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 2000

Subjective

+4

-0

The fourth power of the common difference of an arithmatic progression with integer entries is added to the product of any four consecutive terms of it. Prove that the resulting sum is the square of an integer.

3

IIT-JEE 1999

Subjective

+10

-0

Let a, b, c, d be real numbers in G.P. If u, v, w, satisfy the system of equations

u + 2v + 3w = 6

4u + 5v + 6w = 12

6u + 9v = 4

u + 2v + 3w = 6

4u + 5v + 6w = 12

6u + 9v = 4

then show that the roots of the equation $$\left( {{1 \over u} + {1 \over v} + {1 \over w}} \right){x^2}$$

$$ + [{(b - c)^2} + {(c - a)^2} + {(d - b)^2}]x + u + v + w = 0$$ and $$20{x^2} + 10{(a - d)^2}x - 9 = 0$$ are reciprocals of each other.

4

IIT-JEE 1996

Subjective

+3

-0

The real numbers $${x_1}$$, $${x_2}$$, $${x_3}$$ satisfying the equation $${x^3} - {x^2} + \beta x + \gamma = 0$$ are in AP. Find the intervals in which $$\beta \,\,and\,\gamma $$ lie.

Questions Asked from Sequences and Series (Subjective)

Number in Brackets after Paper Indicates No. of Questions

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