The real value of $a$ for which no value of $m$ satisfies the equation $(a^{2} - 1) m^{2} - (2 a - 3) m + a = 0$ gives the slope of a line parallel to the $y -$ axis is

\frac{3}{2}

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0

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1

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\pm 1

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Solution

The correct option is D $\pm 1$
$m = \frac{(2 a - 3) \pm \sqrt{(2 a - 3)^{2} - 4 a (a^{2} - 1)}}{2 (a^{2} - 1)}$
So denominator should not be zero for real values
$a^{2} - 1 = 0, a = \pm 1$
Hence, option 'D' is correct.

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