Q. 1
Find the domain for which the functions f(x) = 2x -1 and g(x) = 1-3x are equal. Indicate all correct options.
- a. B and E
- b.
- c.
- d.
- e.
- Answer: CD
- Explaination: We have f(x) = g(x) 2x -1 = 1 - 3x 5x = 2 x = 2/5 = 0.4 The functions f(x) and g(x) are equal on the set . Options (B) and (E) are correct.
Q. 2
The average marks obtained by 20 students in an exam is 45. Which of the following statements is true? Indicate all correct options.
- a. The total marks obtained is 900
- b. If 10 students scored 40 and 10 scored 50, the average marks would remain the same
- c. If each student scored 5 marks more, the average would remain the same
- d. If 15 students scored x marks less and 5 students scored x marks more, the average would decrease by x/2
- e. If the marks of 5 students were entered wrongly as 10 lesser, then the correct average would be lesser than 45.
- Answer: BCE
- Explaination: Total marks obtained = Average * number of students = 45*20 = 900 Option A is true. Average marks if 10 students scored 40 and 10 socred 50 = (40*10+50*10)/20 = (400+500)/20 = 900/20 = 45 Option B is true. Average marks if each scored 5 marks more = (900+20*5)/20 = (900+100)/20 = 1000/20 = 50 Option C is false. Average marks if 15 scored x marks less and 5 scored x marks more = [15(45-x) + 5(45+x)]/20 = (675-15x+225+5x)/20 = (900-10x)/20 = 45 - x/2 Option D is true. Correct average if the marks of 5 were entered as 10 lesser = (900+10*5)/20 = (900+50)/20 = 950/20 = 47.5 Option E is false.
Q. 3
If Adam walks at 5/4 of his usual speed, he shall reach his office 6 minutes earlier than he usually does. Which of the following statements is true? Indicate all correct options.
- a. His office is 5 km away
- b. Usually he takes 30 minutes to reach his office
- c. He shall reach his office in 24 minutes if he walks at 5/4 of his usual speed.
- d. Usually he takes 24 minutes to reach his office
- e. He shall reach his office in 18 minutes if he walks at 5/4 of his usual speed.
- Answer: AC
- Explaination: Let his usual speed be x m/min Let his office be y meters away. Time = distance/speed Time taken usually = y/x According to the given conditions, y/x - 6 = y/(5x/4) y/x - 6 = (4/5)y/x (y/x)(1-4/5) = 6 (y/x)(1/5) = 6 y/x = 6*5 = 30 minutes He takes 30 minutes to reach his office usually. He takes 30-6=24 minutes to reach his office if he walks at 5/4 of his usual speed.
Q. 4
A and B start from a point and run in opposite directions along the circumference of a circular park. The circumference of the park is 4200 meters. The speeds of A and B are 500 m/min and 700 m/min respectively. Which of the following is true? Indicate all correct options.
- a. They meet each other in 3.5 minutes
- b. A covers 1750 meters when they meet
- c. B covers 1750 meters when they meet
- d. A covers 2450 meters when they meet
- e. B covers 2450 meters when they meet
- Answer: ABC
- Explaination: Let them meet after x minutes. Speed = distance/time Distance covered by A and B in x minutes = 500x and 700x meters Total distance covered by them in x minutes = 4200 meters 500x+700x = 4200 1200x=4200 x=4200/1200 = 3.5 minutes Distance covered by A and B = 500*3.5 and 700*3.5 = 1750 meters and 2450 meters respectively Options A, B and E are true.
Q. 5
Two cars A and B start from a point in opposite directions at speeds 45 km/hr and 50 km/hr respectively. Which of the following statements is true? Indicate all correct options.
- a. They are 95 meters apart in 1000 seconds
- b. They are 1000 meters apart in 95 seconds
- c. B takes 0.1 hours lesser than A takes to cover 45 km
- d. B covers 45 km within an hour
- e. A covers 50 km within an hour
- Answer: AB
- Explaination: Speed = Distance/time Let the time be x seconds 45 + 50 = 0.095/x x = 95/0.095 = 1000 seconds Option A is true. Time taken by B to cover 45 km = 45/50 = 0.9 hours Time taken by A to cover 45 km = 45/45 = 1 hour Time taken by A = time taken by B + 0.1 Option C is true. B covers 50 km in an hour and hence option D is true. A covers 45 km in an hour and hence option E is false.
Q. 6
Let A = {-1, 0, 2, 3, 5, 6} and f(x) = x^2 -x -2. Find f(A). Indicate all correct options. [x^2 = x*x]
- a. {-1, 0, 2, 3, 5, 6}
- b. {-2, 4, 18, 28}
- c. { 0, 1, 2, 6, 20}
- d. B and D
- e.
- Answer: AB
- Explaination: f(A) = = = {-2, 0, 4, 18, 28} Options (B) and (D) are correct.
Q. 7
A(3, sqrt(3)), B(0,2*sqrt(3)) and O(0,0) are three points in a plane. Which of the following is true? Indicate all correct options.
- a. AB > BO
- b. AO = BO
- c. Angle ABO
- d.
- e.
- Answer: BC