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How many number of two digits are divisible by 7 ?

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Given below are two pairs of statements. Combine these two statements using if and only if : p : If the sum of digits of a number is divisible by 3, then the number is divisible by 3. q : If a number is divisible by 3, then the sum of its digits is divisible by 3.

Statement-1: A 5-digit number divisible by 3 is to be formed using the digits 0,1,2,3,4,5 without repetition, then the total number of ways this can be done is 216. Statement-2: A number is divisible by 3, if sum of its digits is divisible by 3.

MBD-ARITHMETIC PROGRESSION-EXERCISE
  1. Determine the 2nd term of an A.P. whose 6^(th) term is 12 and 8^(th) ...

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  2. The 4th term of an A.P. is equal to 3 times the first term and 7^(th) ...

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  3. How many number of two digits are divisible by 7 ?

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  4. How many numbers between 10 and 200 are exactly divisible by 7 ?

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  5. Prove that a - 5b, a - b and a + 3b are consecutive term of an A.P.

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  6. Which term of the A.P. 3, 5, 7, .... is 43?

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  7. Which term of the A.P 2, 8, 14, .... will be 126 more than its 15th te...

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  8. Find the common difference of the A.P. for which 18^(th) term is 3 mor...

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  9. If six times the sixth term of an A.P. is equal to nine times the nint...

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  10. Which term of the sequence 17, 16 1/5 15 2/5 ,…... is the first negati...

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  11. In an A.P. the 24^(th) term is twice the 10^(th) term. Prove that 72n...

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  12. The ratio of 12^(th) to the 15^(th) term of an A.P. in 19 : 24. Find t...

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  13. The third term of an A.P. is 10 and seventh term is 22. Find the A.P.

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  14. How many terms are there in the A.P. -1,(-5)/6,(-2)/3,(-1)/2…..,10/3?

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  15. If 9th term of an A.P. is zero, prove that its 29th term is double the...

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  16. If (m + l)th term of an A.P. is twice the (n + l)th term, prove that (...

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  17. The first term of an A.P. is 5, the common difference is 3 and the las...

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  18. If the nth term of the A.P. 9, 7, 5, .... is same as the nth term of A...

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  19. Find the second term and nth term of an A.P. whose 6th term is 12 and ...

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  20. The first term of an A.P. is 5 and its 100th term is - 292. Find the 5...

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