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Chapter 3: Problem 234
For \(x \in R, 3^{72}(1 / 3)^{x}(1 / 3)^{\sqrt{x}}>1\) then (a) \(x \in[0,64]\) (b) \(x \in(0,64)\) (c) \(x \in[0,64)\) (d) None of these
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The roots of equation a \((b-c) x^{2}+b(c-a) x+c(a-b)=0\) are equal, then \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) are in (a) A. P. (b) G. P. (c) H. P. (d) None of these
If \(\tan A \& \tan B\) are roots of \(x^{2}-p x+q=0\) then the value of \(\cos ^{2}(\mathrm{~A}+\mathrm{B})=\) (a) \(\left[(1-q)^{2} /\left\\{p^{2}+(1-q)^{2}\right\\}\right]\) (b) \(\left[p^{2} /\left\\{p^{2}+(1-q)^{2}\right\\}\right]\) (c) \(\left[(1-q)^{2} /\left(p^{2}-q^{2}\right)\right]\) (d) \(\left[\mathrm{p}^{2} /\left(\mathrm{p}^{2}+\mathrm{q}^{2}\right)\right]\)
It one root of the equation \(\mathrm{x}^{2}+\mathrm{px}+12=0\) is 4 , while the equation \(\mathrm{x}^{2}+\mathrm{px}+\mathrm{q}=0\) has equal roots, then the value of \(\mathrm{q}\) is (a) \((49 / 4)\) (b) 12 (c) 3 (d) 4
If \(\mathrm{b}^{2}=\) ac, equation \(\mathrm{ax}^{2}+2 \mathrm{bx}+\mathrm{c}=0\) and \(\mathrm{d} \mathrm{x}^{2}+2 \mathrm{ex}+\mathrm{f}=0\) have common roots then \((\mathrm{d} / \mathrm{a}),(\mathrm{e} / \mathrm{b}),(\mathrm{f} / \mathrm{c})\) are in (a) A.P. (b) G.P. (c) H.P. (d) None of these
If the ratio of the roots of the quadratic equation \(2 x^{2}+16 x+3 k=0\) is \(4: 5\) then \(k=\) (a) \([(2560) /(243)]\) (b) \(\overline{[(243) /(2560)]}\) (c) \([(-2560) /(243)]\) (d) \([(-243) /(2560)]\)
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