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Explain why 7*11*13+13 and 7*6*5*4*3*2*1...

Explain why `7*11*13+13` and `7*6*5*4*3*2*1+5` are composite numbers.

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Explain why 7xx11xx13+13 and 7xx6xx5xx4xx3xx2xx1+5 are composite numbers.

Show that 5xx7xx11+11 is a composite number .

Explain why 3 xx 5 xx 7 +7 is a composite number.

Show that the point A(1,-1,3), B(2,-4,5) and C(5,-13,11) are collinear.

Show that the point A (1,-1,3), B ( 2,-4,5) and C ( 5,-13,11) are collinear.

The solution of the equation 7^(logx)-5^(logx+1)=3. 5^(logx-1)-13. 7^(logx-1) is a. an even number b. rational number c. irrational number d. composite number

The solution of the equation 7^(logx)-5^(logx+1)=3*5^(logx-1)-13*7 ^(logx-1)is (a) an even number (b) rational number (c) irrational number (d) composite number

Show by using direction ratios, that the points (2,-4,5), (1,-1,3) and (5,-13,11) are collinear

If the points (5,-1,1),(-1,-3,4) and (1,-6,10) are three vertices of a rhombus taken in order then which one of the following ils the fourth vertex? (A) (7,-4,11) (B) (3,(-7)/2,11/2) (C) (7,-4,7) (D) (7,4,11)

Verify the following: (5,-1,1),(7,-4,7), (1,-6,10) and (-1,-3,4) are the vertices of a rhombus.

RD SHARMA ENGLISH-REAL NUMBERS-All Questions
  1. Find the largest number that will divide 398, 436 and 542 leaving r...

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  2. Find the HCF and LCM of 144, 180 and 192 by prime factorisation method...

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  3. Explain why 7*11*13+13 and 7*6*5*4*3*2*1+5 are composite numbers.

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  4. Prove that a positive integer n is prime number, if no prime p less th...

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  5. Show that every positive even integer is of the form 2q, and that eve...

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  6. prove that there are infinitely many positive integers.

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  7. Determine the prime factorization of each of the following numbers: 13...

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  8. Express each of the following positive integers as the product of its ...

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  9. If a and b are two odd positive integers such that a > b, then prove t...

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  10. Prove that one of every three consecutive positive integers is divi...

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  11. Show that the square of an odd positive integer is of the form 8q+1, f...

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  12. Prove that the square of any positive integer is of the form 5q ,5q+1,...

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  13. Prove that if x and y are odd positive integers, then x^2+y^2 is even ...

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  14. Show that one and only one out of n ,n+2 or n+4 is divisible by 3, whe...

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  15. Prove that n^2-n divisible by 2 for every positive integer n.

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  16. The remainder when the square of any prime number greater than 3 is ...

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  17. Use Euclid’s division algorithm to find the HCF of 4052 and 12576.

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  18. Use Euclid’s division algorithm to find the HCF of 210 and 55.

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  19. If n is a natural number, then 9^(2n)-4^(2n) is always divisible by (a...

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  20. What can you say about the prime factorisations of the denominators of...

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