IIT-JEE 2009 Paper 2 Offline | Sequences and Series Question 26 | Mathematics

1

IIT-JEE 2009 Paper 2 Offline

MCQ (Single Correct Answer)

+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

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

2

IIT-JEE 2008 Paper 2 Offline

MCQ (Single Correct Answer)

+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

3

IIT-JEE 2007 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-1

Let $$\mathrm{A_{1}, G_{1}}, \mathrm{H}_{1}$$ denote the arithmetic, geometric and harmonic means, respectively, of two distinct positive numbers. For $$n \geq 2$$, let $$\mathrm{A}_{n-1}$$ and $$\mathrm{H}_{n-1}$$ have arithmetic, geometric and harmonic means as $$\mathrm{A_{n}}$$, $$\mathrm{G}_{\mathrm{n}}, \mathrm{H}_{\mathrm{n}}$$ respectively.

Which one of the following statements is correct?

A

$$\mathrm{G}_{1} > \mathrm{G}_{2} > \mathrm{G}_{3} >\ldots$$

B

$$\mathrm{G_{1} < G_{2} < G_{3} < \ldots}$$

C

$$\mathrm{G}_{1}=\mathrm{G}_{2}=\mathrm{G}_{3}=\ldots$$

D

$$\mathrm{G}_{1} < \mathrm{G}_{3} < \mathrm{G}_{5}<\ldots$$ and $$\mathrm{G}_{2} > \mathrm{G}_{4} > \mathrm{G}_{6} > \ldots$$

4

IIT-JEE 2007 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-1

Let $$\mathrm{A_{1}, G_{1}}, \mathrm{H}_{1}$$ denote the arithmetic, geometric and harmonic means, respectively, of two distinct positive numbers. For $$n \geq 2$$, let $$\mathrm{A}_{n-1}$$ and $$\mathrm{H}_{n-1}$$ have arithmetic, geometric and harmonic means as $$\mathrm{A_{n}}$$, $$\mathrm{G}_{\mathrm{n}}, \mathrm{H}_{\mathrm{n}}$$ respectively.

Which one of the following statements is correct?

A

$$A_{1} > A_{2} > A_{3} > \ldots$$

B

$$\mathrm{A}_{1} < \mathrm{A}_{2} < \mathrm{A}_{3} < \ldots$$

C

$$A_{1} > A_{3} > A_{5}>\ldots$$ and $$A_{2} < A_{4} < A_{6} < \ldots$$

D

$$A_{1} < A_{3} < A_{5} < \ldots$$ and $$A_{2}>A_{4} > A_{6} > \ldots$$

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