Forum

Real Numbers

Show  that  the  square  of  any  positive  integer  cannot  be  of  the  form  6m  +  2  or 6m + 5 for any integer m.

07/11/2024

Mathematics

10th

Real Numbers

Show  that  the  square  of  any  positive  integer  cannot  be  of  the  form  5q  +  2  or 5q + 3 for any integer q.

07/11/2024

Mathematics

10th

Real Numbers

Show that cube of any positive integer is of the form 4m, 4m + 1 or 4m + 3, for some integer m.

07/11/2024

Mathematics

10th

Real Numbers

Show that the square of any positive integer is either of the form 4q or 4q + 1 for some integer q.

07/11/2024

Mathematics

10th

Real Numbers

Show that the square of an odd positive integer is of the form 8m + 1, for some whole number m.

07/11/2024

Mathematics

10th

Real Numbers

Using Euclid’s division algorithm, find which of the following pairs of numbers are co-prime:

(i) 231, 396         (ii) 847, 2160

07/11/2024

Mathematics

10th

Real Numbers

A rational number in its decimal expansion is 327.7081. What can you say about  the prime factors of q, when this number is expressed in the form p/q  ? Give reasons.

07/11/2024

Mathematics

10th

Real Numbers

Without actually performing the long division, find if   987/  10500 will have terminating  or non-terminating (repeating) decimal expansion. Give reasons for your answer.

07/11/2024

Mathematics

10th

Real Numbers

Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons.

07/11/2024

Mathematics

10th

Real Numbers

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

07/11/2024

Mathematics

10th