eqalign and let a 1111 55 digits right cr and b 1 10 10 2

$$\eqalign{ & {\text{Let, }}a = 111.....1\left( {55{\text{ digits}}} \right), \cr & b = 1 + 10 + {10^2} + ..... + {10^4}, \cr & c = 1 + {10^5} + {10^{10}} + {10^{15}} + ..... + {10^{50}},\,{\text{then}} \cr} $$

A. $$a = b + c$$

B. $$a = bc$$

C. $$b = ac$$

D. $$c = ab$$

Answer : $$a = bc$$

Solution :
$$\eqalign{ & a = 1 + 10 + {10^2} + ..... + {10^{54}} \cr & = \frac{{{{10}^{55}} - 1}}{{10 - 1}} = \frac{{{{10}^{55}} - 1}}{{{{10}^5} - 1}} \cdot \frac{{{{10}^5} - 1}}{{10 - 1}} = bc \cr} $$

Releted MCQ Question on
Algebra >> Sequences and Series

Releted Question 1

If $$x, y$$ and $$z$$ are $${p^{{\text{th}}}},{q^{{\text{th}}}}\,{\text{and }}{r^{{\text{th}}}}$$ terms respectively of an A.P. and also of a G.P., then $${x^{y - z}}{y^{z - x}}{z^{x - y}}$$ is equal to:

A. $$xyz$$

B. 0

C. 1

D. None of these

View Answer

Releted Question 2

The third term of a geometric progression is 4. The product of the first five terms is

A. $${4^3}$$

B. $${4^5}$$

C. $${4^4}$$

D. none of these

View Answer

Releted Question 3

The rational number, which equals the number $$2.\overline {357} $$ with recurring decimal is

A. $$\frac{{2355}}{{1001}}$$

B. $$\frac{{2379}}{{997}}$$

C. $$\frac{{2355}}{{999}}$$

D. none of these

View Answer

Releted Question 4

If $$a, b, c$$ are in G.P., then the equations $$a{x^2} + 2bx + c = 0$$ and $$d{x^2} + 2ex + f = 0$$ have a common root if $$\frac{d}{a},\frac{e}{b},\frac{f}{c}$$ are in-

A. A.P.

B. G.P.

C. H.P.

D. none of these

View Answer

$$\eqalign{ & {\text{Let, }}a = 111.....1\left( {55{\text{ digits}}} \right), \cr & b = 1 + 10 + {10^2} + ..... + {10^4}, \cr & c = 1 + {10^5} + {10^{10}} + {10^{15}} + ..... + {10^{50}},\,{\text{then}} \cr} $$

Releted MCQ Question on
Algebra >> Sequences and Series

If $$x, y$$ and $$z$$ are $${p^{{\text{th}}}},{q^{{\text{th}}}}\,{\text{and }}{r^{{\text{th}}}}$$ terms respectively of an A.P. and also of a G.P., then $${x^{y - z}}{y^{z - x}}{z^{x - y}}$$ is equal to:

The third term of a geometric progression is 4. The product of the first five terms is

The rational number, which equals the number $$2.\overline {357} $$ with recurring decimal is

If $$a, b, c$$ are in G.P., then the equations $$a{x^2} + 2bx + c = 0$$ and $$d{x^2} + 2ex + f = 0$$ have a common root if $$\frac{d}{a},\frac{e}{b},\frac{f}{c}$$ are in-

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$$\eqalign{ & {\text{Let, }}a = 111.....1\left( {55{\text{ digits}}} \right), \cr & b = 1 + 10 + {10^2} + ..... + {10^4}, \cr & c = 1 + {10^5} + {10^{10}} + {10^{15}} + ..... + {10^{50}},\,{\text{then}} \cr} $$

Releted MCQ Question on Algebra >> Sequences and Series

If $$x, y$$ and $$z$$ are $${p^{{\text{th}}}},{q^{{\text{th}}}}\,{\text{and }}{r^{{\text{th}}}}$$ terms respectively of an A.P. and also of a G.P., then $${x^{y - z}}{y^{z - x}}{z^{x - y}}$$ is equal to:

The third term of a geometric progression is 4. The product of the first five terms is

The rational number, which equals the number $$2.\overline {357} $$ with recurring decimal is

If $$a, b, c$$ are in G.P., then the equations $$a{x^2} + 2bx + c = 0$$ and $$d{x^2} + 2ex + f = 0$$ have a common root if $$\frac{d}{a},\frac{e}{b},\frac{f}{c}$$ are in-

Practice More Releted MCQ Question on Sequences and Series

Practice More MCQ Question on Maths Section

Releted MCQ Question on
Algebra >> Sequences and Series

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Sequences and Series