1
IIT-JEE 2001
Subjective
+5
-0
Let $${a_1}$$, $${a_2}$$,.....,$${a_n}$$ be positive real numbers in geometric progression. For each n, let $${A_n}$$, $${G_n}$$, $${H_n}$$ be respectively, the arithmetic mean , geometric mean, and harmonic mean of $${a_1}$$,$${a_2}$$......,$${a_n}$$. Find an expression for the geometric mean of $${G_1}$$,$${G_2}$$,.....,$${G_n}$$ in terms of $${A_1}$$,$${A_2}$$,.....,$${A_n}$$,$${H_n}$$,$${H_1}$$,$${H_2}$$,........,$${H_n}$$.
2
IIT-JEE 2001
Subjective
+6
-0
Let $$a, b, c$$ be real numbers with $${a^2} + {b^2} + {c^2} = 1.$$ Show that

the equation $$\left| {\matrix{ {ax - by - c} & {bx + ay} & {cx + a} \cr {bx + ay} & { - ax + by - c} & {cy + b} \cr {cx + a} & {cy + b} & { - ax - by + c} \cr } } \right| = 0$$

represents a straight line.
3
IIT-JEE 2001
Subjective
+5
-0
Let $$C_1$$ and $$C_2$$ be two circles with $$C_2$$ lying inside $$C_1$$. A circle C lying inside $$C_1$$ touches $$C_1$$ internally and $$C_2$$ externally. Identify the locus of the centre of C.
4
IIT-JEE 2001
Subjective
+5
-0
Let $$\,2{x^2}\, + \,{y^2} - \,3xy = 0$$ be the equation of a pair of tangents drawn from the origin O to a circle of radius 3 with centre in the first quadrant. If A is one of the points of contact, find the length of OA.
EXAM MAP
Medical
NEET