Part - A
Q.1 The area of the triangle formed by joining
the points (2017, 2017), (2027, 2027) and (2037, 2017) is
Q.4 Four males M1,M2,M3,M4
and four females F1, F2, F3 and F4 are sitting around a round table facing away
from the table. If each one moves three positions to his/her right and then one
position to the left, then in which
directions does F4 face ?
Q.5 In the diagram , what
is the ratio of the total shaded area ( of the circle and semi-circle) to the
total area of the square and the rectangle?
Q.6 Which of the following
options is the best choice for the missing number?
Q.7 Fourteen of the
students in a class are girls. Eight students in the class wear blue shirts.
Two are neither girls nor wear blue shirts. Five students who wear blue shirts
are girls. How many students are there in the class?
Q.8 Prof Murthy likes to let her students to
choose who their partners will be; however , no pair of students may work
together for more than seven class periods in a row. Alice and bob Have worked
together for seven class periods in a row. Calvin and Denny worked together for
three class periods in a row. Calvin does not want to work with Alice. Who
should be assigned to work with Bob?
Q.9 Three semi circles are
drawn inside a big circle as shown in the figure. If the radius of the two
identical smaller semi circles is 1/4 th of that of the big circle and the
radius of the bigger semicircle is twice that of the small semi circle,what
proportion of the big circle's area is shaded?
Q.11 Consider a number 54 expressed in a base
different from ten. What is the base of this number system if its equivalent
value in the decimal system is 49?
Q.12 A fuel station sold
diesel costing Rs 15000 to 150 persons on a day. If the lower limit of sale to
a person is Rs 50.what is the maximum amount in rupees for which one person
could have purchased diesel on that day?
Q.13 which of the options is appropriate for the blank
space?
Q.14 If sangeeta's daughter
is my daughter's mother , then how am I related to sangeeta?
Q.15 In a group of 44 players, 26 play
hockey, 24 play football and 24 play cricket. Eight of them play both hockey
and football, 12 play both football and cricket, and 5 play all the three
games. How many play both hockey and cricket ?
4) {x>=0} or {y>=0} or { x>=0 and
y>=0}
Q.17 A long distance runner
find a water station after completing 1/7 th of the total distance. After
covering another another 1/6 th of the total distance he gets medical- aid.
another runner joins him 4km after the medical-aid station. The second runner
stops 4km before the completion of run, covering 1/2 of the total distance.
what is the total distance?
Q.18 A and B move
clockwise around a circle, starting from a common point o. A takes 9 minutes to
complete a round but restarts after a delay of 1 minute. b takes 13 minutes to
complete the round but restarts after a delay of two minutes. How many minutes
after they began would they meet again at O?
Q.1 The area of the triangle formed by joining
the points (2017, 2017), (2027, 2027) and (2037, 2017) is
Solution -
Q.2 A stick of length L is broken into two pieces at random . what is the average length of the smaller piece ?
Solution - The average length is L/2.
Q.3 Number of times a
research paper is viewed and cited is shown in the plot. In which month was the
percentage increase in citation more than double
of the percentage increase in view?
Solution -
Q.4 Four males M1,M2,M3,M4
and four females F1, F2, F3 and F4 are sitting around a round table facing away
from the table. If each one moves three positions to his/her right and then one
position to the left, then in which
directions does F4 face ?
Solution-
Q.5 In the diagram , what
is the ratio of the total shaded area ( of the circle and semi-circle) to the
total area of the square and the rectangle?
Solution-
Q.6 Which of the following
options is the best choice for the missing number?
Solution-
Q.7 Fourteen of the
students in a class are girls. Eight students in the class wear blue shirts.
Two are neither girls nor wear blue shirts. Five students who wear blue shirts
are girls. How many students are there in the class?
Solution-
Q.8 Prof Murthy likes to let her students to
choose who their partners will be; however , no pair of students may work
together for more than seven class periods in a row. Alice and bob Have worked
together for seven class periods in a row. Calvin and Denny worked together for
three class periods in a row. Calvin does not want to work with Alice. Who
should be assigned to work with Bob?
Solution -
Q.9 Three semi circles are
drawn inside a big circle as shown in the figure. If the radius of the two
identical smaller semi circles is 1/4 th of that of the big circle and the
radius of the bigger semicircle is twice that of the small semi circle,what
proportion of the big circle's area is shaded?
Solution-
Q.11 Consider a number 54 expressed in a base
different from ten. What is the base of this number system if its equivalent
value in the decimal system is 49?
Solution-
Q.12 A fuel station sold
diesel costing Rs 15000 to 150 persons on a day. If the lower limit of sale to
a person is Rs 50.what is the maximum amount in rupees for which one person
could have purchased diesel on that day?
Solution-
Q.13 which of the options is appropriate for the blank
space?
Solution-
Q.14 If sangeeta's daughter
is my daughter's mother , then how am I related to sangeeta?
Solution-
Q.15 In a group of 44 players, 26 play
hockey, 24 play football and 24 play cricket. Eight of them play both hockey
and football, 12 play both football and cricket, and 5 play all the three
games. How many play both hockey and cricket ?
Solution- 15
Q.16 It is given that (a)* = a if a>0 and (a)* =0 if a<=0 for any real number a.suppose for any two real numbers x and y (xy)* = (x)*(y)*. Then which of the following is necessarily true?
1) x>0 ans y>0
2) {x<0 and y<0} or { x>0 ans y>0}
3) {x<=0 and y<=0} or { x>=0 and y>=0}
4) {x>=0} or {y>=0} or { x>=0 and
y>=0}
Solution-
Q.17 A long distance runner
find a water station after completing 1/7 th of the total distance. After
covering another another 1/6 th of the total distance he gets medical- aid.
another runner joins him 4km after the medical-aid station. The second runner
stops 4km before the completion of run, covering 1/2 of the total distance.
what is the total distance?
Solution-
Q.18 A and B move
clockwise around a circle, starting from a common point o. A takes 9 minutes to
complete a round but restarts after a delay of 1 minute. b takes 13 minutes to
complete the round but restarts after a delay of two minutes. How many minutes
after they began would they meet again at O?
Solution - 28 minutes
Q.19 Two students are solving the same problem independently. if the probability that the first one solves the problem is 3/5 and the probability that the second solves the problem is 4/5, what is the probability that at least one of them solves the problem?
Solution -
