Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.2>Q 45

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IMPORTANT

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Let $x_{1}, x_{2}, x_{3}, x_{4}$ denote the four roots of the equation
$x^{4} + k x^{2} + 90 x - 2009 = 0$ . If $x_{1} x_{2} = 49$ , find the value of $k$ .

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Important Questions on Algebra

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IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.2>Q 46

Let

x

be a real number such that

x^{2} - 15 x + 1 = 0

. Find the last two digits of

x^{4} + \frac{1}{x^{4}}

.

HARD

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.2>Q 47

If

x, y

and

z

are real numbers such that

x + y + z = 9

and

x y + y z + z x = 24

, find the largest possible value of

z

.

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IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.2>Q 48

It is given that

\sqrt{a} - \sqrt{b} = 20

, where

a

and

b

are real numbers. Find the maximum possible value of

(\frac{a - 5 b}{10})

.

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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.2>Q 49

Given that

169 {(157 - 77 x)}^{2} + 100 {(201 - 100 x)}^{2} = 26 (77 x - 157) (1000 x - 2010)

, find the value of

x

.

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IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.2>Q 50

Evaluate:

\frac{(2020^{2} - 20100) (20100^{2} - 100^{2}) (2000^{2} + 20100)}{10 (2010^{6} - 10^{6})}

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IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.2>Q 51

If

a, b, c

and dare real numbers such that

\frac{b + c + d}{a} = \frac{a + c + d}{b} = \frac{a + b + d}{c} = \frac{a + b + c}{d} = r

, find the sum of all the possible values of

r .

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IOQM - PRMO and RMO

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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.2>Q 52

Find the value of

x

that satisfies the equation

25^{- 2} = \frac{5^{\frac{48}{x}}}{5^{\frac{26}{x}} \cdot 25^{\frac{17}{x}}}

EASY

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IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.2>Q 53

Let the value(s) of

x

is such that

8 x y - 12 y + 2 x - 3 = 0

is true for all values of

y .

Then find

(16 x) .