Manipur Board Class 12 Business Studies Question Paper 2019 with Answer Key (March 2)

BSEM Questions

• 1.

  If \(x, y, z\) are real numbers, \(x \neq 0\), and \(xy = xz\), prove that \(y = z\).

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• 2.

  If three consecutive vertices of a parallelogram are \( A(1,-2) \), \( B(3,6) \) and \( C(5,10) \), find its fourth vertex.

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• 3.

  The ratio of incomes of two persons is \(9:7\) and the ratio of their expenditures is \(4:3\). If each of them saves Rs. \(5000\) per month, find their monthly incomes.

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• 4.

  A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height \(h\). At a point on the plane, the angle of elevation of the bottom of the flagstaff is \(\alpha\) and that of the top of the flagstaff is \(\beta\). Prove that the height of the tower is \(\dfrac{h\tan\alpha}{\tan\beta-\tan\alpha}\).

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• 5.

  Prove that \(x^n - y^n\) is divisible by \(x+y\) only when \(n\) is even.

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• 6.

  Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

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