Algebra: Basics Test-6

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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:

7^g = 1/343
7^g = 1/7³
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:

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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