A) Rs. 80
B) Rs. 120
C) Rs. 30
D) Rs. 60
Correct Answer: D
Solution :
Amount of money Vikas has = Rs.\[({{x}^{2}}+2ax+b)\] Now, he can buy exactly \[(x-1)\]Jeans or \[(x+1)\]shirts. \[\therefore \]\[(x-1)\]and \[(x+1)\]are factors of \[{{x}^{3}}+2ax+b.\] \[\therefore \]\[{{(1)}^{3}}+2a(1)+b=0\Rightarrow 2a+b=-1\] ?(i) and \[{{(-1)}^{3}}-2a+b=0\Rightarrow 2a-6b=-1\] ?(ii) Adding (i) and (ii), we get \[4a=-2\Rightarrow a=\frac{-1}{2}\]? \[\therefore \]\[-1+b=-1\Rightarrow b=0\] So, amount of money he has = Rs.\[({{x}^{3}}-x)\] = Rs. \[({{4}^{3}}-4)=\]Rs.\[(64-4)\]= Rs. 60
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