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Algebra: Basics Test-6

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Question 1
$ \displaystyle if\,\,\,{{7}^{g}}\,\,\,=\frac{1}{343},$<br then the value of g is
A
1/3
B
-1/2
C
-3
D
1/7
Question 1 Explanation: 
7g = 1/343
7g = 1/73
7g = 7-3
g = -3
Question 2
If * is an operation such that d*f= 3d +2f, then 2*3+3*4 is equal to:
A
39
B
25
C
27
D
29
Question 2 Explanation: 
$ \displaystyle \begin{array}{l}Here,\,\,\,d*f=3d+2f\\Therefore\,\,\,\,\,2*3+3*4\\=\left( 3\times 2+2\times 3 \right)+\left( 3\times 3+2\times 4 \right)\\=12+17=29\end{array}$
Question 3
If 0.13 ÷d2=13, then d is equal to
A
10.001
B
0.101
C
0.1000
D
10.011
Question 3 Explanation: 
$ \displaystyle \begin{array}{l}0.13\div {{d}^{2}}=13\\\Rightarrow \frac{0.13}{{{d}^{2}}}=13\\\Rightarrow {{d}^{2}}=\frac{0.13}{13}=\frac{1}{100}\\\Rightarrow d=\frac{1}{10}=0.1\end{array}$
Question 4
If P=4.36, Q=2.39 and R=1.97, then the value of P3-Q3-R3-3PQR
A
-1
B
-1.3
C
2
D
0
Question 4 Explanation: 
$ \displaystyle \begin{array}{l}Here,\,\,\,P-Q-R\\=4.36-2.39-1.97=0\\Therefore\,\,\,\,\,{{P}^{3}}-{{Q}^{3}}-{{R}^{3}}=3PQR\\\Rightarrow {{P}^{3}}-{{Q}^{3}}-{{R}^{3}}-3PQR=0\end{array}$
Question 5
For what value (s) of p is
$ \displaystyle q+\frac{1}{4}\sqrt{q}+{{p}^{2}}$ a perfect square?
A
$ \displaystyle \pm \frac{1}{18}$
B
$ \displaystyle \pm \frac{1}{8}$
C
$ \displaystyle -\frac{1}{5}$
D
$ \displaystyle \frac{1}{4}$
Question 5 Explanation: 
$ \displaystyle \begin{array}{l}q+\frac{1}{4}\sqrt{q}+{{p}^{2}}\\={{\left( \sqrt{q} \right)}^{2}}+2.\sqrt{q.}\frac{1}{8}+{{\left( p \right)}^{2}}\\clearly\,\,\,q=\frac{1}{8}\\Then,\,\,\,\,\exp ression={{\left( \sqrt{q}+\frac{1}{8} \right)}^{2}}\end{array}$
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