1

IIT-JEE 1993

Subjective

+5

-0

Tagent at a point $${P_1}$$ {other than $$(0, 0)$$} on the curve $$y = {x^3}$$ meets the curve again at $${P_2}$$. The tangent at $${P_2}$$ meets the curve at $${P_3}$$, and so on. Show that the abscissae of $${P_1},\,{P_2},{P_3}......{P_n},$$ form a G.P. Also find the ratio.

[area $$\left( {\Delta {P_1},{P_2},{P_3}} \right)$$]/[area $$\left( {{P_2},{P_3},{P_4}} \right)$$]

2

IIT-JEE 1992

Subjective

+6

-0

Determine all values of $$\alpha $$ for which the point $$\left( {\alpha ,\,{\alpha ^2}} \right)$$ lies insides the triangle formed by the lines
$$$\matrix{
{2x + 3y - 1 = 0} \cr
{x + 2y - 3 = 0} \cr
{5x - 6y - 1 = 0} \cr
} $$$

3

IIT-JEE 1991

Subjective

+4

-0

Show that all chords of the curve $$3{x^2} - {y^2} - 2x + 4y = 0,$$ which subtend a right angle at the origin, pass through a fixed point. Find the coordinates of the point.

4

IIT-JEE 1991

Subjective

+4

-0

Find the equation of the line passing through the point $$(2, 3)$$ and making intercept of length 2 units between the lines $$y + 2x = 3$$ and $$y + 2x = 5$$.

Questions Asked from Straight Lines and Pair of Straight Lines (Subjective)

Number in Brackets after Paper Indicates No. of Questions

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