The number of integral solutions of x - y - z - 0 with x - - 5- y - - 5- z - - 5 is

Let x = p 5, y = q 5 and z = r 5, where p, q, r ≥ 0. Then the given equation reduces to p + q + r = 15⋯(1) nbsp; nbsp; Now, we have to find non negati ...

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Standard XI

Mathematics

Multinomial Theorem

The number of...

Question

The number of integral solutions of $x + y + z = 0$ with $x \geq - 5, y \geq - 5, z \geq - 5$ is

134

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136

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138

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140

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Solution

The correct option is B $136$
Let $x = p - 5, y = q - 5$ and $z = r - 5$ , where $p, q, r \geq 0.$
Then the given equation reduces to $p + q + r = 15 \dots (1)$
Now, we have to find non-negative integral solution of equation $(1)$ .
The total number of such solutions
$=^{15 + 3 - 1} C_{3 - 1} =^{17} C_{2} = 136$

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Multinomial Theorem

Standard XI Mathematics

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The number of integral solutions of x+y+z=0 with x≥−5,y≥−5,z≥−5 is

The correct option is B 136Let x=p−5,y=q−5 and z=r−5, where p,q,r≥0. Then the given equation reduces to p+q+r=15⋯(1) Now, we have to find non-negative integral solution of equation (1). The total number of such solutions = 15+3−1C3−1= 17C2=136

The number of integral solutions of $x + y + z = 0$ with $x \geq - 5, y \geq - 5, z \geq - 5$ is