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Addition and Subtraction

Multiple Choice Questions

11.

The sum of all possible values of a, for which the 4-digit number 547a is divisible by 3, is

12.
A common factor of $x^{4} - 256, x^{3} - 4 x^{2} + 3 x - 12 and x^{2} - 7 x + 12 is$

x + 4

x - 3

x - 4

x + 3

x - 4

$x^{4} - 256 = 0 \Rightarrow {(x^{2})}^{2} - {(4^{2})}^{2} = 0 \Rightarrow (x^{2} - 4^{2}) (x^{2} + 4^{2}) = 0 \Rightarrow (x - 4) (x + 4) (x^{2} + 4^{2}) = 0 . . . (i) Now, x^{3} - 4 x^{2} + 3 x - 12 = 0 \Rightarrow x^{2} (x - 4) + 3 (x - 4) = 0 \Rightarrow (x^{2} + 3) (x - 4) . . . (ii) And, x^{2} - 7 x + 12 = 0 \Rightarrow x^{2} - 7 x + 12 = 0 \Rightarrow x^{2} - 4 x - 3 x + 12 = 0 \Rightarrow x (x - 4) - 3 (x - 4) = 0 \Rightarrow (x - 3) (x - 4) = 0 . . . (iii) In all the above eqs (i), (ii) and (iii) (x - 4) is the common factor$

Previous Year Papers

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Multiple Choice Questions

12. A common factor of x4 - 256, x3 - 4x2 + 3x - 12 and x2 - 7x + 12 is x + 4 x - 3 x - 4 x + 3

12.
A common factor of $x^{4} - 256, x^{3} - 4 x^{2} + 3 x - 12 and x^{2} - 7 x + 12 is$

x + 4

x - 3

x - 4

x + 3