Mathematics>Arithmetic>Number Systems>Exponents and Surds

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The $100^{t h}$ root of $10^{(10^{10})}$ is

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Important Questions on Number Systems

MEDIUM

Mathematics>Arithmetic>Number Systems>Exponents and Surds

If

81^{y} = \frac{1}{27^{x}}

, then the value of

x

in terms of

y

is

MEDIUM

Mathematics>Arithmetic>Number Systems>Exponents and Surds

If

\log 2, \log (2^{x} - 1)

and

\log (2^{x} + 3)

are in

A . P .

, then

x

is equal to _________

HARD

Mathematics>Arithmetic>Number Systems>Exponents and Surds

Of which number is

10608049

a square ?

EASY

Mathematics>Arithmetic>Number Systems>Exponents and Surds

The roots of the equation $5^{x + 1} + 5^{2 - x} = 5^{3} + 1$ will be _____.

EASY

Mathematics>Arithmetic>Number Systems>Exponents and Surds

The coefficient of

x^{10}

in the expansion of

{(1 + \frac{x^{2}}{2!} + \frac{x^{4}}{4!} + \dots \dots \dots \infty)}^{2} + {(\frac{x}{1!} + \frac{x^{3}}{3!} + \dots \dots \infty)}^{2} =

MEDIUM

Mathematics>Arithmetic>Number Systems>Exponents and Surds

The value of

(\sqrt[2010]{2 \sqrt{7} - 3 \sqrt{3}}) (\sqrt[4020]{55 + 12 \sqrt{21}})

is

MEDIUM

Mathematics>Arithmetic>Number Systems>Exponents and Surds

If

a, b

and

c

are integers such that

(\sqrt[3]{4} + \sqrt[3]{2} - 2) (\sqrt[3]{4 a} + \sqrt[3]{2 b} + c) = 20

, then which one of the following is true?

HARD

Mathematics>Arithmetic>Number Systems>Exponents and Surds

If

5^{x + 1} + 5^{2 - x} = 126

, then

x

is equal to

EASY

Mathematics>Arithmetic>Number Systems>Exponents and Surds

The sum of the series

1 + \frac{1 + a}{2!} + \frac{1 + a + a^{2}}{3!} + \frac{1 + a + a^{2} + a^{3}}{4!} + \dots \dots \infty

is:

EASY

Mathematics>Arithmetic>Number Systems>Exponents and Surds

{(x^{5} \div x^{4})}^{3} \div x^{2} = ?

MEDIUM

Mathematics>Arithmetic>Number Systems>Exponents and Surds

Value of

{(125)}^{\frac{1}{3}} . {(32)}^{\frac{1}{5}}

will be

EASY

Mathematics>Arithmetic>Number Systems>Exponents and Surds

For every real number

x

, let

f (x) = \frac{x}{1!} + \frac{3}{2!} x^{2} + \frac{7}{3!} x^{3} + \frac{15}{4!} x^{4} + \dots .

Then, the equation

f (x) = 0

EASY

Mathematics>Arithmetic>Number Systems>Exponents and Surds

If x, y and z are positive real numbers and a, b and c are rational numbers, then value of

\frac{1}{1 + x^{b - a} + x^{c - a}} + \frac{1}{1 + x^{a - b} + x^{c - b}} + \frac{1}{1 + x^{b - c} + x^{a - c}}

MEDIUM

Mathematics>Arithmetic>Number Systems>Exponents and Surds

If

\sqrt{5 + \sqrt[3]{x}} = 3

, then the value of

x

is

MEDIUM

Mathematics>Arithmetic>Number Systems>Exponents and Surds

If

\sqrt{512} = 2^{x}, \sqrt{15625} = 5^{y} and \sqrt{343} = 7^{z}

then what will be the value of

x - y + z

EASY

Mathematics>Arithmetic>Number Systems>Exponents and Surds

The value of

\frac{(x^{a + b}) (x^{b + c}) (x^{c + a})}{{(x^{a} \times x^{b} \times x^{c})}^{2}}

is

EASY

Mathematics>Arithmetic>Number Systems>Exponents and Surds

Which of the following statement is true?

MEDIUM

Mathematics>Arithmetic>Number Systems>Exponents and Surds

Determine the greatest number among the following four numbers

EASY

Mathematics>Arithmetic>Number Systems>Exponents and Surds

The sum to infinity of the series

\frac{2}{1!} + \frac{3}{2!} + \frac{4}{3!} + \dots \dots \infty

MEDIUM

Mathematics>Arithmetic>Number Systems>Exponents and Surds

The value of

\frac{2}{1!} + \frac{2 + 4}{2!} + \frac{2 + 4 + 6}{3!} + \dots .

is