# SOLUTION TO CUMMINS PLACEMENT PAPER

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SOLUTION TO CUMMINS PLACEMENT PAPER.

GENERAL APTITUDE QUESTION:-

1.A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
A.
 4
B.
 9
C.
 12
D.
 49

Explanation:

Let the required number of revolutions made by larger wheel be x.

Then, More cogs, Less revolutions (Indirect Proportion)

14 : 6 :: 21 : x       14 x x = 6 x 21

 x = 6 x 21 14

x = 9.

Direction (for Q.No. 2):

Insert the missing number.

2.8, 24, 12, 36, 18, 54, (….)
A.
 27
B.
 108
C.
 68
D.
 72

Explanation:

Numbers are alternatively multiplied by 3 and divided by 2.

So, the next number = 54 ÷ 2 = 27.

3.A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
A.
 45 km/hr
B.
 50 km/hr
C.
 54 km/hr
D.
 55 km/hr

Explanation:

 Speed of the train relative to man = 125 m/sec 10

 = 25 m/sec. 2

 = 25 x 18 km/hr 2 5

= 45 km/hr.

Let the speed of the train be x km/hr. Then, relative speed = (x – 5) km/hr.

x – 5 = 45         x = 50 km/hr.

Direction (for Q.No. 4):
4.
 A man mixes two types of rice (X and Y) and sells the mixture at the rate of Rs. 17 per kg. Find his profit percentage. I. The rate of X is Rs. 20 per kg. II. The rate of Y is Rs. 13 per kg.
A.
 I alone sufficient while II alone not sufficient to answer
B.
 II alone sufficient while I alone not sufficient to answer
C.
 Either I or II alone sufficient to answer
D.
 Both I and II are not sufficient to answer
E.
 Both I and II are necessary to answer

Explanation:

The ratio, in which X and Y are mixed, is not given.

So, both I and II together cannot give the answer.

5.In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:
A.
 2700
B.
 2900
C.
 3000
D.
 3100

Explanation:

Number of valid votes = 80% of 7500 = 6000.

Valid votes polled by other candidate = 45% of 6000

 = 45 x 6000 = 2700. 100

6.A father said to his son, “I was as old as you are at the present at the time of your birth”. If the father’s age is 38 years now, the son’s age five years back was:
A.
 14 years
B.
 19 years
C.
 33 years
D.
 38 years

Explanation:

Let the son’s present age be x years. Then, (38 – x) = x

2x = 38.

x = 19.

Son’s age 5 years back (19 – 5) = 14 years.

7.A person’s present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?
A.
 32 years
B.
 36 years
C.
 40 years
D.
 48 years

Explanation:

Let the mother’s present age be x years.

 Then, the person’s present age = 2 x years. 5

 2 x + 8 = 1 (x + 8) 5 2

2(2x + 40) = 5(x + 8)

x = 40.

8.A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:
A.
 720
B.
 900
C.
 1200
D.
 1800

Explanation:

2(15 + 12) x h = 2(15 x 12)

 h = 180 m = 20 m. 27 3

 Volume = 15 x 12 x 20 m3 = 1200 m3. 3

Direction (for Q.Nos. 9 – 10):

Find out the wrong number in the series.

9.3, 7, 15, 39, 63, 127, 255, 511
A.
 7
B.
 15
C.
 39
D.
 63
E.
 127

Explanation:

Go on multiplying 2 and adding 1 to get the next number.

So, 39 is wrong.

10.190, 166, 145, 128, 112, 100, 91
A.
 100
B.
 166
C.
 145
D.
 128
E.
 112

Explanation:

Go on subtracting 24, 21, 18, 15, 12, 9 from the numbers to get the next number.

`190 - 24 = 166`
`166 - 21 = 145`
`145 - 18 = 127 [Here, 128 is placed instead of 127]`
`127 - 15 = 112`
`112 - 12 = 100 ... and so on.`

Therefore, 128 is wrong.

11.The true discount on a bill of Rs. 540 is Rs. 90. The banker’s discount is:
A.
 Rs. 60
B.
 Rs. 108
C.
 Rs. 110
D.
 Rs. 112

Explanation:

P.W. = Rs. (540 – 90) = Rs. 450.

S.I. on Rs. 450 = Rs. 90.

 S.I. on Rs. 540 = Rs. 90 x 540 = Rs. 108. 450

B.D. = Rs. 108.

13.A sum of Rs. 1360 has been divided among A, B and C such that A gets of what B gets and B gets of what C gets. B’s share is:
A.
 Rs. 120
B.
 Rs. 160
C.
 Rs. 240
D.
 Rs. 300

Direction (for Q.No. 16):

16.
 What is the rate of interest p.c.p.a.? I. An amount doubles itself in 5 years on simple interest. II. Difference between the compound interest and the simple interest earned on a certain amount in 2 years is Rs. 400. III. Simple interest earned per annum is Rs. 2000.
A.
 I only
B.
 II and III only
C.
 All I, II and III
D.
 Any two of the three
E.
 I only or II and III only

Explanation:

 I. P x R x 5 = P         R = 20. 100

 II. P 1 + R 2 – P – P x R x 2 = 400         PR2 = 4000000. 100 100

 III. P x R x 1 = 2000         PR = 200000. 100

 PR2 = 4000000 R = 20. PR 200000

Thus I only or (II and III) give answer.

17.If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?
A.
 2 : 5
B.
 3 : 7
C.
 5 : 3
D.
 7 : 3

Explanation:

 Let 40% of A = 2 B 3

 Then, 40A = 2B 100 3

 2A = 2B 5 3

 A = 2 x 5 = 5 B 3 2 3

A : B = 5 : 3.

18.Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is:
A.
 75
B.
 81
C.
 85
D.
 89

20.A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
A.
 2.91 m
B.
 3 m
C.
 5.82 m
D.
 None of these

Explanation:

Area of the park = (60 x 40) m2 = 2400 m2.

Area of the lawn = 2109 m2.

Area of the crossroads = (2400 – 2109) m2 = 291 m2.

Let the width of the road be x metres. Then,

60x + 40xx2 = 291

x2 – 100x + 291 = 0

(x – 97)(x – 3) = 0

x = 3.

.1   An ohmmeter is connected across an inductor and the pointer indicates zero ohms.     The inductor is
A.
 good
B.
 open
C.
 shorted
D.
 partly shorted

2.The mesh method can be applied to circuits with any number of loops.
A.
 True
B.
 False

5.Inductance is indirectly proportional to the square of the number of turns, the permeability, and the cross-sectional area of the core.
A.
 True
B.
 False

Explanation:

Some factors that affect the inductance of a coil include:

1. The inductance is proportional to the square of the number of turns;
2. The inductance increases directly as the permeability of the core material increases;
3. The inductance increases directly as the cross-sectional area increases; and
4. The inductance decreases as its length increases.

6.When the current through the coil of an electromagnet reverses, the
A.
 direction of the magnetic field reverses
B.
 direction of the magnetic field remains unchanged
C.
 magnetic field expands
D.
 magnetic field collapses

7.If the capacitor in an integrator becomes leaky,
A.
 the time constant will be effectively reduced
B.
 the waveshape of the output voltage across C is altered
C.
 the amplitude of the output is reduced
D.
 all of the above

10.When converting 0.16 mA to microamperes, the result is
A.
 16 µA
B.
 160 µA
C.
 1,600 µA
D.
 0.0016 µA

11.Fourteen milliamperes can be expressed as
A.
 14 MA
B.
 14 µA
C.
 14 kA
D.
 14 mA

12.The number 65,000 expressed in scientific notation as a number between 1 and 10 times a power of ten is
A.
 0.65 × 104
B.
 6.5 × 104
C.
 65 × 104
D.
 650 × 103

13.In a two-source circuit, one source acting alone produces 12 mA through a given branch. The other source acting alone produces 10 mA in the opposite direction through the same branch. The actual current through the branch is
A.
 22 mA
B.
 12 mA
C.
 10 mA
D.
 2 mA

14.Five light bulbs are connected in parallel across 110 V. Each bulb is rated at 200 W. The current through each bulb is approximately
A.
 2.2 A
B.
 137 mA
C.
 1.8 A
D.
 9.09 A

15.The rising and falling edges of a pulse waveform contain the higher frequency component.
A.
 True
B.
 False

16.In an RL differentiating circuit, the output voltage is taken across the resistor.
A.
 True
B.
 False

17.The conductance of an 8 ohm resistance is
A.
 12.5 mS
B.
 8 mS
C.
 12 S
D.
 125 mS

18.Which of the following is not a type of energy source?
A.
 generator
B.
 rheostat
C.
 solar cell
D.
 battery

19.A wiper is the sliding contact in a
A.
 switch
B.
 photoconductive cell
C.
 thermistor
D.
 potentiometer

20.The power rating of a carbon-composition resistor that is to handle up to 1.2 W should be
A.
 2 W
B.
 1 W
C.
 5 W
D.
 0.5 W