In the first 100 natural numbers, how many numbers have even number of factors?
Sol Only perfect squares have odd number of factors Hence there 10 numbers in first 100 natural numbers that have odd number of factors, Rest 90 numbers have even number of factors.
Find the number of subsets S of {1,2,….., 63}the sum of whose elements is 2008.
1 + 2 + _ _ _ + 63 = 2016. So the problem is equivalent to finding the number of subsets of{1,2,….., 63} whose sum of elements is 8. We can count this manually : {8}, {1,7} , {2,6} , {3,5} , {1,2,5} , { 1,3,4} Hence , 6
A 5-member cricket team has to be selected for a new format of cricket named Hong Kong Super Five! It must be composed of 2 batswomen, 2 bowlers and one wicket-keeper.There are three batting contenders viz. Supriya, Sumaya and Sanjana. There are two wicket-keeping contenders viz. Sunita and Sarita. There are three bowling contenders viz. Savita, Sujata and Suprita. If Savita is selected in the team, then Suprita cannot be selected. If Sanjana is selected, then Savita cannot be selected. If Sumaya is selected, then Sanjana also has to be selected.
If Savita and Sujata are selected, then which of the following statements must be true?
I. Sarita is selected.
II. Both Supriya and Sumaya are selected as batswomen.
III. Sunita is selected.
1. Only I
2. Only II and III
3. Only III
4. None of these
For solution check : Puzzles of the Day: 96
Let f(x) be a quadratic polynomial with f(2) = 10 and f(–2) = – 2. Then the coefficient of x in f(x) is
1. 3
2. 2
3. 5
4. Cannot be determined
f(2) = 10, f(–2) = –2 f(x) = ax2 + bx + c 10 = 4a + 2b + c ….. (1) –2 = 4a – 2b + c …… (2) From (1) and (2) b = 3
A 5-member cricket team has to be selected for a new format of cricket named Hong Kong Super Five! It must be composed of 2 batswomen, 2 bowlers and one wicket-keeper.There are three batting contenders viz. Supriya, Sumaya and Sanjana. There are two wicket-keeping contenders viz. Sunita and Sarita. There are three bowling contenders viz. Savita, Sujata and Suprita. If Savita is selected in the team, then Suprita cannot be selected. If Sanjana is selected, then Savita cannot be selected. If Sumaya is selected, then Sanjana also has to be selected.
Which of the following player must be selected in the team?
1. Supriya
2. Sumaya
3. Savita
4. Sujata
For solution check : Puzzles of the Day: 96
How many positive integers less than 1200 have no repeating digits ?
(no repeating digits means no digit occurs more than once)
There are 9 such 1-digit numbers, Similarly the number of such 3-digit numbers is 9×9×8 = 648, since the third digit cannot equal to either of the first two. For 4-digit numbers beginning 10, there are 8×7 and there are none beginning 11.
9×9 = 81 such 2- digit numbers (since the first digit can be 1 to 9 and the second digit any other number from 0 to 9).
Hence , 9 + 81 + 648 + 56 = 794
A 5-member cricket team has to be selected for a new format of cricket named Hong Kong Super Five! It must be composed of 2 batswomen, 2 bowlers and one wicket-keeper.There are three batting contenders viz. Supriya, Sumaya and Sanjana. There are two wicket-keeping contenders viz. Sunita and Sarita. There are three bowling contenders viz. Savita, Sujata and Suprita. If Savita is selected in the team, then Suprita cannot be selected. If Sanjana is selected, then Savita cannot be selected. If Sumaya is selected, then Sanjana also has to be selected.
Which of the following is the list of people who can be selected in a team?
1. Sujata,Sumaya,Sunita,Suprita,Supriya
2. Sanjana,Sarita,Savita,Sujata,Sumaya
3. Sanjana,Sarita,Sujata,Sumaya,Suprita
4. Sarita,Savita,Sumaya,Suprita,Supriya
For solution check : Puzzles of the Day: 96
Mr. X, his sister, his son, and his daughter are chess players.
I. The best player’s twin and the worst player are of the opposite sex.
II.The best player and the worst player are of the same age.
Who is the worst player?
1.X
2.X’s son
3. X’s daughter
4. X’s sister
The best player and the best player’s twin are of the same age; the best player and the worst player are of the same age and the best player’s twin and the worst player are different people. Hence, three people are of the same age. Since Mr. X must be older than his children, his children and his sister must be of the same age. Hence, his son and daughter are twins. One of them is the best player, and Mr. X’s sister is the worst player. Hence, the best player is Mr. X’s daughter.
See our previous ‘Puzzles of the Day’:
