IIT-JEE 2009 Paper 2 Offline | Sequences and Series Question 20 | Mathematics

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IIT-JEE 2009 Paper 2 Offline

MCQ (Single Correct Answer)

-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

$${{n\left( {4{n^2} - 1} \right){c^2}} \over 6}$$

$${{n\left( {4{n^2} + 1} \right){c^2}} \over 3}$$

$${{n\left( {4{n^2} - 1} \right){c^2}} \over 3}$$

$${{n\left( {4{n^2} + 1} \right){c^2}} \over 6}$$

IIT-JEE 2008 Paper 2 Offline

MCQ (Single Correct Answer)

-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.

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

STATEMENT-1 is True, STATEMENT-2 is True;
STATEMENT-2 is NOT a correct explanation for
STATEMENT-1

STATEMENT-1 is True, STATEMENT-2 is False

STATEMENT-1 is False, STATEMENT-2 is True

IIT-JEE 2007

MCQ (Single Correct Answer)

-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 $${T_r} = \,{V_{r + 1}} - \,{V_r} - 2\,\,\,and\,\,\,{Q_r} = \,{T_{r + 1}} - \,{T_r}\,for\,r = 1,2,...$$

$${T_r}$$ is always

an odd number

an even number

a prime number

a composite number

IIT-JEE 2007

MCQ (Single Correct Answer)

-1

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 ?

$${H_1} > {H_2}\, > {H_3} > ...$$

$${H_1} < {H_2}\, < {H_3} < ...$$

$${H_1} > {H_2}\, > {H_3} > ...$$ and $${H_1} < {H_2}\, < {H_3} < ...$$

$${H_1} < {H_2}\, < {H_3} < ...$$ and $${H_1} > {H_2}\, > {H_3} > ...$$

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