question_answer1)
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 \[(p+q-n)\].
View Answer play_arrowquestion_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.
View Answer play_arrowquestion_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.
View Answer play_arrowquestion_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 \[\left( \frac{pq+1}{2} \right)\].
View Answer play_arrowquestion_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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