Solved papers for 10th Class Mathematics Solved Paper - Mathematics-2015 Outside Delhi Term-II Set-II

1) If \[A(4,3),B(-1,y)\] and \[C(3,4)\] are the vertices of a right triangle ABC, right-angled at A, then find the value of y.

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2) All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if the area of the circle is\[1256\text{ }c{{m}^{2}}\]. [Use\[\pi =3.14\]]

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3) Solve for x: \[2{{x}^{2}}+6\sqrt{3}x-60=0\]

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4) The 16th term of an AP is five times its third term. If its 10th term is 41, then find the sum of its first fifteen terms.

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5) A bus travels at a certain average speed for a distance of 75 km and then travels a distance of 90 km at an average speed of 10 km/h more than the first speed. If it takes 3 hours to complete the total journey, find its first speed.

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6) Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

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7) Construct a right triangle ABC with \[AB=6\text{ }cm,\,\,\,BC=8\text{ }cm\] and \[\angle B=90{}^\circ \]. Draw BD, the perpendicular from B on AC. Draw the circle through B, C and D and construct the tangents from A to this circle.

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8) Find the values of k so that the area of the triangle with vertices \[(k+1,1,)\text{ (}4,-3)\]and \[(7,-k)\] is 6 sq. units.

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