11. A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both spade. Find the probability of the lost card being a spade.
Answer: 11/50
Explanation:Here is no explanation for this answer
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12. Two decks of cards are there. Each deck contains 20 cards, with numbers from 1 to 20 written on them. A card is drawn of random from each deck, getting the numbers x and y What is the probability that log x + log y is a positive integer. Logs are taken to the base 10.
Answer: 29/200
Explanation:Log x + log y = log(xy)
log xy is integer when (x,y) = (1, 10), (10, 1), (10, 10), (5, 20), (20, 5), (2, 5), (5, 2)
So required probability = 7/400
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13. A bag contains 1100 tickets numbered 1, 2, 3, ... 1100. If a ticket is drawn out of it at random, what is the probability that the ticket drawn has the digit 2 appearing on it?
Answer: 290/1100
Explanation:Numbers which dont have 2 from 1 to 9 = 8 Numbers which dont have 2 from 10 to 99:
Let us take two places _ _. Now left most place is fixed in 8 ways. Units place is filled with 9 ways. Total 72 numbres.
Numbers which dont have 2 from 100 to 999 =_ _ _ = 8 * 9 * 9 = 648 Numbers which dont have 2 from 1000 to 1099 =10_ _ = 9 * 9 = 81 Finally 1100 does not have 2. So 1.
Total number with no 2 in them = 8 + 72 + 648 + 81 + 1= 810 Tickets with 2 in them = 1100 - 810 = 290
Required probability = 290 / 1100
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14. In this question, A^B refers to A raised to the power B.Ten tickets numbered 1, 2, 3, ..., 10. Six tickets are selected at random one of a time with replacement. The probability of the largest number appearing on the selected ticket is 7 is
Answer: (7^6 - 6^6)/10^6
Explanation:Let's first find out probability of that maximum number being any number between 1 to 7.
P(1 to 7) = (7/10) * (7/10) * (7/10) ... 6 times
Now find out probability of that maximum number being any number between 1 to 6.
P(1 to 6) = (6/10) * (6/10) * (6/10) ... 6 times
Now, probability that maximum number is exactly 7
= P(1 to 7) - P (1 to 6)
= (7^6 - 6^6) / 10^6
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15. Two urns contain respectively 2 red 3 white and 3 red,5 white balls.One ball is drawn at random from the first urn and transferred into the second.A ball is now drawn from the second urn and it turns out to be red. What is the probability that the transferred ball was white?
Answer: 9/17
Explanation:According to baye's theorem:
p(no of way to drawn a ball from 2nd urns is red and ball transferred from 1 urns)=(3c1/5c1)*(3c1/9c1)=9/45
Total=(2c1/5c1)*(4c1/9c1)+(3c1/5c1)*(3c1/9c1)=17/45
so probability=9/45/17/45=9/17;
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16. Which is the smallest no divides 2880 and gives a perfect square?
Answer: 5
Explanation:Here is no explanation for this answer
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17. What is the value of [(3x+8Y)/(x-2Y)]; if x/2y=2?
Answer: 10
Explanation:Here is no explanation for this answer
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18. Six friends go to pizza corner there are 2 types of pizzas. And six different flavors are there they have to select 2 flavors from 6 flavors. In how many ways we can select?
Answer: 6C2
Explanation:Here is no explanation for this answer
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19. Average salary of 17 teachers is 45000.3 teachers left and the average salary dropped by 2500.What is the sum of salaries of 3 teachers who left?
Answer: 170000
Explanation:Total Initial Salary : 17*45000 = 765000
Average Salary After removal of 3 Teachers = 45000-2500 = 42500
Total Final Salary : 14*42500 = 595000
Sum of Salaries of 3 teachers who left : 765000 - 595000 = 170000
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20. Find a two digit number which is doubled and after that add +2 in it. and then reverse the number we would get the actual number.
(Example : xy * 2 = pq => pq+2 = xy )
Answer: 25
Explanation:Lets assume the two digit number be 10x+y
Adding 2 after doubling the number is reverse of the number.
So 2(10x+y)+2 = 10y+x
19x -8y +2=0 ----- (i)
The above equation (i) satisfies for the value, x=2, y=5
So, the number = 10*2+5= 25
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