OPQR is a square and M, N are the middle points of the sides PQ and QR, respectively, Then the ratio of the area of the square to that of triangle OMN is&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi><mo>:</mo><mi>β</mi><mtext>&nbsp;then&nbsp;</mtext><mi>α</mi><mo>+</mo><mi>β</mi><mo>=</mo></math>

The number of points, having both coordinates as integers, that lie in the interior of the triangle with vertices (0,0)(0,41) and (41,0) is :

If the coordinate of a point is (0, 5), then it lies on _______.

In which of the following quadrant does point P(−3, 5) lie?

In the following reaction the identity of &nbsp;'X' is<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathsize="14px"><msub><mrow>&nbsp;</mrow><mn>7</mn></msub><msup><mi mathvariant="normal">N</mi><mn>14</mn></msup><msub><mo>+</mo><mn>2</mn></msub><msup><mi>He</mi><mn>4</mn></msup><mo>→</mo><mi mathvariant="normal">X</mi><msub><mo>+</mo><mn>1</mn></msub><msup><mi mathvariant="normal">H</mi><mn>1</mn></msup></mstyle></math>

Given that&nbsp;<math><mrow><mi>A</mi><mrow><mo>(</mo><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></math>&nbsp; and&nbsp;<math><mrow><mi>B</mi><mrow><mo>(</mo><mrow><mn>4</mn><mo>,</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow></math>&nbsp; are two points and&nbsp;<math><mi>D</mi></math>&nbsp; is a point on&nbsp;<math><mrow><mi>A</mi><mi>B</mi></mrow></math>&nbsp; produced such that&nbsp;<math><mrow><mi>A</mi><mi>D</mi><mo>=</mo><mn>3</mn><mi>A</mi><mi>B</mi></mrow></math>&nbsp;, find the co ordinates of&nbsp;<math><mrow><mo>'</mo><mi>D</mi><mo>'</mo></mrow></math>&nbsp;.

OPQR is a square and M, N are the middle points of the sides PQ and QR, respectively, Then the ratio of the area of the square to that of triangle OMN is $α : β then α + β =$

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OPQR is a square and M, N are the middle points of the sides PQ and QR, respectively, Then the ratio of the area of the square to that of triangle OMN is α:β then α+β=

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OPQR is a square and M, N are the middle points of the sides PQ and QR, respectively, Then the ratio of the area of the square to that of triangle OMN is $α : β then α + β =$