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CBSE Class 10 Mathematics Solved Question Paper 2016

Short Answer Type

In Fig. , PQ is tangent at point C to a circle with centre O. If AB is a diameter and ∠CAB = 30°, find ∠PCA.

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For what value of k will k+9, 2k-1 and 2k+7 are the consecutive terms of an A.P?

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A ladder leaning against a wall makes an angle of 60° with the horizontal. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder.

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A card is drawn at random from a well -shuffled fled pack of 52 playing cards. Find the probability of getting neither a red card nor a queen.

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If -5 is a root of the quadratic equation 2x² + px – 15 = 0 and the quadratic equation p(x² + x)k = 0 has equal roots, find the value of k.

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Let P and Q be the points of trisection of the line segment joining the points A(2, -2) and B(-7, 4) such that P is nearer to A. Find the coordinates of P and Q.

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In Fig.2, a quadrilateral ABCD is drawn to circumscribe a circle, with centre O, in such a way that the sides AB, BC, CD and DA touch the circle at the points P, Q, R and S respectively. Prove that AB + CD = BC + DA.

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8.
Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right-angled isosceles triangle.

Given, the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right-angled isosceles triangle.
Therefore,
Let A (3,0), B (6,4) and C (-1,3) be the given points.
Now,

$AB space equals space square root of left parenthesis 6 minus 3 right parenthesis squared plus left parenthesis 4 plus 0 right parenthesis squared end root space equals space square root of 3 squared plus 4 squared end root space equals space square root of 9 plus 16 end root space equals square root of 25 BC equals square root of negative left parenthesis 1 minus 6 right parenthesis squared plus left parenthesis 3 minus 4 right parenthesis squared end root space equals square root of left parenthesis negative 7 right parenthesis squared plus left parenthesis negative 1 right parenthesis squared end root space equals space square root of 49 plus 1 end root space equals square root of 50 AC equals square root of left parenthesis negative 1 minus 3 right parenthesis squared plus left parenthesis 3 minus 0 right parenthesis squared end root space equals space square root of left parenthesis negative 4 right parenthesis squared plus 3 squared space end root space equals space square root of 16 plus 9 end root space equals square root of 25 Since space AB equals BC therefore AB squared equals left parenthesis square root of 25 right parenthesis squared space equals 25 BC squared space equals left parenthesis square root of 50 right parenthesis end root squared space equals 50 AC squared space equals space left parenthesis square root of 25 right parenthesis squared space equals 25 therefore space AB squared plus AC squared space equals space BC squared Thus comma space increment ABC space is space right space minus angled space isosceles space triangle$