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1) A box contains 8 Pink balls, 5 black balls, 4 orange balls and 3 white balls. If four balls are drawn out randomly, then the probability of getting a different colour balls?
A) 11/35
B) 32/323
C) 18/189
D) 34/77
E) None of these
2) The ratio of the age of P after 3 years and 6 years ago, the age of Q is 3: 4. The present age of R is 2 times the present age of P. The difference between the present age of Q and R is 6 years. Find the present age of P?
A) 22 years
B) 20 years
C) 24 years
D) 16 years
E) None of these
3) The volume of cylinder 1 and 2 is in the ratio of 3: 1 and the height of the cylinder 1 and 2 is in the ratio of 3: 4. Find the ratio between the radius of cylinder 1 and cylinder 2?
A) 7: 5
B) 5: 2
C) 4: 3
D) 2: 1
E) None of these
4) The present age of Janvi and her husband is 5: 6. The present age Janvi’s daughter is (1/5) of Janvi’s present age. Janvi’s daughter is 3 years younger than her son. Find the sum of the present age of Janvi and her husband, if the age of Janvi’s son, after 7 years is 15 years?
A) 58 years
B) 66 years
C) 55 years
D) 62 years
E) None of these
5) The length of train A is 200 m and that of train B is 300 m. These two trains are running in the opposite direction with the velocities of 60 km/hr and 40 km/hr respectively. Find the time taken to cross each other?
A) 14 sec
B) 21 sec
C) 18 sec
D) 25 sec
E) None of these
6) The volume of sphere 1 and 2 is in the ratio of 27: 125. Find the ratio of the radius of sphere 1 to that of sphere 2?
A) 5: 9
B) 10: 13
C) 3: 5
D) 6: 7
E) None of these
7) Rajeev scored 412 marks in an exam and Sanjay got 75 % marks in the same exam which is 8 marks more than Rajeev. If the minimum passing marks in the exam is 35 %, then how much more marks did Rajeev score than the minimum passing marks?
A) 185
B) 172
C) 216
D) 198
E) 223
8) 200 m long train crosses another train of length 150 m in 9 sec, running in opposite direction. If the speed of the first train is 80 km/hr, then find the speed of the second train (in km/hr)?
A) 80 km/hr
B) 70 km/hr
C) 50 km/hr
D) 60 km/hr
E) None of these
9) A certain sum is divided among A, B and C in such a way that A gets 20 less than the 2/5 of the sum and B gets 1/3 of the sum and C gets Rs. 500. Find the sum?
A) Rs. 900
B) Rs. 1800
C) Rs. 2700
D) Rs. 3000
E) None of these
10) The average score of 50 students of a class is 72. If the last five students are removed, the average drops by 4 marks. If these five marks are consecutive integers, then find the least score?
A) 118
B) 106
C) 124
D) 112
E) None of these
Answers :
Directions (1-10) :
1) Answer: B
Total probability n(S) = 20C4
Required probability = n(E) = 8C1Â and 5C1Â and 4C1Â and 3C1
P(E) = n(E)/n(S)
P(E) = (8C1Â and 5C1Â and 4C1Â and 3C1)/20C4
P(E) = 32/323
2) Answer: C
The ratio of 3 years after, the age of P and 6 years ago, the age of Q = 3: 4 (3x, 4x)
Present age of P and Q = 3x – 3, 4x + 6
The age of R = 2 * P = 2 * (3x – 3) = 6x – 6
(6x – 6) – (4x + 6) = 6
6x – 6 – 4x – 6 = 6
2x = 6 + 12
2x = 18
x = 9
Present age of P = 3x – 3 = 27 – 3 = 24 years
3) Answer: D
Volume of the cylinder = πr2h
The ratio of volume of cylinder 1 and 2 = 3: 1
The ratio of height of cylinder 1 and 2 = 3: 4
The ratio between the heights of cylinder 1 to that of cylinder 2,
= > [Ï€ * (3x) * r12]/[Ï€ * (4x) * r22] = (3/1)
= > r12/r22Â = (4/1)
= > r1: r2Â = 2: 1
4) Answer: C
The present age of Janvi and her husband = 5: 6 (5x, 6x)
The present age Janvi’s daughter = (1/5) * Janvi’s present age
Janvi’s daughter = Janvi’s son – 3
Janvi’s son after 7 years = 15 years
Janvi’s son’s present age = 8 years
Janvi’s daughter = 8 – 3 = 5 years
Janvi’s present age = 5 * 5 = 25 years
5’s = 25
1’s = 5
Present age of Janvi’s husband = 6x = 30 years
Required sum = 25 + 30 = 55 years
5) Answer: C
T = D/S
T = (200 + 300)/[(60 + 40) * (5/18)]
T = (500 * 18)/(100 * 5)
T = 18 sec
6) Answer: C
Volume of the sphere = (4/3) * πr3
The ratio of volume of sphere 1 and 2 = 27: 125
The ratio of the radius of sphere 1 to that of sphere 2
= > [(4/3) * π * r13]/[(4/3) * π * r23] = (27/125)
= > r13/r23Â = (27/125)
= > r1: r2 = 3: 5
7) Answer: C
Let x be the total mark in that exam, then
Rajeev’s score = 412 marks, Sanjay = 75 % = Rajeev’s score – 8
Sanjay = 412 + 8 = 420 = 75 % of total marks
(75/100) * x = 420
x = 420 * (100/75) = 560
Minimum passing marks = 35 % of total marks
= > (35/100) * 560 = 196
Rajeev scored 216 marks more than the passing marks.
8) Answer: D
T = D/S
According to the question,
9 = (200 + 150)/[(80 + x) * (5/18)]
9 * [(80 + x) * (5/18)] = 350
80 + x = 140
x = 60 km/hr
9) Answer: B
Let total sum be x,
A = (2/5) * x – 20
B = (1/3) * x
C = 500
A + B + C = x
(2/5) * x – 20 + (1/3) * x + 500 = x
(11/15) * x + 480 = x
480 = x – (11/15) * x
(4/15) * x = 480
x = 480 * (15/4) = Rs. 1800
10) Answer: B
The average score of 50 students = 72
Total score of 50 students = 50 * 72 = 3600
If the last five students are removed, the average drops by 4 marks.
So,
The average score of 45 students = 68
Total score of 45 students = 45 * 68 = 3060
x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 540
5x + 10 = 540
5x = 530
x = 106
Least score = 106
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