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LINGAYA’S UNIVERSITY
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SAMPLE PAPER - B.ARCH EXAM
MATHEMATICS
1.
3

2
The probability that the roots of the equation x  2nx   4    0 are not real numbers
n

where n  N such that n  5 is
(a)
2.
2/5
(b)
4/5
(c)
1/5
(d) 3/5
If A is area lying between the curve y = cos x and x-axis between x = 0 and x = /2, then the area
of the region between the curve y  cos 2 x / 2 and the x-axis in the same interval is given by
(a)
  A / 2
(b)
  / 4  A
(c)
  / 2  A
(d)
  / 4    A / 2
(c)
1
1
3.
x
dx is equal to
|x|
1

(a)
4.
2
(b)
7.
is
(a)
 x  1 cos  3x  4 
(b)
sin  3x  4   3  x  1 cos  3x  4 
(c)
sin  3x  4
(d)
none
4
4
The coefficient of x10 in the expansion of 1  x 2  1  x  is
(a)
6.
(d) 0
If the area bounded by the curve y  f  x  , x-axis and the ordinates x=1 and x = b is
 b  1 sin  3b  4 , then f  x 
5.
–2
15
(b)
20
(c)
10
(d) 6
Which one of the following is TRUE for any x
(a)
1
1
1


x5 x2 x2
(b)
1
1
1


x 2 x 2 x 5
(c)
1
1
1


x5 x3 x2
(d)
1
1
1


x3 x2 x5
dy
yx

dx
The order and degree of the differential equation
(a)
1, 2
(b)
1, 4
(c)
a
dy
dx
 dy 
1 

 dx 
1,5 2
2
is
(d) 1, 3
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8.
9.


 x/y 
dx  e x/y  1   x / y   dy  0
The general solution of the differential equation 1  e
(a)
y  xe x/y   C
(b)
x  ye x/y   C
(c)
x  C  ye  x/y 
(d)
y  ye x/y   C
The triangle with vertices A = (2, 7), B = (4, y) and C = (–2, 6) is right angled at B if the value of
y is
(a)
10 or –3
(b)
–10 or –3
(c)
10 or 3
(d)
9 or 4
10. The point equidistant from the three lines x + y = 1, y = 1 and x = 1 is
(a)
 1
1 
,


2
2

(b)
 1
1 
,


2
2

(c)
 1
1 
,


3
2

(d)
 1
1 
,


2
3

11. The equation of the line mid parallel to the two lines 5x  2y  9  0 and 5x  2y  7  0 is
(a)
x  5y  8  0
(b)
5x  y  1  0
(c)
2x  5y  6  0
(d)
5x  2y  1  0
12. The straight line 3x  4y  4  0 is moved parallelly so that its distance from the point  3,  2
is increased by 4 units. Then its equation in the new position is
(a)
3x  4y  30  0
(b)
3x  4y  24  0
(c)
3x  4y  21  0
(d)
3x  4y  24  0
13. If a, b, c are AM, GM and HM respectively of two equal numbers, then
(a)
2b = a + c
(b)
b = 2ac / (a + c)
(c)
b2 = ac


(d) ab2 = c




2
14. The harmonic mean of the roots of the equation is 7  3 x  6  7 x  12  2 7  0
(a)
8
(b)
6
(c)
3
(d) 4
15. The general solution of x satisfying the system of equations 5 sin x sin y   1 ; 25sin 2x  sin 2y   5 is
(a)
n   / 6
(b)
2n   / 6
(c)
n    / 6
(d)
n   / 6
ENGLISH
Against each key word are given some suggested meanings. Choose the word or phrase which is
nearest in meaning to the key word.
1.
2.
Lethargy
(a)
Serenity
(b)
Listhessness
(c)
Impassivity
(d)
Laxity
Prognosis
(a)
Scheme
(b)
Forecast
(c)
Preface
(d)
Identification
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3.
Enigmatic
(a)
4.
(b)
Puzzling
(c)
Learned
(d) Short sighted
(b)
Failure
(c)
Radiculous plan
(d) Misfortune
Fiasco
(a)
5.
Displeased
Festival
Consummation
(a)
act of devouring
(b)
act of forgiveness
(c)
failure
(d)
ultimate completion
(c)
Devotee
(d) Secularist
(c)
Treasury
(d) Bank
One Word Substitute
6.
One who believes in God
(a)
7.
9.
(b)
Theist
A place where money is coined
(a)
8.
Agnostic
Mint
(b)
Press
One who hates manhind
(a)
Philanthropist
(b)
Misanthrope
(c)
Hater
(d)
Rebel
Unable to pay one’s debt
(a)
Beggar
(b)
Insolvent
(c)
Poor
(d) Borrower
(b)
Sonnet
(c)
Lyrac
(d) Epic
10. A poem of mourning
(a)
Elegy
Analogy :
The following questions comprise two words each that have a certain relationship between
them. Select the lettered pair that has the same relation as original words.
11. Shrub : Prune
(a)
Beard : Share
(b)
Hair : Trim
(c)
Lawn : Mow
(d)
Wool : Shear
12. Shield : Soldier
(a)
Stethoscope : Dcotor
(b)
Book : Author
(c)
Advocate : Court
(d)
Helmet : Rider
13. Fox : Cunning
(a)
Cat : Playful
(b)
Horse : Runner
(c)
Vixen : Cute
(d)
Ant : Industrious
14. Sonnet : Poem
(a)
Ballad : Stanza
(b)
Murder : Crime
(c)
Chapter : Book
(d)
Lie : Falsehood
15. Wrestler : Arena
(a)
Cricket : Pitch
(b)
Ring : Finger
(c)
Farmer : Field
(d)
Assistant : Cleark
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GENERAL APTITUDE (GI)
1.
A sphere of radius 4 cm is carved from a homogeneous sphere of radius 8 cm and mass 160 g.
The mass of the smaller sphere is
(a)
2.
4.
(b)
60 g
(c)
1 minute
(b)
2 minutes
(c)
There is no empty basket
(b)
There are exactly (n – k) baskets with at least one ball
(c)
There is at least one basket with two or more balls
(d)
There are (n – k) baskets with exactly two balls
(d) 4 minutes
An ant is crawling along the x-axis such that the graph of its position on the x-axis versus time
is a semi-circle (see figure). The total distance covered in the 4 s is
x[m]
4m
(b)
2m
t[s]
(c)
2 m
(d) 4 m
In a bag containing only blue, red and green marbles, all but 15 are blue, all but 13 are red and
all but 12 are green. How many are red?
(a)
13
(b)
7
(c)
25
(d) 20
Find the missing numbers in the bottom middle circle. (Clue : left halves of the central circles
relate to the left circles and the right halves to the right circles)
1
2
5
6
3
5
4
3
1
(a)
10, 20
2 4
2
12
30 3
3
15 4
3
8
? ?
2
4
2
7.
3 minutes
(a)
(a)
6.
(d) 20 g
There are k baskets and n balls. The balls are put into the baskets randomly. if k < n,
4
5.
40 g
Two boys A and B are at two diametrically opposite points on a circle. AT one instant the two
start running on the circle; A anticlockwise with constant speed v and B clockwise with constant
speed 2v. In 2 minutes, they pass each other for the first time. How much later will they pass
each other for the second time?
(a)
3.
80 g
(b)
6
1 4
6
3
9
2 8
15, 15
6
5 10
(c)
21, 2
(d) 6, 2
(c)
X
(d) B
Identify the missing letter.
Y
B
V
M
N
Z
(a)
W
(b)
A
E
?
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8.
Identify the figure that comes next in the sequence.
(a)
9.
(b)
(c)
(d)
A person buys a shirt with marked price Rs. 300/- at 20% discount. In order to make a profit of
20% the person should sell the shirt for
(a)
Rs. 288/-
(b)
Rs. 300/-
(c)
Rs. 240/-
(d) Rs. 360/-
10. A uniform cylindrical container is half filled with water. The height of the cylinder is twice its
diameter. The cylinder is gradually tilted until the water touches the brim. At this instant, the
container is inclined at
(a)
30° to vertical
(b)
45° to vertical
(c)
60° to vertical
(d)
75° to vertical
Speed
11. A car is moving along a straight road. The graph below shows how the speed varies with time.
Time
(b)
Distance
(a)
Distance
Which of the following graphs represents the distance covered by the car with time?
Time
(d)
Time
Distance
(c)
Distance
Time
Time
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12. In triangle ABC, shown in the figure, AB is perpendicular to BC. Further, BD is perpendicular
to AC. If AD = 9 cm and DC = 4 cm, the length BD is
B
A
(a)
6 cm
(b)
9 cm
C
4 cm
D
6.5 cm
(c)
36
cm
13
(d)
13
cm
36
13. A box of sticks of equal lengths is provided. The minimum number sticks needed to build a
frame to enclose a 3 dimensional volume is
(a)
6
(b)
12
(c)
3
(d) 8
14. 5 kg of adulterated rice has 2% stones in it and the rest is rice. Half of the stone content was
removed. Now the percentage of stone content in it is
(a)
0.99%
(b)
1%
(c)
1.1%
(d) 1.01%
15. A coin is tossed six times. The probability that heads will occur at least once is
63
64
(a)
(b)
1
3
(c)
1
64
(d)
3
2
16. Two parameters TC and TF are related as shown in the table. Find the value of TF corresponding
to a TC of 75.
TC
0
25
50
75
100
TF
32
77
122
?
212
(a)
167
(b)
162
(c)
150
(d) 200
17. Several identical cubes are arranged in a close-packed single layer. If the area of the layer is
A and the volume of the layer is V, then the number of cubes in the collection is
(a)
V/A
(b)
A3 / V2
(c)
V2 / A3
(d)
A/V
18. Circle PQR is inscribed in a quadrilateral ABCD. The circle touches side AD at point S. SP = 8
cm, QC = 3 cm and DC = 6 cm. The length of side AD is
B
P
Q
C
A
R
S
(a)
9 cm
(b)
10 cm
D
(c)
11 cm
(d) 12 cm
19. The distribution of wages in a population is shown below for 2 years.
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number of persons
2000
1999
wages
The average wage (s)
(a)
in 1999 is greater than that in 2000
(b)
in 1999 is less than that in 2000
(c)
in the two years are equal, but the variances are unequal
(d)
in the two years are unequal, but the variances are equal
20. The graph below shows crime rates and convictions for 5 years in a certain society.
2000
number of cases
1999
years
Which of the following is correct?
(a)
The cause of convictions being on the rise is better law of enforcement
(b)
Falling crime rates have slowly reduced the conviction rates also
(c)
There are fewer convictions because crime rate has fallen
(d)
The graph must be wrong
21. A number is as much greater than 75 as it is smaller than 117. The number is :
(a)
91
(b)
93
(c)
89
(d) 96
22. The professor ordered to the students to go out of the class.
I
II
III
IV
Which of the above underlined parts of the sentence is grammatically incorrect?
(a)
I
(b)
II
(c)
III
(d) IV
23. Which of the following options is the cloasest in meaning to the word given below :
Primeval
(a)
Modern
(b)
Historic
(c)
Primitive
(d) Antique
24. Friendship, no matter how ____________ it is, has its limitations.
(a)
cordial
(b)
intimate
(c)
secret
(d) pleasant
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25. Select the pair that best expresses a relationship similar to that expressed in the pair :
Medicine : Health
(a)
Science : Experiment
(b)
Wealth : Peace
(c)
Education : Knowledge
(d)
Money : Happiness
26. X and Y are two positive real numbers such that 2X  Y  6 and X  2Y  8 . For which of the
following values of (X, Y) the functions f (X, Y) = 3X + 6Y will give maximum value?
(a) (4/3, 10/3)
(b) (8/3, 20/3)
(c)
(8/3, 10/3)
(d) (4/3, 20/3)
27. If |4X  7|  5 , then the values of 2|X|  |  X| is :
(a)
2, 1/3
(b)
1/2, 3
(c)
3/2, 9
(d) 2/3, 9
28. Following table provides figures (in rupees) on annual expenditure of a firm for two years - 2010
and 2011.
Category
2010
2011
Rawmaterial
5200
6240
Power & fuel
7000
9450
Salary & wages
9000 12600
Plant & machinery
20000 25000
Adverti sin g
15000 19500
Re search & Development 22000 26400
In 2011, which of the following two catagories have registered increase by same percentage?
(a)
RAw material and Salary & Wages
(b)
Salary and wages and Advertising
(c)
Power & fuel and Advertising
(d)
Raw material and Research & Development
29. A firm is selling its product at Rs. 60 per unit. The total cost of production is Rs. 100 and firm is
earning total profit of Rs. 500. Later, the total cost increased by 30% . By what percentage the
price should be increased to maintained the same profit level.
(a)
5
(b)
10
(c)
15
(d) 30
30. Abhishek is elder to Savar.
Savar is younger to Anshul.
Which of the given conclusions is logically valid and is inferred from the above statements?
(a)
Abhishek is elder to Anshul
(b)
Anshul is elder to Abhishek
(c)
Abhishek and Anshul are of the same age
(d)
No conclusion follows
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