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If \(y=(1+x)\left(1+x^{2}\right)\left(1+x^{4}\right) \ldots . .\left(1+x^{2 n}\right)\) then the value of \(\left(\frac{\text { dy }}{d x}\right)\) at \(x=0\) is
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The value of \(\cos 15^{\circ} \cos 7 \frac{1}{2} \sin 7 \frac{1^{\circ}}{2}\) is (A) \(\frac{1}{2}\) (B) \(\frac{1}{8}\) (C) \(\frac{1}{4}\) (D) \(\frac{1}{16}\)
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Let \(A\) and \(B\) two events such that \(P(A \cap B)=\frac{1}{6}, P(A \cup B)=\frac{31}{45}\) and \(P(\bar{B})=\frac{7}{10}\) then (A) \(A\) and \(B\) are independent (B) \(A\) and \(B\) are mutually exclusive (C) \(\mathrm{P}\left(\frac{\mathrm{A}}{\mathrm{B}}\right)<\frac{1}{6}\) (D) \(P\left(\frac{B}{A}\right)<\frac{1}{6}\)
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The smallest positive root of the equation tan x – x = 0 lies in
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Dec 7, 2021
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Sets, relations and functions
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1. Let A and B two events such that ( ) 1 31 7 P A B , P(A B) and P(B) ∩ = ∪ = = then 6 45 10
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