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Use Euclid's division lemma to show that...

Use Euclid's division lemma to show that the square of any positive integer is either of the form `3m` or `3m+1` for some integer m. [Hint: Let x be any positive integer then it is of the form `3q` , `3q+1` or `3q+2` Now square each of these and sho

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    X BOARD PREVIOUS YEAR PAPER ENGLISH|Exercise SECTION-C|5 Videos

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X BOARD PREVIOUS YEAR PAPER ENGLISH-X Boards-All Questions
  1. For what value of k, are the roots of the quadratic equation kx (x-2) ...

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  2. Find the number of terms of the AP 18, 31/2, 13, ....., -99/2 and find...

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  3. Use Euclid's division lemma to show that the square of any positive ...

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  4. The horizontal distance between two poles is 15 m. The angle of depres...

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  5. Show that the points (7, 10), (-2, 5), and (3, -4) are the vertices of...

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  6. Find the ratio in which the y-axis divides the line segment joining th...

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  7. In the given figure, AB and CD are two diameters of circles ( with cen...

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  8. A vessel is in the form of a hollow hemisphere mounted by a hollow ...

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  9. Represent the following pair of equations graphically and write the co...

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  10. For what value of n, the n^(t h) terms of the following two A.Ps are t...

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  11. A wooden article was made by scooping out a hemisphere from each en...

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  12. In a circle of radius 21cm, an arc subtends an angle of 60^0 at the ce...

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  13. Solve for: 1/(2a+b+2x)=1/(2a)+1/b+1/(2x)

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  14. Sum of the areas of two squares is 400 cm. If the difference of their ...

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  15. If the sum of first 7 terms of an AP is 49 and that of 17 terms is ...

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  16. Prove that the tangent at any point of circle is perpendicular to the ...

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  17. l and m are two parallel tangents to a circle with centre O, touching...

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  18. The angle of elevation of the top of a building from the foot of the t...

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  19. A group consists of 12 persons, of which 3 are extremely patient, othe...

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  20. Three vertices of a parallelogram ABCD are A(3,-4),B(-1,-3)a n dC(-6,2...

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