Q.1.
If $$a=\log_35 $$ and $$b= \log_725$$ then correct option is:
-
70%
$$a < b$$
-
19%
$$ a > b$$
-
8%
$$a= b$$
-
3%
None of these
Q.2.
$$\dfrac{8^{-1}\times 5^3}{2^{-4}\times 625}=$$
-
12%
$$\dfrac{5}{2}$$
-
71%
$$\dfrac{2}{5}$$
-
12%
$$25$$
-
4%
$$5$$
Q.3.
Multiple Correct:
Which of the following statements are true
-
12%
$$\log _{ 2 }{ 3 } <\log _{ 12 }{ 10 } $$
-
14%
$$\log _{ 6 }{ 5 } <\log _{ 7 }{ 8 } $$
-
52%
$$\log _{ 3 }{ 26 } <\log _{ 2 }{ 9 } $$
-
22%
$$\log _{ 16 }{ 15 } >\log _{ 10 }{ 11 } >\log _{ 7 }{ 6 }$$
Q.4.
If the approximate value of $$ \log _{ 10 }{ (4.04) }$$is $$\ abcdef,$$ it is given that $$\log _{ 10 }{ (4) }=0.6021$$ &$$ \log _{ 10 }{ (e) }=0.4343,$$ then the value of abcd must be
-
37%
$$6064$$
-
35%
$$6063$$
-
12%
$$6065$$
-
16%
N.O.T
Q.5.
If $$\log_{10}e=0.4343$$, then $$\log_{10}1016$$ is
-
5%
$$2.99$$
-
11%
$$3$$
-
81%
$$3.006949$$
-
3%
$$3.02$$
Q.6.
The number of zeroes after decimal and before first significant digit in $$(50)^{-100}$$ is equal to : (take $$log_{10}$$ 5=0.699)
-
14%
168
-
52%
169
-
28%
170
-
7%
171
Explanation
Q.7.
Find the value of $$\log_{10}{\left(0.\bar{9}\right)}$$
-
40%
$$0$$
-
30%
$$1$$
-
27%
$$-1$$
-
3%
$$2$$
Q.8.
If $$\log 4=1.3868$$, then the approximate value of $$\log\, (4.01)$$
-
21%
$$1.3968$$
-
29%
$$1.3898$$
-
42%
$$1.3893$$
-
8%
$$1.9338$$
Q.9.
The equation $$\log_{e}x+\log_{e}(1+x)=0$$ can be written as
-
7%
$$x^{2}+x-e=0$$
-
73%
$$x^{2}+x-1=0$$
-
13%
$$x^{2}+x+1=0$$
-
7%
$$x^{2}+xe-e=0$$
Q.10.
The logarithmic form of $$4 = 2^2$$ is
-
50%
$$ log_{ 2 }^{ 4 }= 2$$
-
33%
$$ log_{ 2 }^{ 2 }= 2$$
-
12%
$$ log_{ 2 }^{ 4 }=4$$
-
4%
None of these
Q.11.
If $$x=500,y=100$$ and $$z=5050$$, then the value of $$(\log _{ xyz }{ { x }^{ z } } )(1+\log _{ x }{ yz } )$$ is equal to.
-
0%
500
-
0%
100
-
100%
5050
-
0%
10
Q.12.
The greatest value of $$(4\log_{10}{x}-\log_{x}{(0.0001)})$$ for $$0 < x < 1$$ is
-
5%
$$4$$
-
15%
$$-4$$
-
75%
$$8$$
-
5%
$$-8$$
Q.13.
The value of $$ 3 ^{log_4 5} -5 ^{log_4 3}$$
-
33%
$$0$$
-
22%
$$1$$
-
33%
$$2$$
-
11%
None of these
Q.14.
The number of $$\log_2 7 $$ is
-
6%
an integer
-
0%
a rational number
-
89%
an irrational number
-
6%
a prime number
Q.15.
The value of $$0.2^{log_{\sqrt{5}} \Big( \dfrac{1}{4} + \dfrac{1}{8} + \dfrac{1}{16} + \dots \Big)}$$ is
-
65%
$$4$$
-
18%
$$log 4$$
-
18%
$$log 2$$
-
0%
none of these
Q.16.
The value of $$\frac { \log _{ 2 }{ 24 } }{ \log _{ 96 }{ 2 } } -\frac { \log _{ 2 }{ 192 } }{ \log _{ 12 }{ 2 } } $$ is:
-
53%
3
-
33%
0
-
7%
2
-
7%
1
Q.17.
$$(-4)^{4}\times (4)^{1}=(4)^{5}$$
-
69%
True
-
31%
False
Q.18.
$$\left(\dfrac{2}{3}\right)^{2}\times \left(\dfrac{2}{3}\right)^{5}=\left(\dfrac{2}{3}\right)^{10}$$
-
25%
True
-
75%
False
Q.19.
$$a\times a\times b\times b\times b$$ can be written as
-
100%
$$a^2b^3$$
-
0%
$$a^3b^2$$
-
0%
$$a^3b^3$$
-
0%
$$a^5b^5$$
Q.20.
$$\left(-\dfrac{8}{2}\right)^{0}=0$$
-
40%
True
-
60%
False
Q.21.
$$(-7)^{4}\times (-7)^{2}=(-7)^{6}$$
-
80%
True
-
20%
False
Q.22.
$$(-5)^{2}\times (-5)^{3}=(-5)^{6}$$
-
13%
True
-
87%
False
Q.23.
$$\left(\dfrac {1}{10}\right)^0$$ is equal to
-
18%
$$0$$
-
18%
$$\dfrac {1}{10}$$
-
65%
$$1$$
-
0%
$$10$$
Q.24.
By solving $$(6^0 -7^0) \times (6^0+7^0)$$, we get ________.
-
13%
$$1$$
-
67%
$$0$$
-
13%
$$2$$
-
7%
$$-1$$
Q.25.
If $$x$$ be any integer different from zero and $$m,n$$ be any integers then $$({x^m})^n$$ is equal
-
0%
$$x^{m+n}$$
-
100%
$$x^{mn}$$
-
0%
$$\dfrac {m}{x^n}$$
-
0%
$$x^{m-n}$$
Q.26.
State whether the following statement is true (T) or false (F):
$$5^0 \times 3^0 = 8^0$$
$$5^0 \times 3^0 = 8^0$$
-
73%
True
-
27%
False
Q.27.
$$\log_{\sqrt{2}} x = 4$$ then value of $$x$$ will be
-
21%
$$4\sqrt{2}$$
-
7%
$$\frac{1}{4}$$
-
64%
$$4$$
-
7%
$$4*\sqrt{2}$$
Q.28.
The value of $$\log (1 + 2 * 3)$$:
-
0%
$$2\log3$$
-
7%
$$\log1.\log.2+\log3$$
-
7%
$$\log1+\log2+\log3$$
-
87%
$$\log7$$
Q.29.
Number $$\log_{2} 7$$ is:
-
0%
Integer
-
0%
Rational
-
93%
Irrational
-
7%
Prime
Q.30.
$$\log_{x} 243 = 2.5$$, then value of $$x$$ will be:
-
62%
$$9$$
-
23%
$$3$$
-
8%
$$1$$
-
8%
$$81$$