PART-A
(Questions are labelled with RED and answers with GREEN)
A cart wheel rolls along a straight line. If the distance covered is
equal to the diameter of the wheel, what is the angle through which the
wheel has turned?
1. 90°
2. between 90° and 120°
3. between 120° and 150°
4. between 150° and 180°
2.In a class of 10 students, 3 failed in History, 6 failed in geography and
2 failed in both. How many passed in both the subjects?
1. 1
2. 2
3. 3
4. 0
3.
As shown in the diagram above, a sphere is placed on the top of an
incline. It rolls down the incline without slipping in exactly 50 turns.
The radius of the sphere is
1. (5/π) cm
2. (5/π) m
3. (10/π) cm
4. 10 cm
4. A set of concentric circles of integer radii 1,2, ... N is shown in the
figure above. An ant starts at point A1, goes round the first circle,
returns to A1, moves to A2, goes round the second circle, returns to A2,
moves to A3 and repeats this until it reaches AN. The distance covered
by the ant is
1. N (N + 1) π
2. 2N π + N
3. π (N + l)N + N - 1
4. π (N - l) N + N - 1
5. The figure
shows an infinite series of triangles, in which rl >
r2> r3 ... What is the total length of the solid line segments in the figure?
1. r1/r2+r2/r3+…..
2. r21/r1-r2
3. r21/r1+r2
4. r1-r2/ r21
6. If ai, bi and Ci are distinct, how many terms will the expansion of the
product (a1 + a2 + a3) (b1 + b2 + b3 + b4) (C1+C2 + C3 + C4 + C5) contain?
1. 12
2. 30
3.23
4. 60
7. The BELOW plot depicts the number of research publications of a
scientist along with the number of citations.
Which of the following statements is not correct?
1. In the year 2012, 50% more papers were published but
citations decreased by 25%.
2. In the year 2012, 100% more papers were published but citations
were 75% of the number of papers in that year.
3. The papers published in year 2011 is only 33.33% of the total
number of papers in both years.
4. The total number of citations for both years is 16.66% more than the
total number of papers.
8. The next number of the sequence 1, 5, 14, 30, 55, . . . is
1. 85
2. 90
3. 91
4. 95
9. The distribution of heights and weights in a population is shown
above in a 2-parameter scatter plot. The size of the square is
proportional to the number of persons having a particular combination
of weight and height. Which statement best describes the trend in the
population?
1. Height and weight are strongly correlated.
2. Height and weight are anti-correlated.
3. Large heights do not imply proportionately large weights.
4. Height and weight are independent characteristics.
10. What is the maximum sum of the numbers of Saturdays and
Sundays in a leap year?
1. 104
2. 105
3. 106
4. 107
11. Two trains of length 150 m and 250 m pass each other with
constant speeds on parallel tracks in opposite directions. The drivers
and guards are at the extremities of the trains. The time gap between
the drivers passing each other and first driver-guard pair passing each
other is 30 s. How much later will the other driver-guard pair pass by?
1. 10 s
2. 20 s
3. 30 s
4. 50 s
12. In a room, we have one grandfather, two fathers, two sons, and a
grandson. The age of one father is seven times the age of his son. The
age' of the other father is twice his son's age. Assuming that there are
only 3 people in the room and the grandfather is 70 years old, how old
is the grandson?
1. 1
2. 2
3. 5
4. Cannot be determined
13. A hemispherical bowl is being filled with water at a constant
volumetric rate. The level of water in the bowl increases
1. in direct proportion to time
2. in inverse proportion to time
3. faster than direct proportion to time
4. slower than direct proportion to time
14. Equal masses of two liquids of densities 6 kg/m3 and 4 kg/m3 are
mixed thoroughly. The density of the mixture is
1. 4.8 kg/m3.
2. 5.0 kg/m3.
3. 5.2 kg/m3.
4. 5.4 kg/m3.
15. Two points A and B on the surface of the Earth have the following
latitude and longitude co-ordinates.
A: 300 N, 450 E
B: 300 N, 1350 W
If R is the radius of the Earth, the length of the shortest path from A to
B is
1. √3/2πR
2. π. R/3
3. πR/6
4. 2πR/3
16. Amoebae are known to double in 3 min. Two identical vessels A &
B, respectively contain one and two amoebae to start with. The vessel B
gets filled in 3 hours. When will A get filled?
1. 3 hours
2. 2 hours 57 min
3. 3 hours 3 min
4. 6 hours
17. Students of a school are divided into 4 groups. What is the
probability that three friends get into the same group?
1. ¾
2. 1/64
3. 1/16
4. 1/3
18. A fruit vendor buys 120 Shimla apples at 4 for Rs. 100, and 120
Golden apples at 6 for Rs. 100. She decides to mix them and sell at 10
for Rs. 200. She will make
1. no profit, no loss
2. a loss of 4%
3. a gain of 4%
4. a loss of 10 %
19. 40 + 42 + 4-2 + 41/2 + 4-1/2 =
1. 4°
2. 42.5 + 4-2.5
3. 199/16
4. 229/16
20. In an enclosure there were both crows and cows. If there were 30
heads and 100 legs, what fraction of them are crows?
1. 1/3
2. 1/4
3. 1/10
4. 3/10
(Questions are labelled with RED and answers with GREEN)
A cart wheel rolls along a straight line. If the distance covered is
equal to the diameter of the wheel, what is the angle through which the
wheel has turned?
1. 90°
2. between 90° and 120°
3. between 120° and 150°
4. between 150° and 180°
2.In a class of 10 students, 3 failed in History, 6 failed in geography and
2 failed in both. How many passed in both the subjects?
1. 1
2. 2
3. 3
4. 0
3.
As shown in the diagram above, a sphere is placed on the top of an
incline. It rolls down the incline without slipping in exactly 50 turns.
The radius of the sphere is
1. (5/π) cm
2. (5/π) m
3. (10/π) cm
4. 10 cm
4. A set of concentric circles of integer radii 1,2, ... N is shown in the
figure above. An ant starts at point A1, goes round the first circle,
returns to A1, moves to A2, goes round the second circle, returns to A2,
moves to A3 and repeats this until it reaches AN. The distance covered
by the ant is
1. N (N + 1) π
2. 2N π + N
3. π (N + l)N + N - 1
4. π (N - l) N + N - 1
5. The figure
shows an infinite series of triangles, in which rl >r2> r3 ... What is the total length of the solid line segments in the figure?
1. r1/r2+r2/r3+…..
2. r21/r1-r2
3. r21/r1+r2
4. r1-r2/ r21
6. If ai, bi and Ci are distinct, how many terms will the expansion of the
product (a1 + a2 + a3) (b1 + b2 + b3 + b4) (C1+C2 + C3 + C4 + C5) contain?
1. 12
2. 30
3.23
4. 60
7. The BELOW plot depicts the number of research publications of a
scientist along with the number of citations.
Which of the following statements is not correct?
1. In the year 2012, 50% more papers were published but
citations decreased by 25%.
2. In the year 2012, 100% more papers were published but citations
were 75% of the number of papers in that year.
3. The papers published in year 2011 is only 33.33% of the total
number of papers in both years.
4. The total number of citations for both years is 16.66% more than the
total number of papers.
8. The next number of the sequence 1, 5, 14, 30, 55, . . . is
1. 85
2. 90
3. 91
4. 95
9. The distribution of heights and weights in a population is shown
above in a 2-parameter scatter plot. The size of the square is
proportional to the number of persons having a particular combination
of weight and height. Which statement best describes the trend in the
population?
1. Height and weight are strongly correlated.
2. Height and weight are anti-correlated.
3. Large heights do not imply proportionately large weights.
4. Height and weight are independent characteristics.
10. What is the maximum sum of the numbers of Saturdays and
Sundays in a leap year?
1. 104
2. 105
3. 106
4. 107
11. Two trains of length 150 m and 250 m pass each other with
constant speeds on parallel tracks in opposite directions. The drivers
and guards are at the extremities of the trains. The time gap between
the drivers passing each other and first driver-guard pair passing each
other is 30 s. How much later will the other driver-guard pair pass by?
1. 10 s
2. 20 s
3. 30 s
4. 50 s
12. In a room, we have one grandfather, two fathers, two sons, and a
grandson. The age of one father is seven times the age of his son. The
age' of the other father is twice his son's age. Assuming that there are
only 3 people in the room and the grandfather is 70 years old, how old
is the grandson?
1. 1
2. 2
3. 5
4. Cannot be determined
13. A hemispherical bowl is being filled with water at a constant
volumetric rate. The level of water in the bowl increases
1. in direct proportion to time
2. in inverse proportion to time
3. faster than direct proportion to time
4. slower than direct proportion to time
14. Equal masses of two liquids of densities 6 kg/m3 and 4 kg/m3 are
mixed thoroughly. The density of the mixture is
1. 4.8 kg/m3.
2. 5.0 kg/m3.
3. 5.2 kg/m3.
4. 5.4 kg/m3.
15. Two points A and B on the surface of the Earth have the following
latitude and longitude co-ordinates.
A: 300 N, 450 E
B: 300 N, 1350 W
If R is the radius of the Earth, the length of the shortest path from A to
B is
1. √3/2πR
2. π. R/3
3. πR/6
4. 2πR/3
16. Amoebae are known to double in 3 min. Two identical vessels A &
B, respectively contain one and two amoebae to start with. The vessel B
gets filled in 3 hours. When will A get filled?
1. 3 hours
2. 2 hours 57 min
3. 3 hours 3 min
4. 6 hours
17. Students of a school are divided into 4 groups. What is the
probability that three friends get into the same group?
1. ¾
2. 1/64
3. 1/16
4. 1/3
18. A fruit vendor buys 120 Shimla apples at 4 for Rs. 100, and 120
Golden apples at 6 for Rs. 100. She decides to mix them and sell at 10
for Rs. 200. She will make
1. no profit, no loss
2. a loss of 4%
3. a gain of 4%
4. a loss of 10 %
19. 40 + 42 + 4-2 + 41/2 + 4-1/2 =
1. 4°
2. 42.5 + 4-2.5
3. 199/16
4. 229/16
20. In an enclosure there were both crows and cows. If there were 30
heads and 100 legs, what fraction of them are crows?
1. 1/3
2. 1/4
3. 1/10
4. 3/10
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