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UPSC NDA 2 2016 Mathematics Solved Paper

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Consider the following for the next two (02) items that follow:

Let

ax^{3}+bx^{2}+cx+d=\begin{vmatrix} x+1 & 2x & 3x \\ 2x+3 & x+1 & x \\ 2-x & 3x+4 & 5x-1 \end{vmatrix}

then

[NDA II 2016]

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Question : 21 of 120

Marks: +1, -0

What is the value of c ?

$-1$
$34$
$35$
$50$

Solution:

ax^{3}+bx^{2}+cx+d

=(x+1)[(x+1)(5x-1)-x(3x+4)]-2x[(2x+3)(5x-1)-x(2-x)]+3x[(2x+3)(3x+4)-(2-x)(x+1)]

\Rightarrow ax^{3}+bx^{2}+cx+d=x^{3}+28x^{2}+35x-1

\Rightarrow c=35

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