Some questions on progressions for IITJEE Mains

Multiple Answer Questions.

(1) If \log_{2}(5.2^{x}+1), _{4}(2^{1-x}+1) and 1 are in AP, then x is equal to

(a) \frac{\log (5)}{\log (2)}

(b) \log_{2}(2/5)

(c) 1-\frac{\log (5)}{\log (2)}

(d) \frac{\log (2)}{\log (5)}

(2) Values of the positive integer m for which n^{m}+1 divides 1+n+n^{2}+ \ldots+n^{127} are

(a) 8 (b) 16 (c) 32 (d) 64

(3) If p, q, r are positive and are in AP, the roots of the quadratic equation px^{2}+qx+r=0 are all real for

(a) |\frac{r}{p}-7| \geq 4\sqrt{3} (b) |\frac{q}{r}-4| \geq 2\sqrt{3}

(c) |\frac{p}{r}-7| \geq 4\sqrt{3} (d) |\frac{q}{p}-4| \geq 2\sqrt{3}

(4) If sum of the GP p,1, \frac{1}{p^{2}}, \frac{1}{p^{3}}, … is 9/2, the value of p is

(a) 3

(b) 2/3

(c) 3/2

(d) 1/3

(5) The roots of x^{3}+bx^{2}+cx+d=0 are

(a) in AP if 2b^{3}-9bc+27d=0

(b) in GP if b^{3}d=c^{3}

(c) in GP if 27d^{3}=9bcd^{2}-2c^{3}d

(d) equal if c^{3}=b^{3}+3bc

Let me know your comments, answers, etc.

Nalin Pithwa

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