10

# A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 59.29, the number of the member is the group is:

 A) 57 B) 67 C) 77 D) 87

Explanation:

Money collected = (59.29 x 100) paise = 5929 paise.

${\color{Blue}&space;\therefore&space;}$  Number of members = ${\color{Blue}&space;\sqrt{5929}}$ = 77.

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• Related Questions

$\inline \fn_jvn {\color{Black}If\; a= \frac{\sqrt{5}+1}{\sqrt{5}-1}\; and\; b=\frac{\sqrt{5}-1}{\sqrt{5}+1},the\; value\; of\; \left [ \frac{a^{2}+ab+b^{2}}{a^{2}-ab+b^{2}} \right ]is:}$

 A) 3/4 B) 4/3 C) 3/5 D) 5/3

Explanation:

$\inline \fn_jvn {\color{Blue}a=\frac{(\sqrt{5}+1)}{(\sqrt{5}-1)}\times \frac{(\sqrt{5}+1)}{(\sqrt{5}+1)}=\frac{(\sqrt{5}+1)^2}{(5-1)}=\frac{5+1+2\sqrt{5}}{4}=\frac{3+\sqrt{5}}{2}}$

$\inline \fn_jvn {\color{Blue}b=\frac{(\sqrt{5}-1)}{(\sqrt{5}+1)}\times \frac{(\sqrt{5}-1)}{(\sqrt{5}-1)}=\frac{(\sqrt{5}-1)^2}{(5-1)}=\frac{5+1-2\sqrt{5}}{4}=\frac{3-\sqrt{5}}{2}}$

$\inline \fn_jvn {\color{Blue}\therefore\; \; a^{2}+b^{2}=\frac{(3+\sqrt{5})^2}{4}+\frac{(3-\sqrt{5})^2}{4}=\frac{(3+\sqrt{5})^2+(3-\sqrt{5})^2}{4}=\frac{2(9+5)}{4}=7}$

$\inline \fn_jvn {\color{Blue}Also,ab=\frac{(3+\sqrt{2})}{2}\times \frac{(3-\sqrt{2})}{2}=\frac{9-5}{4}=1}$

$\inline \fn_jvn {\color{Blue}\therefore \; \; \frac{a^{2}+ab+b^{2}}{a^{2}-ab+b^{2}}=\frac{(a^{2}+b^{2})+ab}{(a^{2}+b^{2})-ab}=\frac{7+1}{7-1}=\frac{8}{6}=\frac{4}{3}}$

Subject: Square Roots and Cube Roots - Quantitative Aptitude - Arithmetic Ability

3

$\inline \fn_jvn {\color{Black}If \; x=(7-4\sqrt{3}),then\; the \; value\; of\; \left ( x+\frac{1}{x} \right )is:}$

 A) 3sqrt{3} B) 8sqrt{3} C) 14 D) 14+8sqrt{3}

Explanation:

$\inline \fn_jvn {\color{Blue} x+\frac{1}{x} =(7-4\sqrt{3})+\frac{1}{(7-4\sqrt{3})}\times \frac{(7+4\sqrt{3})}{(7+4\sqrt{3})}=(7-4\sqrt{3})+\frac{(7+4\sqrt{3})}{(49-48)}}$

$\inline \fn_jvn {\color{Blue} =(7-4\sqrt{3})+(7+4\sqrt{3})=14}$

Subject: Square Roots and Cube Roots - Quantitative Aptitude - Arithmetic Ability

22

$\inline \fn_jvn {\color{Black} \frac{3+\sqrt{6}}{5\sqrt{3}-2\sqrt{12}-\sqrt{32}+\sqrt{50}}=?}$

 A) 3 B) 3sqrt{2} C) 6 D) None of these

Explanation:

$\inline \fn_jvn {\color{Blue}Given\; exp.= \frac{3+\sqrt{6}}{5\sqrt{3}-4\sqrt{3}-4\sqrt{2}+5\sqrt{2}}=\frac{3+\sqrt{6}}{\sqrt{3}+\sqrt{2}}}$

$\inline \fn_jvn {\color{Blue}= \frac{3+\sqrt{6}}{\sqrt{3}+\sqrt{2}}\times \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}}=\frac{3\sqrt{3}-3\sqrt{2}+3\sqrt{2}-2\sqrt{3}}{3-2}=\sqrt{3}}$

Subject: Square Roots and Cube Roots - Quantitative Aptitude - Arithmetic Ability

7

$\inline \fn_jvn {\color{Black}If\; \frac{5+2\sqrt{3}}{7+4\sqrt{3}}=a+b\sqrt{3},then:}$

 A) a=-11,b=-6 B) a=-11,b=6 C) a=11,b=-6 D) a=11,b=6

Explanation:

$\inline \fn_jvn {\color{Blue} a+b\sqrt{3}=\frac{(5+2\sqrt{3})}{(7+4\sqrt{3})}\times \frac{(7-4\sqrt{3})}{(7-4\sqrt{3})}=\frac{35-20\sqrt{3}+14\sqrt{3}-24}{(7)^{2}-(4\sqrt{3})^{2}}=\frac{11-6\sqrt{3}}{49-48}=11-6\sqrt{3}}$

$\inline \fn_jvn {\color{Blue} \therefore a=11,b=-6}$

Subject: Square Roots and Cube Roots - Quantitative Aptitude - Arithmetic Ability

3

$\inline \fn_jvn {\color{Black}\left [ \frac{3\sqrt{2}}{\sqrt{6}-\sqrt{3}}-\frac{4\sqrt{3}}{\sqrt{6}-\sqrt{2}} -\frac{6}{\sqrt{8}-\sqrt{12}}\right ]=?}$

 A) sqtr{3}-sqrt{2} B) sqtr{3}+sqrt{2} C) 5sqrt{3} D) 1

Explanation:

$\inline \fn_jvn {\color{Blue}Given \; exp.= \frac{3\sqrt{2}}{\sqrt{6}-\sqrt{3}}\times \frac{\sqrt{6}+\sqrt{3}}{\sqrt{6}+\sqrt{3}}-\frac{4\sqrt{3}}{\sqrt{6}-\sqrt{2}}\times \frac{\sqrt{6}+\sqrt{2}}{\sqrt{6}+\sqrt{2}}-\frac{6}{2(\sqrt{2}-\sqrt{3})}}$

$\inline \fn_jvn {\color{Blue}= \frac{3\sqrt{2}(\sqrt{6}+\sqrt{3})}{6-3}-\frac{4\sqrt{3}(\sqrt{6}+\sqrt{2})}{6-2}+\frac{3}{(\sqrt{3}-\sqrt{2})}\times \frac{(\sqrt{3}+\sqrt{2})}{(\sqrt{3}+\sqrt{2})}}$

$\inline \fn_jvn {\color{Blue}=\sqrt{2}(\sqrt{6}+\sqrt{3})-\sqrt{3}(\sqrt{6}+\sqrt{2})+3(\sqrt{3}+\sqrt{2}) }$

$\inline \fn_jvn {\color{Blue}=\sqrt{12}+\sqrt{6} -\sqrt{18}-\sqrt{6}+3\sqrt{3}+3\sqrt{2}}$

$\inline \fn_jvn {\color{Blue}=2\sqrt{3}-3\sqrt{2}+3\sqrt{3}+3\sqrt{2}=5\sqrt{3}}$