	C. 2002-2003
	D. 2003-2004

Question

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

Possible Answers

Selected	Possible Answer
	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 Sample Papers 2007

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