NEW
New Website Launch
Experience the best way to solve previous year questions with mock tests (very detailed analysis), bookmark your favourite questions, practice etc...
1

IIT-JEE 1999

Subjective
Let $${T_1}$$, $${T_2}$$ be two tangents drawn from (- 2, 0) onto the circle $$C:{x^2}\,\, + \,{y^2} = 1$$. Determine the circles touching C and having $${T_1}$$, $${T_2}$$ as their pair of tangents. Further, find the equations of all possible common tangents to these circles, when taken two at a time.

Answer


$${(x - y)^2} + \,{y^2} = {3^2}\,\,\,and\,\,{\left( {x + \,{4 \over 3}} \right)^2} + \,{y^2} = \,{\left( {{1 \over 3}} \right)^2};$$
$$y = \pm \,{5 \over {\sqrt {39} \,}}\left( {x + {4 \over 5}} \right)$$
2

IIT-JEE 1998

Subjective
$$C_1$$ and $$C_2$$ are two concentric circles, the radius of $$C_2$$ being twice that of $$C_1$$. From a point P on $$C_2$$, tangents PA and PB are drawn to $$C_1$$. Prove that the centroid of the triangle PAB lies on $$C_1$$.

Answer

solve it
3

IIT-JEE 1997

Subjective
Let C be any circle with centre $$\,\left( {0\, , \sqrt {2} } \right)$$. Prove that at the most two rational points can to there on C. (A rational point is a point both of whose coordinates are rational numbers.)

Answer

solve it
4

IIT-JEE 1996

Subjective
Find the intervals of value of a for which the line y + x = 0 bisects two chords drawn from a point $$\left( {{{1\, + \,\sqrt 2 a} \over 2},\,{{1\, - \,\sqrt 2 a} \over 2}} \right)$$ to the circle $$\,\,2{x^2}\, + \,2{y^2} - (\,1\, + \sqrt 2 a)\,x - (1 - \sqrt 2 a)\,y = 0$$.

Answer

$$a\, \in \,]\, - \infty ,\,\, - \,2\,[U]\,\,2,\,\,\infty \,[$$

Joint Entrance Examination

JEE Main JEE Advanced WB JEE

Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN

Medical

NEET

CBSE

Class 12