Educazione
Pisa Edu
TIL-I Denemesi-5
ADMISSION TEST FOR DEGREE COURSE
IN ENGINEERING TIL-I
2020/2021 Academic Year
pisaedu.com
Mathematics
1
Solve the inequality x2 6 x
A
B
C
D
E
2
- 3 and x
- 3 and x
- 3 and x
- 3 and x
2 only
2
2
2
2
How many times do y = x3 and y = x intersect?
A
B
C
D
E
3
x
x
x
x
x
0
1
2
3
4
I have two identical unfair dice, where the probability that the dice get a 6 is twice as
high as the probability of any other outcome, which are all equally likely. What is the
probability that when I roll both dice the total will be 12?
A
0
B
C
1
D
E
None of the above
4
A is inversely proportional to the square root of B. When A = 4, B = 25.
Calculate the value of A when B = 16.
A
B
C
D
E
5
6
0.8
4
5
6
10
Solve 3x2 + 11x 20 = 0
A
0.75 and
B
-0.75 and
C
-5 and
D
5 and
E
12 only
S, T, U and V are points on the circumference of a circle, and
O is the center of the circle.
Given that angle SVU = 89 , calculate the size of the smaller
angle SOU.
A
B
C
D
E
89
91
102
178
182
7
Express the volume of a cube, V, in terms of its surface area, S.
A
B
C
D
E
8
The equation cos2 =
A
B
C
D
E
9
V = (S/6)3/2
V = S3/2
V = (6/S)3/2
V = (S/6)1/2
V = (S/36)1/2
+
is only possible when?
x = -y
x y
x=y
x y
None of the above
If one of the zeroes of the quadratic polynomial (k - 1)x2 + kx + 1 is 3, then what is
the value of k?
A
B
−
C
D
E
−
1
10
There are two tennis players. The first player wins with probability p, and the second
player wins the point with probability 1 p. The rules of tennis say that the first
player to score four points wins the game, unless the score is 4 3. At this point the
first player to get two points ahead wins.
What is the probability that the first player wins in exactly 5 rounds?
A
B
C
D
E
11
Solve
A
B
C
D
E
12
4p4(1
p4(1
4p(1
4p(1
4p5(1
−
p)
p)
p)
p)4
p)
+
𝑥
1
1
1.5
3
3.5
4.5
If log + log = log (a + b), then which of the following is correct?
A
B
C
D
E
a+b=1
a b=1
a=b
a2 b2 = 1
None of the above
13
Fully factorize: 3a3 30a2 + 75a
A
B
C
D
E
14
3a(a 3)3
a(3a 5)2
3a(a2 10a + 25)
3a(a 5)2
3a(a + 5)2
The hypotenuse of an isosceles right-angled triangle is x cm. What is the area of the
triangle in terms of x?
A
√
B
C
D
E
15
1
Solve 3x 5y = 10 and 2x + 2y = 13.
1
A
(x, y) = (1 , 1 )
B
(x, y) = ( ,
1
1
1
1
)
C
(x, y) = ( ,
D
(x, y) = (
E
No solutions possible
1
)
1
1
,
1
1
)
16
If a.b = (ab) + (a + b), then calculate the value of (3.4).5
A
B
C
D
E
17
When 5 is subtracted from 5x the result is half the sum of 2 and 6x. What is the value
of x?
A
B
C
D
E
18
19
54
100
119
132
0
1
2
3
4
The two inequalities x + y 3 and x3 y2 3 define a region on a plane. Which of the
following points is inside the region?
A
B
C
D
E
(2, 1)
(2.5, 1)
(1, 2)
(3, 5)
(1, 2.5)
Physics
19
A 1,000 kg rocket is launched during a thunderstorm and reaches a constant velocity
30 seconds after launch. Suddenly, a strong gust of wind acts on it for 5 seconds with
a force of 10,000 N in the direction of movement. What is the resulting change in
velocity?
A
B
C
D
E
20
Miss Orrell lifts her 37.5 kg bike for a distance of 1.3 m in 5 s. The acceleration of free
fall is 10 m/s2. What is the average power that she develops?
A
B
C
D
E
21
0.5 m/s
5 m/s
50 m/s
500 m/s
5000 m/s
9.8 W
12.9 W
57.9 W
79.5 W
97.5 W
Which of he follo ing a emen be define Ohm Law?
A
B
C
D
E
The current through an insulator between two points is indirectly
proportional to the potential difference across two points.
The current through an insulator between two points is directly proportional
to the potential difference across two points.
The current through a conductor between two points is inversely
proportional to the potential difference across two points.
The current through a conductor between two points is proportional to the
square of the potential difference across two points.
The current through a conductor between two points is directly proportional
to the potential difference across two points.
22
Which of the following statements are true about vectors?
A
B
C
D
E
23
A 20 V battery is connected to a circuit consisting of a 1
parallel. Calculate the overall current of the circuit.
A
B
C
D
E
24
Vectors can be added or subtracted.
All vector quantities have a defined magnitude.
All vector quantities have a defined direction.
Displacement is an example of a vector quantity.
All of the above.
6.67 A
8A
10 A
12 A
30 A
A candle is placed in front of a concave
mirror. The image produced by the mirror
is which of the following?
A
B
C
D
E
Real, inverted and magnified
Real, inverted and demagnified
Virtual, upright and magnified
Virtual, upright and demagnified
Real, upright and magnified
and 2
resistor in
25
A container with rigid walls filled with a sample of ideal gas. The absolute
temperature of the gas is doubled. What happens to the pressure of the gas?
A
B
C
D
E
26
When we touch a piece of metal and a piece of wood that are placed in the same
room, the piece of metal feels much colder than the piece of wood. This happens
because of the difference in:
A
B
C
D
E
27
Doubles
Quadruples
Triples
Decreased to one-half
Decreased to one-fourth
Specific heat
Temperature
Density
Thermal conductivity
Latent heat
A 5,000 kg freight car moving at 2 m/s collides with a 10,000 kg freight car at rest.
They couple upon collision and move away at:
A
B
C
D
E
2 m/s
1 m/s
2/3 m/s
1/3 m/s
3 m/s
28
A metal sphere of unknown mass is dropped from an altitude of 1 km and reaches
terminal velocity 300 m before it hits the ground. Given that resistive forces do a
total of 10 kJ of work for the last 100 m before the ball hits the ground, calculate the
mass of the ball. Take g = 10 m/s2.
A
B
C
D
E
29
The acceleration due to gravity on the Earth is six times greater than that on the
moon. Dr. Tyson records the weight of a rock as 250 N on the moon.
Calc la e he ock den i gi en ha i ha a ol me of
cm3. Take g of Earth =
10 m/s2.
A
B
C
D
E
30
1 kg
2 kg
5 kg
10 kg
20 kg
0.2 kg/cm3
0.5 kg/cm3
0.6 kg/cm3
0.7 kg/cm3
0.8 kg/cm3
Which of the follo ing a emen ega ding Ne on Second La a e co ec
1
For objects at rest, Resultant Force must be 0 Newtons
2
Force = Mass x Acceleration
3
Force = Rate of change of Momentum
A
B
C
D
E
1 only
2 only
3 only
1 and 3
1, 2 and 3
Logical Reasoning and Verbal Comprehension
31
Pilbury is south of Westside, which is south of Harrington. Twotown is north of
Pilbury and Crewville but not further north than Westside. Crewville is:
A
B
C
D
E
32
Alex, Bertha, David, Gemma, Charlie, Elena and Frankie are all members of the same
family consisting of three children, two of whom, Frankie and Gemma are girls. No
other assumption of gender based on name can be established. There are also four
adults Ale i a doc o and i Da id b o he One of hem i ma ied o Elena and
they have two children. Bertha is married to David; Gemma is their child.
Who is Charlie?
A
B
C
D
E
33
South of Westside, Pilbury and Harrington but not necessarily Twotown.
North of Pilbury and Westside.
South of Westside and Twotown but north of Pilbury
South of Westside, Harrington and Twotown but not necessarily Pilbury.
South of Harrington, Westside, Twotown and Pilbury.
Ale da gh e
F ankie fa he
Gemma b o he
Elena on
Gemma i e
Piyanga writes a coded message for Nishita. Each letter of the original message is
coded as a letter a specific number of characters further on in the alphabet (the
specific number i he ame fo all le e
Pi anga coded me age incl de he
o d PJVN Wha co ld he o iginal o d a
A
B
C
D
E
CAME
DAME
FAME
GAME
LAME
34
Ellie, her brother Tom, her sister Georgia, her mum and her dad line up in height
order from shortest to tallest for a family photograph. Ellie is shorter than her dad
but taller than her mum. Georgia is shorter than both her parents. Tom is taller than
both his parents.
If 1 is shortest and 5 is tallest, what position is Ellie in the line?
A
B
C
D
E
35
If the mean of 5 numbers is 7, the median is 8 and the mode is 3, what must be the
two largest numbers in the set of numbers add up to?
A
B
C
D
E
36
1
2
3
4
5
14
21
24
26
35
The university gym has an upfront cost of 35 with no contract fee, but classes are
charged at 3 each. The local gym has no joining fee and is 15 per month. What is
the minimum number of classes I need to attend in a 12 month period to make the
local gym cheaper than the university gym?
A
B
C
D
E
40
48
49
50
55
37
Fear of death prompted us to develop technology that helps people live longer. But
those same technological advances have condemned us to fear of infirmity and
dementia, since so many of us will live to an advanced age. So as to eliminate this
new fear, once we have reached old age we should be assisted to die if we choose
death over a sad decline. According to current estimates, dementia affects almost 50
per cent of people by the age of 85, and bodily infirmity is guaranteed to develop
further the older we get. There is no cure for old age.
Which one of the following best expresses the main conclusion of the above
argument?
A
B
C
D
E
38
Technology has advanced to the point where we can now choose when to
die.
Euthanasia should be readily available to people who have reached a certain
age.
The fear of infirmity and dementia is worse than the fear of death.
We must develop technology to cure dementia and infirmity.
We should focus on the health of the young instead of that of the old.
There is an urgent need to improve the recruitment procedures for teaching
positions at universities. There have been numerous cases in which academics have
failed to hire outstanding young researchers and talented lecturers. For example, a
research fellow from Germany complained that his applications for lecturing jobs
were rejected despite his impressive research and publication record. Another
scholar from Spain, who had received the Excellence in Teaching Award, also failed
to get a job. A number of similar complaints have forced the Department of
Education to introduce a policy which requires universities to staff the relevant
selection committees with representatives from independent human resources
consultancies. This measure will improve recruitment procedures.
Which one of the following is an underlying assumption of the above argument?
A
B
C
D
E
Academics are driven by egoistic interests when they recruit faculty
members.
Human resources consultants will be able to spot suitable candidates for
teaching positions.
A good publication record can diminish your chances of being hired.
The primary goal of universities is to maintain the quality of teaching, rather
than excellence in research.
Graduates of German and Spanish universities have fewer chance of being
hired for teaching positions.
39
Thousands of parents have recently been prosecuted by local education authorities
for taking their children out of school to go on holiday during term time. I took my
daughter out of primary school for a two-week holiday every year. The headmistress
made no objection and said it would give the other kids time to catch up with her!
She was able to learn a foreign language and spend some rewarding time with her
French pen-pal. She eventually achieved top grades at school and a degree in
mathematics, so it obviously did her no harm! Parents, not governments, know best
how to raise children. This law is quite unnecessary.
Which one of the following is the best statement of the flaw in the above argument?
A
B
C
D
E
40
It is an appeal to tradition because it suggests that taking children on holiday
in term time used to be acceptable.
I i ba ed on a ho i a i e he headmi e
lack of objec ion in
support.
I a me ha beca e he da gh e good g ade e e achie ed af e he
foreign holidays, they were the result of the holidays.
It is based entirely on the one example of the daughter and generalizes from
that.
It assumes that learning some French adequately compensated for the work
the daughter missed.
There has been a significant rise in the number of children with rickets. This has
resulted from the airless, indoor world we have created for ourselves. Rickets is
caused by a deficiency of vitamin D, which is produced in response to sunlight on the
skin. Where children used to play outside they mostly stay indoors immersed in
virtual realities via various electronic media. Instead of long summer evenings
outdoors, we close the curtains to prevent sunlight falling on our screens. The lure of
technology is compounded by adult fears of the risks to children if they are left to
roam free in the outside world; in any case there are fewer accessible public spaces
for open air activity. Curing this will require an awful lot more than vitamin pills.
Which one of the following, if true, most weakens the above argument?
A
B
C
D
E
There has been a large growth in areas designated as national parks and in
urban parkland.
Diet has a much more significant effect on vitamin D intake than sunlight.
The incidence of rickets is confined to a few hundred cases a year.
In the 19th century, when the incidence of rickets was much higher, terrible
air pollution and smog affected the large population of city dwellers.
Man eo le can affo d o be elied on o ake i amin D
lemen
41
A new supermarket scheme awards money-off vouchers to customers who spend
£40 a week on their grocery shopping. As your weekly shop only costs £15, you are
not eligible for vouchers.
Which one of the following most closely parallels the reasoning used in the above
argument?
A
B
C
D
E
42
A discount is given to gym members who introduce new customers. You
brought two friends who joined up, so you will get a discount.
Dessert is given to all those who have completed their main course. You have
not eaten your main course so you will not be given dessert.
Anyone between the ages of 18 30 inclusive gets admission into the
nightclub half-price. You are 30 so you will not pay full price.
A bursary is given to those on incomes below £10 000. You earn £9000 so you
will receive a bursary.
Only experienced wine drinkers can appreciate a good wine. You prefer poor
quality wine as you have only recently started drinking wine.
A Prime Minister has a difficult judgement to make when deciding whether to sack
one of their ministers or not. Faced, for example, with a minister involved in some
kind of scandal, the Prime Minister might feel they should sack them to show they
stand up for integrity and high moral standards, or, on the other hand, allow them to
remain in post for other reasons such as loyalty to a colleague or a belief that they
are, on balance, doing a good job. Sacking ministers shows that the Prime Minister is
prepared to live by principles, even if by so doing they lose valued colleagues. The
electorate will judge the Prime Minister to have acted with integrity: that is an
invaluable perception for anyone wishing to remain in power.
Which one of the following can be drawn as a conclusion from the above passage?
A
B
C
D
E
I i in he P ime Mini e elec o al in e e
o e on he ide of acking
Restoring public trust at a time when the reputation of politicians is low is a
priority.
Ministers are often sacked for a relatively minor wrongdoing when this is not
in the interests of the country.
Ministers involved in scandals should always be sacked.
Politicians seek to stay in power at all costs.