1

### IIT-JEE 2012 Paper 2 Offline

Let $${a_1},{a_2},{a_3},.....$$ be in harmonic progression with $${a_1} = 5$$ and $${a_{20}} = 25.$$ The least positive integer $$n$$ for which $${a_n} < 0$$ is
A
22
B
23
C
24
D
25
2

### IIT-JEE 2009

In the sum of first $$n$$ terms of an A.P. is $$c{n^\angle }$$, then the sum of squares of these $$n$$ terms is
A
$${{n\left( {4{n^2} - 1} \right){c^2}} \over 6}$$
B
$${{n\left( {4{n^2} + 1} \right){c^2}} \over 3}$$
C
$${{n\left( {4{n^2} - 1} \right){c^2}} \over 3}$$
D
$${{n\left( {4{n^2} + 1} \right){c^2}} \over 6}$$
3

### IIT-JEE 2008

Suppose four distinct positive numbers $${a_1},\,{a_{2\,}},\,{a_3},\,{a_4}\,$$ are in G.P. Let $${b_1} = {a_1},{b_2} = {b_1} + {a_2},\,{b_3} = {b_2} + {a_{3\,\,}}\,\,\,and\,\,\,{b_4} = {b_3} + {a_4}$$.

STATEMENT-1: The numbers $${b_1},\,{b_{2\,}},\,{b_3},\,{b_4}\,$$ are neither in A.P. nor in G.P. and

STATEMENT-2 The numbers $${b_1},\,{b_{2\,}},\,{b_3},\,{b_4}\,$$ are in H.P.

A

STATEMENT-1 is True, STATEMENT-2 is True;
STATEMENT-2 is a correct explanation for
STATEMENT-1
B

STATEMENT-1 is True, STATEMENT-2 is True;
STATEMENT-2 is NOT a correct explanation for
STATEMENT-1
C
STATEMENT-1 is True, STATEMENT-2 is False
D
STATEMENT-1 is False, STATEMENT-2 is True
4

### IIT-JEE 2007

Let $${A_1}$$, $${G_1}$$, $${H_1}$$ denote the arithmetic, geometric and harmonic means, respectively, of two distinct positive numbers. For $$n \ge 2,\,Let\,{A_{n - 1}}\,\,and\,\,{H_{n - 1}}$$ have arithmetic, geometric and harminic means as $${A_n},{G_n}\,,{H_n}$$ repectively.

Which one of the following statements is correct ?

A
$${H_1} > {H_2}\, > {H_3} > ...$$
B
$${H_1} < {H_2}\, < {H_3} < ...$$
C
$${H_1} > {H_2}\, > {H_3} > ...$$ and $${H_1} < {H_2}\, < {H_3} < ...$$
D
$${H_1} < {H_2}\, < {H_3} < ...$$ and $${H_1} > {H_2}\, > {H_3} > ...$$

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