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JEE Math Practice Question

The range of a$$\in$$R for which the function f(x) = (4a $$-$$ 3)(x + loge 5) + 2(a $$-$$ 7) cot$$\left( {{x \over 2}} \right)$$ sin2$$\left( {{x \over 2}} \right)$$, x $$\ne$$ 2n$$\pi$$, n$$\in$$N has critical points, is :

  1. A.[1, $$\infty $$)
  2. B.($$-$$3, 1)
  3. C.$$\left[ { - {4 \over 3},2} \right]$$
  4. D.($$-$$$$\infty $$, $$-$$1]

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