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

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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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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 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

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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) ?

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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.2>Q 56

Find the number of pairs

(m, n)

of integers which satisfy the equation

m^{3} + 6 m^{2} + 5 m = 27 n^{3} + 9 n^{2} + 9 n + 1 .

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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 57

How many real numbers

x

satisfy the equation

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

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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 58

If

y + 4 = (x - 2)^{2}, x + 4 = (y - 2)^{2}

and

x \neq y,

then what is the value of

x^{2} + y^{2}

?

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IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.2>Q 59

For how many integers is the number

x^{4} - 51 x^{2} + 50

negative?