11). If \( \Large log_{2} x + log_{2} y \ge 6 \), then the least value of \( \Large \left(x + y\right) \) is
A). 4 |
B). 9 |
C). 16 |
D). 32 |
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12). If \( \Large 4^{log_{3}\frac{31}{2}} + 9^{log2^{2}} = 10^{log_{x}83} \), (x belongs to R), then x is:
A). 4 |
B). 9 |
C). 10 |
D). none of these |
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13). Which of the following is not true?
A). \( \Large \frac{1}{log_{3} \pi } + \frac{1}{log_{4} \pi }>2 \) |
B). \( \Large log_{3}5 \) |
C). \( \Large \sqrt{8x} = \frac{10}{3} => x = 16 \) |
D). \( \Large log_{x} \left(a^{2}+1\right)<0 \), (a?0) then 0 |
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14). If \( \Large y = \frac{1}{a^{1-log ax}} \) and \( \Large z = \frac{1}{a^{1+log_{a}y}} \) then x is equal to:
A). \( \Large \frac{1}{a^{1+log_{a}z}} \) |
B). \( \Large \frac{1}{a^{z+log_{a}z}} \) |
C). \( \Large \frac{1}{a^{1-log_{a}z}} \) |
D). none of these |
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15). The least value of n in order that the sum of first n terms of an infinite series \( \Large 1 + \frac{3}{4} + \left(\frac{3}{4}\right)^{2} + \left(\frac{3}{4}\right)^{3}+ .... \) should differ from the sum of the series by less then \( \Large 10^{-6} \) is
[\( \Large\ Given\ log_{10}2=0.30103, log_{10}3=0.47712 \)]
A). 14 |
B). 27 |
C). 53 |
D). 57 |
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16). Solution of the equation \( \Large x log^{x^{2}} = log3 \left(x+y\right) \) and \( \Large x^{2}+y^{2} = 65 \) is:
A). x = 8, y = 1 |
B). x = 1, y = 8 |
C). (x=8, y=1); (x=1, y=8) |
D). none of the above |
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17). The identity \( \Large log_{a}n\ log_{b}n\ +\ log_{b}n\ log_{c}n\ +\ log_{c}n\ log_{a}n \) ls:
A). \( \Large \frac{log_{a}n\ log_{b}n\ log_{c}n}{log_{abc}n} \) |
B). \( \Large \frac{log_{abc}n}{log_{a}n} \) |
C). \( \Large \frac{log_{b}n}{log_{abc}n} \) |
D). none of these |
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18). The least value of the expression \( \Large 2\ log_{10}x\ -\ logx\ \left(0.01\right) \) for x > 1, is:
A). 10 |
B). 2 |
C). -0.01 |
D). none of the above |
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19). \( \Large log_{10}1000 \) =
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20). Simplify: \( \Large log_{10}2500 \)
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