Csir Net/Jrf Mathematics - 2018- Part A- General Aptitude - Solutions

 Part - A 

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 -