1
IIT-JEE 2012 Paper 2 Offline
+4
-1
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 Paper 2 Offline
+3
-1

If the sum of first $$n$$ terms of an A.P. is $$c{n^2}$$, 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 Paper 2 Offline
+3
-1
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
+4
-1
Let $$\,{V_r}$$ denote the sum of first r terms of an arithmetic progression (A.P.) whose first term is r and the common difference is (2r-1). Let $${T_r} = \,{V_{r + 1}} - \,{V_r} - 2\,\,\,and\,\,\,{Q_r} = \,{T_{r + 1}} - \,{T_r}\,for\,r = 1,2,...$$

The sum $${V_1}$$+$${V_2}$$ +...+$${V_n}$$ is

A
$${1 \over {12}}n(n + 1)\,(3{n^2} - n + 1)$$
B
$${1 \over {12}}n(n + 1)\,(3{n^2} + n + 2)$$
C
$${1 \over 2}n(2{n^2} - n + 1)$$
D
$${1 \over 3}(2{n^3} - 2n + 3)$$
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