11. The least number which must be added to the greatest number of 4 digits in order that the sum may be exactly divisible by 307 is:
12. If 7-digit number 678p37q is divisible by 75 and p is not a composite, then the values of p and q are:
13. What is the sum of first 20 terms of the following series?
1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + . . . . . . . .
1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + . . . . . . . .
14. How many numbers are there from 400 to 700 in which the digit 6 occurs exactly twice?
15. Which one of the following is the minimum value of the sum of two integers whose products is 24?
16. A four-digit pin, say 'abcd', of a lock has different non-zero digits. The digits satisfy b = 2a, c = 2b, d = 2c. The pin is divisible by . . . . . . . .
17. The real number to be added to 13851 to get a number which is divisible by 87 is:
18. Weight of a bucket when filled fully with water is 17 kg. If the weight of the bucket when half filled with water is 13.5 kg, what is the weight of empty bucket?
19. 5349 is added to 3957. Then 7062 is subtracted from the sum. The result is not divisible by
20. If each of the two numbers 516 and 525 are divided by 6, the remainders are R1 and R2 respectively. What is the value of $$\frac{{{{\text{R}}_1} + {{\text{R}}_2}}}{{{{\text{R}}_2}}}?$$
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