Manipur Board Class 12 Music Question Paper 2018 with Answer Key (March 21, 2018)

BSEM Questions

• 1.

  If \( \cos A = \dfrac{3}{5} \), calculate \( \sin A \) and \( \tan A \).

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• 2.

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

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• 3.

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

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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.

  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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• 6.

  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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