1. A bag contains 8 black and 10 white balls. Two draws of one ball each are made without replacement. What is the probability that one is black and other is white?
(1) 48/95
(2) 24/95
(3) 80/153
(4) 8/15
(5) None of these
2. In how many ways can 6 examination papers be arranged so that the best and the worst papers never come together?
(1) 120
(2) 240
(3) 360
(4) 480
(5) None of these
3. How many groups of 7 persons can be formed from 6 men and 9 women?
(1) 6435
(2) 51480
(3) 715
(4) 6453
(5) None of these
4. The area of playground is 4800 sq metres. Find the cost of covering it with gravel 1 cm deep, if the gravel costs Rs 480 per cubic metre.
(1) Rs 23400
(2) Rs 24300
(3) Rs 23040
(4) Rs 24030
(5) None of these
5. Find the area of a triangle with two sides equal, each being 5.1 metres and the third side 4.6 metres.
(1) 10 sq m
(2) 10.5 sq m
(3) 10.46 sq m
(4) 11.46 sq m
(5) None of these
Directions (Q.6-10): Study the following information carefully and answer the given questions.
In a pool of 1000 cricket players we find following percentage distribution of players, w.r.t. total number of players, who played Test Cricket, One Day International and First Class matches.
Played only Test Cricket = 15%
Played only ODI = 16%
Played only First Class match = 25%
Played Test and ODI but not First Class = 12%
Played ODI and First Class but not Test = 14%
Played Test and First Class but not ODI = 8%
Played all three forms of cricket = 10%
6. How many players played Test and ODI both?
(1) 220
(2) 120
(3) 100
(4) 240
(5) None of these
7. How many players played First Class matches?
(1) 470
(2) 570
(3) 250
(4) 430
(5) None of these
8. How many players who played exactly two forms of cricket?
(1) 340
(2) 240
(3) 220
(4) 180
(5) None of these
9. How many players who played at most two forms of cricket?
(1) 800
(2) 900
(3) 340
(4) 570
(5) None of these
10. How many players are there who played at least two forms of cricket?
(1) 560
(2) 340
(3) 440
(4) 900
(5) None of these
Directions (Q. 11-15): Each question below is followed by two statements I and II. You are to determine whether the data given in the statement is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers.
Give answer—
(1) If the data given in one of the statement alone are sufficient to answer the question while the data given in another statement alone are not sufficient to answer the question.
(2) If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
(3) If the data in both the Statements I and II even together are not sufficient to answer the question.
(4) If the data in both the Statements I and II together are necessary to answer the question.
(5) None of these
11. What is the population of a city?
I. If population growth rate is 10% per year.
II. If one year back its population was 12 lakh.
12. What is the rate of simple interest?
I. If total interest is Rs 200.
II. If amount is invested for 5 years.
13. In a party the ratio of male and female is 5 : 3. How many male are there?
I. If total number of male and female 32.
II. If difference between male and female is 8.
14. Is Rani’s age less than 8 years?
I. Subhash’s age is less than 10 years but he is elder than Rani.
II. Dinesh is 9 years old and younger than Rani.
15. How many small cubes are hidden inside a big cube?
I. Total number of small cubes used to make a big cube is less than 400.
II. Total number of small cubes used to make a big cube is more than 300.
ANSWERS
1. 3;
n(S) = 18C2 = 9 × 17 = 153
n(E) = 8C1 × 10C1 = 8 × 10 = 80
P(E) = 80/153
2. 4;
Number of permutation of 6 papers without restriction is 6P6 = 6!
If we consider the best and worst as one paper then number of permutation of (6 – 2 + 1) = 5 papers is
5P5 = 5!
These two papers are arranged beteween themself in 2! ways.
So number of arrangement when the best and worst never comes together is 6! – 5! × 2!
= 720 – (120 × 2) = 720 – 240 = 480
3. 1;
Total persons = 6 + 9 = 15
Number of groups that can be formed of 7 persons
= 15C7 = (15*14*13*12*11*10*9)/(1*2*3*4*5*6*7) = 6435
4. 3;
Cost of covering the playground = 4800 × 0.01 × 480
= Rs 23040
5. 3
Solutions (5-10):
6. 1
7. 2
8. 1
9. 2
10. 3
Solutions (11-15)
11. 4; Population = 12 * 110/100 = 13.2 lakh
12. 3; Data not sufficient
r = (100 * SI)/ P*t
We have ‘S.I.’ and ‘t’ but we need ‘P’ also.
13. 2; Let number of male be 5x and female 3x.
From (I)
5x + 3x = 32
x = 4
Male = 20
From (II)
5x – 3x = 8
x = 4
So, male = 20
14. 1
15. 4
(1) 48/95
(2) 24/95
(3) 80/153
(4) 8/15
(5) None of these
2. In how many ways can 6 examination papers be arranged so that the best and the worst papers never come together?
(1) 120
(2) 240
(3) 360
(4) 480
(5) None of these
3. How many groups of 7 persons can be formed from 6 men and 9 women?
(1) 6435
(2) 51480
(3) 715
(4) 6453
(5) None of these
4. The area of playground is 4800 sq metres. Find the cost of covering it with gravel 1 cm deep, if the gravel costs Rs 480 per cubic metre.
(1) Rs 23400
(2) Rs 24300
(3) Rs 23040
(4) Rs 24030
(5) None of these
5. Find the area of a triangle with two sides equal, each being 5.1 metres and the third side 4.6 metres.
(1) 10 sq m
(2) 10.5 sq m
(3) 10.46 sq m
(4) 11.46 sq m
(5) None of these
Directions (Q.6-10): Study the following information carefully and answer the given questions.
In a pool of 1000 cricket players we find following percentage distribution of players, w.r.t. total number of players, who played Test Cricket, One Day International and First Class matches.
Played only Test Cricket = 15%
Played only ODI = 16%
Played only First Class match = 25%
Played Test and ODI but not First Class = 12%
Played ODI and First Class but not Test = 14%
Played Test and First Class but not ODI = 8%
Played all three forms of cricket = 10%
6. How many players played Test and ODI both?
(1) 220
(2) 120
(3) 100
(4) 240
(5) None of these
7. How many players played First Class matches?
(1) 470
(2) 570
(3) 250
(4) 430
(5) None of these
8. How many players who played exactly two forms of cricket?
(1) 340
(2) 240
(3) 220
(4) 180
(5) None of these
9. How many players who played at most two forms of cricket?
(1) 800
(2) 900
(3) 340
(4) 570
(5) None of these
10. How many players are there who played at least two forms of cricket?
(1) 560
(2) 340
(3) 440
(4) 900
(5) None of these
Directions (Q. 11-15): Each question below is followed by two statements I and II. You are to determine whether the data given in the statement is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers.
Give answer—
(1) If the data given in one of the statement alone are sufficient to answer the question while the data given in another statement alone are not sufficient to answer the question.
(2) If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
(3) If the data in both the Statements I and II even together are not sufficient to answer the question.
(4) If the data in both the Statements I and II together are necessary to answer the question.
(5) None of these
11. What is the population of a city?
I. If population growth rate is 10% per year.
II. If one year back its population was 12 lakh.
12. What is the rate of simple interest?
I. If total interest is Rs 200.
II. If amount is invested for 5 years.
13. In a party the ratio of male and female is 5 : 3. How many male are there?
I. If total number of male and female 32.
II. If difference between male and female is 8.
14. Is Rani’s age less than 8 years?
I. Subhash’s age is less than 10 years but he is elder than Rani.
II. Dinesh is 9 years old and younger than Rani.
15. How many small cubes are hidden inside a big cube?
I. Total number of small cubes used to make a big cube is less than 400.
II. Total number of small cubes used to make a big cube is more than 300.
ANSWERS
1. 3;
n(S) = 18C2 = 9 × 17 = 153
n(E) = 8C1 × 10C1 = 8 × 10 = 80
P(E) = 80/153
2. 4;
Number of permutation of 6 papers without restriction is 6P6 = 6!
If we consider the best and worst as one paper then number of permutation of (6 – 2 + 1) = 5 papers is
5P5 = 5!
These two papers are arranged beteween themself in 2! ways.
So number of arrangement when the best and worst never comes together is 6! – 5! × 2!
= 720 – (120 × 2) = 720 – 240 = 480
3. 1;
Total persons = 6 + 9 = 15
Number of groups that can be formed of 7 persons
= 15C7 = (15*14*13*12*11*10*9)/(1*2*3*4*5*6*7) = 6435
4. 3;
Cost of covering the playground = 4800 × 0.01 × 480
= Rs 23040
5. 3
Solutions (5-10):
6. 1
7. 2
8. 1
9. 2
10. 3
Solutions (11-15)
11. 4; Population = 12 * 110/100 = 13.2 lakh
12. 3; Data not sufficient
r = (100 * SI)/ P*t
We have ‘S.I.’ and ‘t’ but we need ‘P’ also.
13. 2; Let number of male be 5x and female 3x.
From (I)
5x + 3x = 32
x = 4
Male = 20
From (II)
5x – 3x = 8
x = 4
So, male = 20
14. 1
15. 4
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