Topics

1). If $$\Large log3 \times log4\ x > 0$$, then
 A). $$\Large x > 1$$ B). $$\Large x > 4$$ C). $$\Large x > 64$$ D). none of these
2). $$\Large log \frac{1}{4} \left(a^{2}-1\right) < log_\frac{1}{2} \left(a+1\right)^{2}$$
 A). $$\Large a<1$$ B). $$\Large a<-1$$ C). $$\Large a>1$$ D). none of these
3). If $$\Large log_{e} \left(\frac{a+b}{2}\right) = \frac{1}{2} \left(log_{e} a+log_{e} b\right)$$ then:
 A). a = b B). a = b/2 C). 2a = b D). $$\Large a = \frac{b}{3}$$
4). If $$\Large 2 log \left(x+1\right)-10g \left(x^{2}-1\right) = log^{2}$$, then x equals
 A). 1 B). 0 C). 2 D). 3
5). The number $$\Large log 2^{7}$$ is:
 A). an integer B). a rational number C). an irrational number D). a prime number

6). If $$\Large y = 2^{\frac{1}{logx}\left(8\right)}$$, then x is equal to:
 A). y B). $$\Large y^{2}$$ C). $$\Large y^{3}$$ D). none of these
7). If $$\Large log_{05} \sin x = 1 - log_{05} \cos x$$, then number of solution of $$\Large x ? \left[ -2 \pi , 2 \pi \right]$$ is:
 A). 1 B). 2 C). 3 D). 4
8). If a, b, c are in GP. then $$\Large log ax^{x}, log_{bx}x, log_{cx}x$$ are in:
 A). GP B). HP C). AP D). none of these
9). Consider the following statements:
1. Solution of the inequality $$\Large log_{5} \left(x^{2}-11x+43\right)<2$$ is (0, 2)
2. If $$\Large [x - 1]^{ \left(log_{3}x^{2} - 2Logx^{9}\right)} = \left(x - 1\right)^{7}$$, then x is 2 and 81.
Which of these is/are correct?

 A). only(1) B). only 2 C). both of these D). none of these
10). $$\Large log \cos x \sin x \ge 2$$ and  $$\Large x \epsilon \left[ 0, 3 \pi \right]$$, then $$\Large \sin x$$ lines in the interval:
 A). $$\Large \left[ 0, \frac{1}{2} \right]$$ B). $$\Large \left[\frac{\sqrt{5}-1}{2}, 1 \right]$$ C). $$\Large \left[ 0, \frac{\sqrt{5}-1}{2} \right]$$ D). none of these
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