# $\int\limits_0^{ - 2a} {f(x)dx} = .........$

If the system of equations 2x – y + z =0, x- 2y + z = 0 and ax – y + 2z = 0 has infinitely many solutions and f(x) is continuous function satisfying f(x)+f(x+5) = 2, then

is equal to

a) 0
b) 5
c) a
d) –2a

Solution

For system of given equations to have infinitely many solutions, we must have

or, 2x(-3) + 2-a + (-1+2a) = 0

or, a = 5

Now,

= –10 = -2a

Hence, (d).

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