For B.Tech.
Topic
No. of Ques.
Physics
Timing
20
Maths
45
(Algebra, Coordinate Geometry,
Probability, Trigonometry, Calculus,
Differential Equations, Vector,
Statistics, Dynamics and Statistics)
2:00 Hr.
English
25
(Antonym, Synonyms, Spellings,
Common Errors, One Word
Substitutions, Sentence Completion,
Preposition and Articles)
TOTAL
90
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MODEL TEST PAPER
GLA University, Mathura
(For B.Tech.)
Q.1. Dimensional formula for force is
(a) MLT –2
–1
(b) MLT
–2
(c) MT
(d) ML
Q.2.
Q.3.
Q.4.
Q.5.
Q.6.
Q.7.
Q.8.
Q.9. A man is sitting on a revolving stool with
his arms outstretched. When he pulls his
¨
arms suddenly inside then
¨
(a) his angular velocity decreases
¨
¨
(b) his moment of inertia decreases
¨
¨
(c) his angular velocity remains constant ¨
(d) his angular momentum increases
¨
On decreasing the temperature of a liquid
its rate of evaporation
Q.10. A p-type crystal is
¨
(a) increases
(a) positive
¨
¨
(b) decreases
(b) negative
¨
(c) first increases and then decreases ¨
(c)
neutral
¨
¨
(d) remains unaffected
(d) may be positive or negative
¨
Bernoulli’s theorem is based upon
Q.11. The resistance of a wire is R. If the length
¨
(a) conservation of energy
of the wire is doubled, then its resistance
¨
(b) conservation of charge
will be
¨
(c) conservation of momentum
(a) 2R
¨
¨
(d) none of these
(b) 4R
¨
(c) 8R
¨
In an isochoric process
(d) 16R
¨
¨
(a) temperature remains constant
¨
(b) pressure remains constant
Q.12. Diamagnetism exist in the substances on
¨
(c) volume remains constant
account of
¨
(d) no exchange of heat takes place
(a) paired electrons
¨
(b)
unpaired
electrons
¨
Temperature of two bodies are T1 and T2.
(c)
presence
of
protons
¨
If they are in thermal equilibrium then
(d)
presence
of
domains
¨
¨
(a) T1 > >T2
¨
(b) T1 > T2
Q.13. You are given a wire of length 50 cm and
¨
(c) T1 < T2
battery of negligible resistance. In which
¨
(d) T1 = T2
case the maximum amount of Heat is
generated ?
Of the following cases, velocity of sound
(a) when the wire is connected across the ¨
at 30° will be least through
battery directly
(a) N2
(b) hen the wire is divided into two
¨
¨
(b) O2
parts and both the parts are connected
¨
(c) SO2
across the battery in parallel
¨
(d) CO2
(c) when wire is divided into four parts ¨
¨
and all the parts are connected across
Two tuning forks have the frequencies
battery in parallel
512 Hz and 516 Hz. Number of beats
(d) None of these
¨
produced by these forks per second will
be
Q.14. The temperature of the sun is measured
(a) 1028
with
¨
(b) 4
(a) platinum resistance thermometer
¨
¨
(c) 1/4
(b)
gas
thermometer
¨
¨
(d) 1/1028
(c) vapour pressure thermometer
¨
¨
(d) pyrometer
¨
Matter waves are
(a) mechanical waves
¨
Q.15. For the production of x-rays of
(b) electromagnetic waves
¨
wavelength 0.1 A, the minimum potential
(c) quantum mechanical waves
¨
difference will be
(d) none of these
¨
¨
(a) 12.4 KV
(b) 124 KV
(c) 6.2 KV
(d) 62 KV
(b) 1 : 12
¨
¨
(c) 1 : 5
¨
¨
(d) 5 : 1
¨
¨
Q.16. If the elements of n > 4 were not exists in
Q.22. Two cards are drawn at random from a
nature, then possible number of elements
pack of 52 cards. The probability of
in nature were
getting at least a spade and an ace is
(a) 60
(a) 1/34
¨
¨
(b) 32
(b) 8/221
¨
¨
(c) 4
(c)
1/26
¨
¨
(d) 64
(d) 2/51
¨
¨
Q.17. An electron in an atom (Z = 4) is in first
Q.23. A five digit number is formed by the
energy state. The ionization energy of the
digits 1, 2, 3, 4, 5 without repetition. Find
atom will be
the probability that the number formed is
(a) 0 eV
divisible by 4 :
¨
(a) 1/5
(b) − 13.6 eV
¨
¨
(b) 6/5
(c) 13.6 eV
¨
¨
(c)
4/5
(d) 217.6 eV
¨
¨
(d) None of these
¨
Q.18. Bohr’s Quantum condition is( where Iω
Q.24. A bag contains 30 balls numbered from 1
is moment of inertia and ω is angular
to 30. One ball is drawn at random. The
velocity)
probability that the number of the ball
(a) Iω = 2π/ nh
¨
drawn will be a multiple of 3 or 7 is :
(b) Iω = nh/ 2π
¨
(a) 14/30
(c) Iω2 = nh/ 2π
¨
¨
(b) 40/900
(d) Iω = nh/ 4π
¨
¨
(c) 13/30
¨
Q.19. N equal resistors are first connected in
(d) None of these
¨
series and then connected in parallel.
Q.25. A probability that a leap year selected at
Ratio of maximum to the minimum
random contains either 53 sundays or 53
resistance is
mondays, is :
(a) N
¨
2
(a) 2/7
(b) N
¨
¨
2
(b) 4/7
¨
¨
(c) 1/N
(c) 3/7
¨
¨
(d) 1/N
(d) 1/7
¨
Q.20. Which of the following is true in case of
Q.26. The number of 6 digit numbers that can
longitudinal stationary waves?
be made with the digits 0, 1, 2, 3, 4 and 5,
¨
(a) variation in pressure and density is
so
that even digit occupy odd places is
¨
maximum at nodes
(a) 24
(b) variation in pressure is maximum and ¨
¨
(b) 36
variation in density is minimum at
¨
(c)
48
nodes
¨
(d) None of these
(c) variation in pressure and density is
¨
minimum at nodes
Q.27. Let f(x) = 2 x + 1. Then the number of
(d) variation in pressure is minimum and ¨
real values of x for which the three
variation in density is maximum at
unequal
numbers f(x), f(2x), f(4x) are in
Nodes
G.P. is
¨
(a) 1
Q.21. In a single throw with two dice, the
¨
(b) 0
odds against drawing 7 is
¨
(c)
2
(a) 1 : 6
¨
¨
(d) None of these
Q.28. The system of simultaneous equations
K x + 2 y – z = 1, (K – 1) y – 2 z = 2,
( K + 2 ) z = 3 have a unique solution if
K is
(a) – 2
(b) 0
(c) – 1
(d) 1
Q.35. If in a triangle PQR, sin P, sin Q, sin R are
in A.P. Then :
(a) the altitudes are in A.P.
¨
(b) the altitudes are in H.P.
¨
(c) the medians are in G.P.
¨
¨
(d) the medians are in A.P.
¨
¨
¨
¨
Q.36. The distance between the parallel lines
Q.29. The number of values of a for which
y = 2x + 4 and 6x = 3y + 5 is :
¨
(a²–3a + 2) x² + (a² – 5 a + 6) x + a² – 4 = 0
(a) 17/Ö
3
¨
is an identity in x is
(b) 1
¨
¨
(a) 0
(c) 3/Ö
5
¨
¨
(b) 2
(d) 17Ö
5 / 15
¨
(c) 1
¨
(d) 3
The line segment joining the points
Q.37. (– 3, – 4) and (1 , – 2) is divided by
Q.30. Set A has 3 elements and set B has 4
y - axis in the ratio
elements. The number of injections that
¨
(a) 1 : 3
can be defined from A to B is
¨
(b) 2 : 3
(a) 144
¨
¨
(c) 3 : 1
(b) 12
¨
¨
(d) 3 : 2
(c) 64
¨
Q.38. The curve represented by x=3(cos t + sin t),
(d) 24
¨
y = 4 ( cos t – sin t ) is
The
value
of
cos
15°
is
equal
to
¨
(a)
Ellipse
Q.31.
(a) [(√3 +1)/2√2]
¨
¨
(b) Parabola
(b) [(√3 -1)/2√2]
¨
¨
(c) Hyperbola
(c) 2 – √3
¨
¨
(d) Circle
(d) 2 + √3
¨
Q.39. Which of the following is the equation of
a plane?
Q.32. The value of tan 10° + tan 35° + tan 10°.
tan 35° is equal to:
¨
(a) l x + my = n
(a) 0
¨
¨
(b) z = 0
(b) 1/2
¨
¨
(c) 2x + 3y = 0
(c) – 1
¨
¨
(d) y = – x
(d) 1
¨
Q.40. The eccentricity of the ellipse
The
value
of
Ö
3
cosec
20°
–
sec
20°
is
Q.33.
9x2 + 5y2 – 30y = 0 is
¨
equal to :
(a) 1/3
¨
¨
(a) 2
(b) 2/3
¨
¨
(b) 1
(c) 3/4
¨
¨
(c) 4
(d) None of these
¨
(D) None of these
Q.41. The function f(x) = 1 / x on its domain is
¨
(a) increasing
3,
Q.34. In a right angled ABC, a = 2, b = 1+ Ö
¨
(b) decreasing
Ð
C = 60° then the side c is equal to :
¨
¨
(c)
constant
(a) Ö
3–1
¨
¨
(d)
information
insufficient
(b) Ö
2+1
¨
(c) Ö
6
Q.42. The maximum value of x y subject to
¨
(D) None of these
x + y = 8 is
¨
(a) 8
¨
(b) 16
Q.50. If a, b and c are three non-coplanar
¨
¨
vectors then (a + b + c).{(a + b) ´
(a + c )}
equals
¨
Q.43. ∫ [ cos 2x / cos x ] dx is equal to
(a) 0
¨
(a) 2 sin x + log ( sec x – tan x ) + c
¨
(b) [a b c]
¨
(b) 2 sin x – log ( sec x – tan x ) + c ¨
(c) 2 [a b c]
¨
(c) 2 sin x + log ( sec x + tan x ) + c ¨
(d) – [a b c]
(d) 2 sin x – log ( sec x + tan x ) + c ¨
Q.51. A train of length 200 m. travelling at 30
Q.44. If √( x + y ) + √( y – x ) = c where c is
m./sec. overtakes another of length 300
a constant then d2y/dx2 is equal to
m. travelling at 20 m. /sec. The time taken
(a) 2 / c
by the first train to pass the second is
¨
2
¨
(b) – 2 / c
(a) 30 sec.
¨
2
¨
(b) 50 sec.
(c) 2 / c
¨
¨
(c) 10 sec.
(d) None of these
¨
¨
(d) 40 sec.
Q.45. The area of the region bounded by
y = | x – 1 | and y = 1 is
Q.52. The resultant of the forces 4, 3, 4 and 3
¨
units acting along sides AB, BC, CD and
(a) 1
¨
DA
of square ABCD of side a
(b) 2
¨
respectively
is
(c) 1/2
¨
(a) a null force
¨
(d) None of these
(b) a force of magnitude 5√2 through ¨
Q.46. If a, b, c are three non zero vectors then
centre of square
¨
the equation a . b = a . c implies
(c)
a couple of moment 7 a
¨
¨
(a) b = c
(d) none of these
¨
(b) a is orthogonal to b – c
¨
(c) both (i) and (ii)
Q.53. A man wishes to cross a river to an
¨
(d) None of these
exactly opposite point on the other bank,
if he can swim with twice the velocity of
the current, then the inclination to the
Q.47. If i, j and k are unit orthonormal vectors
then i .( j ´
k) + j. (K ´
i) + k. ( i ´
j)
current of the direction in which he
is equal to
should swim is
¨
(a) 1
(a) 1 : 1
¨
¨
(b) 3
(b) √2 : 1
¨
¨
(c) – 3
(c) 1 : √2
¨
¨
(d) 0
(d) 3 : 2
¨
(c) 20
(d) 24
Q.54. A rod can turn freely about one of its ends
Q.48. The points with position vectors 10 i + 3j,
12 i – 5 j & a i + 11j are collinear if a is
which is fixed. At the other end, a
equal to
horizontal force equal to half of the
¨
(a) – 8
weight of the rod is acting. In the position
¨
(b) 4
of equilibrium, the rod is inclined to the
¨
(c) 8
vertical at an angle
¨
(d) 12
(a) 30˚
¨
(b) 45˚
¨
(c) 60˚
Q.49. If | a | = 7, | b | = 11, | a + b | = 10√3
¨
then |a – b| is equal to
(d) None of these
¨
(a) 10
¨
(b) √10
Q.55. Forces 7, 5 and 3 acting on a particle are
¨
(c) 2√10
in equilibrium. The angle between the
¨
(d) 20
last
pair of forces is
¨
(a) 120˚
¨
2
2
¨
Q.63. If f(x) = cos x + sec x , its value
¨
always is
¨
¨
(a) less than 1
¨
(b) equal to 1
Q.56. The mean marks of 100 students were
¨
(c) between 1 and 2
found to be 40. Later on, it was
¨
(d) greater than or equal to 2
discovered that a score of 53 was misread
4
as 83. The correct mean is
Q.64. (sin θ + i cos θ) is equal to
(a) 35.3
¨
¨
(a) cos 4 θ – i sin 4 θ
(b) 36.9
¨
¨
(b) sin 4 θ + i cos 4 θ
(c) 41.2
¨
¨
(c) sin 4 θ – i cos 4 θ
(d) 39.7
¨
¨
(d) cos 4 θ + i sin 4 θ
(b) 90˚
(c) 60˚
(d) 30˚
Q.57. The measure which takes into account all
Q.65. If tan p θ = tan q θ then the values of θ
the data items is
form a series in
(a) Mean
¨
¨
(a) A.P.
(b) Median
¨
¨
(b) G.P.
(c) Mode
¨
¨
(c) H.P.
(d) None of these
¨
¨
(d) None of these
Q.58. The scores of a batsman in ten innings are
Q.66. Choose the appropriate Antonym of
38, 70,48, 34, 42, 55, 63, 46, 54, 44. The
'Undertaking’
mean deviation about the median is
¨
(a) Resignation
(a) 9.2
¨
¨
(b) Trial
(b) 8.6
¨
¨
(c) Refusal
(c) 7.4
¨
¨
(d) Denial
(d) 6.6
¨
Q.67. Choose the appropriate Antonym of
Q.59. The sum of 10 items is 12 and sum of their
'Sympathy’
squares is 18.Therefore the standard
¨
(a) Enmity
deviation will be
¨
(b) Cruelty
(a) 5/3
¨
¨
(c) Abhorrence
(b) 3/5
¨
¨
(d) Apathy
(c) 9/25
¨
(d) 25/9
¨
Q.68. Choose the appropriate Antonym of
Absolve’
Q.60. One of the methods of determining mode is
¨
(a) bless
(a) Mode = 2 Median – 3 Mean
¨
¨
(b) blame
(b) Mode = 2 Median + 3 Mean
¨
¨
(c) melt
(c) Mode = 3 Median – 2 Mean
¨
¨
(d) repent
(d) Mode = 3 median + 2 Mean
¨
Q.69. Choose the appropriate Antonym of
x
1– x
Indigenous’
Q.61. The minimum value of 4 + 4 , x ε R is
(a) 1
(a) foreign
¨
¨
(b) 2
(b) destitute
¨
¨
(c) 4
(c) insulting
¨
¨
(d) None of these
(d)
livid
¨
¨
Q.70. Choose the appropriate Synonym of
Q.62. The sum of all odd proper divisors of 360
'INHIBIT’
is
¨
¨
(a) Prevent
(a) 77
¨
¨
(b) Violate
(b) 78
¨
¨
(c)
Reside
(c) 81
¨
¨
(d) Not to exhibit
(d) None of these
Q.71. Choose the appropriate Synonym of
'GALORE’
(a) Short
(b) In abundance
(c) Complete
(d) Regular supply
Q.79. Choose the most suitable One Word‘A workman who fits and repairs pipes’
(a) Mechanic
¨
¨
(b) Blacksmith
¨
¨
(c) Plumber
¨
¨
(d) Technocrat
¨
¨
Q.72. Choose the appropriate Synonym of
Q.80. Choose the most suitable One Word‘Study of books in regard to their
'LIQUIDATE’
outward
form, authors, subjects,
(a) Prolong
¨
editions,
etc.’
(b) destroy
¨
(a) autobiography
(c) liberate
¨
¨
(b)
biography
(d) persist
¨
¨
(c) bibliography
¨
(D) philately
Q.73. Choose the appropriate Synonym of
¨
'ABASH’
¨
Q.81. Fill in the blank selecting correct
(A) Strike
¨
Preposition from the alternatives given
(b) Deduct
¨
below sentence (c) Forsake
¨
He aspires ….. the post of a professor.
(d) Confound
¨
(a) about
¨
(b) for
Q.74. Choose the appropriate Synonym of
¨
(c) to
‘HARASS’
¨
(d) on
(a) rave
¨
(b) shelter
¨
Q.82. Fill in the blank selecting correct
(c) torment
¨
Preposition from the alternatives given
(d) pierce
¨
below sentence Q.75. Choose the correctly spelt word(a) pernicious
(b) parnicious
(c) pernishes
(d) pernecious
Q.76. Choose the correctly spelt word(a) marrygible
(b) marriageable
(c) marriagable
(d) marriageble
I do not know how to manage …….
four hundred francs.
¨
¨
(a) with
¨
¨
(b) without
¨
¨
(c) by
¨
¨
(d) for
¨
Q.83. Choose the most appropriate
¨
preposition:
¨
He was advised to abstain _______ all
¨
alcoholic drinks.
¨
(a) in
¨
(b) at
Q.77. Choose the most suitable One Word¨
(c) from
‘Child whose parents are not married.’
¨
¨
(d) by
(a) bastard
¨
(b) foster-child
¨
Q.84. Choose the most appropriate
(c) posthumous-child
¨
preposition:
(d) fondling
Take this medicine and you will get rid
_______ the bad cold.
Q.78. Choose the most suitable One Word(a) from
‘A child born after the death of his
¨
(b) over
father.’
¨
(c) at
¨
(a) posthumous
¨
(d) of
¨
(b) orphan
¨
¨
(c) bastard
¨
(d) progenitor
Q.85. Choose the most appropriate
preposition:
My cousin has invested a lot of money
_______ farming.
(a) on
(b) for
(c) in
(d) into
¨
¨
¨
¨
¨
¨
¨
¨
¨
¨
Q.86. Fill in the blank selecting correct
¨
Preposition from the alternatives given
¨
below sentence ‘I am fond …………… vegetables.’
(a) into
¨
¨
(b) since
¨
¨
(c) of
¨
¨
(d) for
¨
¨
Q.87. Fill in the blank with a suitable Article
‘The man is ……… social animal.’
(a) a
(b) an
(c) the
(d) None of these
¨
¨
¨
¨
¨
¨
¨
¨
¨
¨
¨
¨
¨
¨
¨
¨
¨
Q.89. Fill in the blank with a suitable Article
¨
‘Cold on …… Himalayas is terrible.’
¨
(a) a
¨
¨
(b) an
¨
(c) the
¨
(d) None of these
¨
¨
¨
Q.90. Complete the sentence:
¨
All of us should abide ______ the laws
¨
of our country.
(a) on
¨
(b) to
¨
¨
(c) by
¨
¨
(d) in
¨
¨
¨
Q.88. Fill in the blank with a suitable Article
‘Mohan gave me ……… useful book.’
(a) a
(b) an
(c) the
(d) None of these
***
*
¨
¨
¨
¨