# Solved papers for 10th Class Mathematics Solved Paper - Mathematics 2017 Delhi Set-III

### done Solved Paper - Mathematics 2017 Delhi Set-III

 In the figure, AB and CD are common tangents to two circles of unequal radii. Prove that AB = CD.

• question_answer2) If the ${{p}^{th}}$ term of an A. P. is q and ${{q}^{th}}$ term is p, prove that its ${{n}^{th}}$ term is $(p+q-n)$.

• question_answer3) A solid metallic sphere of diameter $16\text{ }cm$ is melted and recasted into smaller solid cones, each of radius $4\text{ }cm$ and height$8\text{ }cm$. Find the number of cones so formed.

• question_answer4) The angle of elevation of the top of a hill at the foot of a tower is $60{}^\circ$ and the angle of elevation of the top of the tower from the foot of the hill is $30{}^\circ$. If height of the tower is 50 m, find the height of the hill.

• question_answer5) If the ${{p}^{th}}$ term of an A.P. is $\frac{1}{q}$ and ${{q}^{th}}$ term is $\frac{1}{p}$, prove that the sum of first $pq$ terms if the A.P. is $\left( \frac{pq+1}{2} \right)$.

• question_answer6) An observer finds the angle of elevation of the top of the tower from a certain point on the ground as $30{}^\circ$. If the observer moves $20\text{ }m$ towards the base of the tower, the angle of elevation of the top increases by $15{}^\circ$, find the height of the tower.

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