Column - 1 contains definitions of various functions f(x) in terms of

1.	Column - 1 contains definitions of various functions f(x) in terms of real parameter 'a'. Column - 2 contains information about the coefficient of x2 in the binomial expansion of f(x) for small numerical values of x. Column - 3 contains the corresponding value of 'a'. Column 1Column 2Column 3(I)f(x)=a(2−3x)(1−2x)(2+x), \|x\|<12(i)14(P)10(II)f(x)=√1+2x4−x, \|x\|<1(ii)164(Q)4(III)f(x)=1√1−ax−√1+ax, \|x\|<1a(iii)10(R)14(IV)f(x)=a(1−x)1+x+x2+x3, \|x\|<1(iv)4(S)√8 What of the following options is the only INCORRECT combination ?
Answer» Column - 1 contains definitions of various functions f(x) in terms of real parameter 'a'. Column - 2 contains information about the coefficient of $x^{2}$ in the binomial expansion of f(x) for small numerical values of x. Column - 3 contains the corresponding value of 'a'. $\begin{matrix} Column 1 & Column 2 & Column 3 (I) & f (x) = \frac{a (2 - 3 x)}{(1 - 2 x) (2 + x)}, \| x \| < \frac{1}{2} & (i) & \frac{1}{4} & (P) & 10 (II) & f (x) = \sqrt{\frac{1 + 2 x}{4 - x}}, \| x \| < 1 & (ii) & \frac{1}{64} & (Q) & 4 (III) & f (x) = \frac{1}{\sqrt{1 - a x}} - \sqrt{1 + a x}, \| x \| < \frac{1}{a} & (iii) & 10 & (R) & \frac{1}{4} (IV) & f (x) = \frac{a (1 - x)}{1 + x + x^{2} + x^{3}}, \| x \| < 1 & (iv) & 4 & (S) & \sqrt{8} \end{matrix}$ What of the following options is the only INCORRECT combination ?

Column - 1 contains definitions of various functions f(x) in terms of real parameter 'a'. Column - 2 contains information about the coefficient of x2 in the binomial expansion of f(x) for small numerical values of x. Column - 3 contains the corresponding value of 'a'. Column 1Column 2Column 3(I)f(x)=a(2−3x)(1−2x)(2+x), |x|<12(i)14(P)10(II)f(x)=√1+2x4−x, |x|<1(ii)164(Q)4(III)f(x)=1√1−ax−√1+ax, |x|<1a(iii)10(R)14(IV)f(x)=a(1−x)1+x+x2+x3, |x|<1(iv)4(S)√8 What of the following options is the only INCORRECT combination ?

Answer»

Column - 1 contains definitions of various functions f(x) in terms of real parameter 'a'.

Column - 2 contains information about the coefficient of $x^{2}$ in the binomial expansion of f(x) for small numerical values of x.

Column - 3 contains the corresponding value of 'a'.

$\begin{matrix} Column 1 & Column 2 & Column 3 (I) & f (x) = \frac{a (2 - 3 x)}{(1 - 2 x) (2 + x)}, | x | < \frac{1}{2} & (i) & \frac{1}{4} & (P) & 10 (II) & f (x) = \sqrt{\frac{1 + 2 x}{4 - x}}, | x | < 1 & (ii) & \frac{1}{64} & (Q) & 4 (III) & f (x) = \frac{1}{\sqrt{1 - a x}} - \sqrt{1 + a x}, | x | < \frac{1}{a} & (iii) & 10 & (R) & \frac{1}{4} (IV) & f (x) = \frac{a (1 - x)}{1 + x + x^{2} + x^{3}}, | x | < 1 & (iv) & 4 & (S) & \sqrt{8} \end{matrix}$

What of the following options is the only INCORRECT combination ?

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