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

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IMPORTANT

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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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Important Questions on Algebra

MEDIUM

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})

.

MEDIUM

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IMPORTANT

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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IOQM - PRMO and RMO

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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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) .

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IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.2>Q 54

If

p, q

and

r

are distinct roots of

x^{3} - x^{2} + x - 2 = 0,

then

p^{3} + q^{3} + r^{3}

equals

HARD

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.2>Q 55

Let

g (x) = x^{5} + x^{4} + x^{3} + x^{2} + x + 1

What is the remainder when the polynomial

g (x^{12})

is divided by the polynomial

g (x) ?