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Algebra: Basics Test6
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Question 1 
$ \displaystyle if\,\,\,{{7}^{g}}\,\,\,=\frac{1}{343},$<br
then the value of g is
1/3  
1/2  
3  
1/7 
Question 1 Explanation:
7^{g} = 1/343
7^{g} = 1/7^{3}
7^{g} = 7^{3}
g = 3
7^{g} = 1/7^{3}
7^{g} = 7^{3}
g = 3
Question 2 
If * is an operation such that d*f= 3d +2f, then 2*3+3*4 is equal to:
39  
25  
27  
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 ÷d^{2}=13, then d is equal to
10.001  
0.101  
0.1000  
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 P^{3}Q^{3}R^{3}3PQR
1  
1.3  
2  
0

Question 4 Explanation:
$ \displaystyle \begin{array}{l}Here,\,\,\,PQR\\=4.362.391.97=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?
$ \displaystyle q+\frac{1}{4}\sqrt{q}+{{p}^{2}}$ a perfect square?
$ \displaystyle \pm \frac{1}{18}$  
$ \displaystyle \pm \frac{1}{8}$  
$ \displaystyle \frac{1}{5}$  
$ \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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