the least value of 2log 100a log a00001a 1 is 356020660

The least value of $$2{\log _{100}}a - {\log _a}0.0001,a > 1$$ is

A. 2

B. 3

C. 4

D. none of these

Answer : 4

Solution :
$$\eqalign{ & 2{\log _{100}}a - {\log _a}{\left( {\frac{1}{{100}}} \right)^2} = 2\left\{ {{{\log }_{100}}a + {{\log }_a}100} \right\}. \cr & {\text{Also, }}\frac{{{{\log }_{100}}a + {{\log }_a}100}}{2} \geqslant \sqrt {{{\log }_{100}}a \times {{\log }_a}100} = 1. \cr} $$

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

The least value of $$2{\log _{100}}a - {\log _a}0.0001,a > 1$$ is

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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The least value of $$2{\log _{100}}a - {\log _a}0.0001,a > 1$$ is

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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Releted MCQ Question on
Algebra >> Sequences and Series

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Sequences and Series