Number System Test
Number of questions:10
Q.1 When numbers are written to the base 11, how many two – digit numbers are possible which are thrice the numbers formed by reversing their respective digits?
Q.2 In a number system the product of 44 and 11 is 2124. The number 3111 of this system, when converted to the decimal number system, becomes:
Q.3 In a 4-digit number, the sum of the first two digits is equal to that of the last two digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other two digits. What is the third digit of the number?
Q.4 Sudheer has certain number of toffees between 80 and 100 with him. If he distributes them equally among all his 4 children, there will be 3 left. If he distributes them equally among his wife and children, he is left with four toffees. If he decides to distribute the toffees amongst himself, his wife and children how many will be left over?
Q.5 I had some sweets (less than 80) with me. I distributed them among Sachin and Saurav. After distributing the sweets, it was found that both of them had got a different number of sweets, but both the numbers had the same unique properties. Both the numbers could be expressed as the sum of the squares of two different numbers and also as the difference of the cubes of two different numbers. If Saurav got less sweets than Sachin, then how many sweets did Sachin get?
Q.6 I had some sweets (less than 80) with me. I distributed them among Sachin and Saurav. After distributing the sweets, it was found that both of them had got a different number of sweets, but both the numbers had the same unique properties. Both the numbers could be expressed as the sum of the squares of two different numbers and also as the difference of the cubes of two different numbers. How many sweets did I distribute to the two of them?
Q.7 N! (N >= 2004) is divided by 10th to leave a remainder of r(r >= 0). If m is the maximum possible are r is the minimum possible, then the last digit of the quotient is
Q.8 Imagine you have 26 constants labeled A to Z. Each constant is assigned a value in the following manner: A = 1 B = 2C (2 raised to the power of the position value of C in the alphabet, i.e., 23) C = 2D (2 raised to the power of the position value of D in the alphabet, i.e. 24) and so on till Z = 2A (2 raised to the power of the position value of A in the alphabet, i.e. 21) What is the exact numerical value of the following expression? (T – A)* (T – B)* …..(T – Y)* (T – Z)
Q.9 In a number system to the base 20, letters A, B, C, ….. to K of the English alphabet are sequentially used to digitally represent the values 10, 11, 12, ….. to 20 (to the base 10). Calculate the value of [CAKE(20) – BAKE(20)] to the base 10.
Q.10 Consider z = 2222^5555 + 5555^2222. Which of the following statements is/are true?
