11.
R is a positive number. It is multiplied by 8 and then squared. The square is now divided by 4 and the square root is taken. The result of the square root is Q. What is the value of Q ?
(A) 3R
(B) 4R
(C) 7R
(D) 9R
Show Answer
Solution:
$$\eqalign{ & \Rightarrow {\text{Q}} = \sqrt {\frac{{{{\left( {8{\text{R}}} \right)}^2}}}{4}} \cr & \Rightarrow {\text{Q}} = \frac{{\sqrt {{{\left( {8{\text{R}}} \right)}^2}} }}{{\sqrt 4 }} \cr & \Rightarrow {\text{Q}} = \frac{{8{\text{R}}}}{2} \cr & \Rightarrow {\text{Q}} = 4{\text{R}} \cr} $$
12.
Determined the value of ÃÂÃÂ ÃÂÃÂ ÃÂÃÂ ÃÂÃÂ
Show Answer
Solution:
Given expressing, $$ = \frac{1}{{\sqrt 1 + \sqrt 2 }}{\text{ + }}\frac{1}{{\sqrt 2 + \sqrt 3 }}$$ $$ + \frac{1}{{\sqrt 3 + \sqrt 4 }}$$ $$ + ...... + $$ $$\frac{1}{{\sqrt {120} + \sqrt {121} }}$$ $$ = \frac{1}{{\sqrt 2 + \sqrt 1 }}{\text{ + }}\frac{1}{{\sqrt 3 + \sqrt 2 }}$$ $$ + \frac{1}{{\sqrt 4 + \sqrt 3 }}$$ $$ + ...... + $$ $$\frac{1}{{\sqrt {121} + \sqrt {120} }}$$ $$ = \frac{1}{{\sqrt 2 + \sqrt 1 }} \times $$ $$\frac{{\sqrt 2 - \sqrt 1 }}{{\sqrt 2 - \sqrt 1 }}{\text{ + }}$$ $$\frac{1}{{\sqrt 3 + \sqrt 2 }} \times $$ $$\frac{{\sqrt 3 - \sqrt 2 }}{{\sqrt 3 - \sqrt 2 }} + $$ $$\frac{1}{{\sqrt 4 + \sqrt 3 }} \times $$ $$\frac{{\sqrt 4 - \sqrt 3 }}{{\sqrt 4 - \sqrt 3 }} + $$ $$...... + $$ $$\frac{1}{{\sqrt {121} + \sqrt {120} }} \times $$ $$\frac{{\sqrt {121} - \sqrt {120} }}{{\sqrt {121} - \sqrt {120} }}$$ $$ = \frac{{\sqrt 2 - \sqrt 1 }}{{2 - 1}} + \frac{{\sqrt 3 - \sqrt 2 }}{{3 - 2}}$$ $$ + \frac{{\sqrt 4 - \sqrt 3 }}{{4 - 3}}$$ $$ + ...... + $$ $$\frac{{\sqrt {121} - \sqrt {120} }}{{121 - 120}}$$ $$ = \sqrt 2 - \sqrt 1 + \sqrt 3 - \sqrt 2 $$ $$ + \sqrt 4 - \sqrt 3 $$ $$ + ...... + $$ $$\sqrt {121} - \sqrt {120} $$ $$ = - 1 + \sqrt {121} $$ $$ = - 1 + 11$$ $$ = 10$$
13.
Show Answer
Solution:
$$\eqalign{ & = \sqrt {\frac{{25}}{{81}} - \frac{1}{9}} \cr & = \sqrt {\frac{{25 - 9}}{{81}}} \cr & = \sqrt {\frac{{16}}{{81}}} \cr & = \frac{{\sqrt {16} }}{{\sqrt {81} }} \cr & = \frac{4}{9} \cr} $$
14.
If ÃÂÃÂ the value of x is = ?
(A) 52
(B) 58
(C) 62
(D) 68
Show Answer
Solution:
$$\eqalign{ & \Leftrightarrow \frac{{52}}{x}{\text{ = }}\sqrt {\frac{{169}}{{289}}} \cr & \Leftrightarrow \frac{{52}}{x} = \frac{{13}}{{17}} \cr & \Leftrightarrow x = \left( {\frac{{52 \times 17}}{{13}}} \right) \cr & \Leftrightarrow x = 68 \cr} $$
15.
What is ÃÂÃÂ ÃÂÃÂ ÃÂÃÂ equal to ?
Show Answer
Solution:
$$\eqalign{ & {\text{Given,}} \cr & \frac{{5 + \sqrt {10} }}{{5\sqrt 5 - 2\sqrt {20} - \sqrt {32} + \sqrt {50} }}{\text{ }} \cr & = \frac{{5 + \sqrt {10} }}{{5\sqrt 5 - 2 \times 2\sqrt 5 - 2 \times 2\sqrt 2 + 5\sqrt 2 }} \cr & = \frac{{5 + \sqrt {10} }}{{5\sqrt 5 - 4\sqrt 5 - 4\sqrt 2 + 5\sqrt 2 }} \cr & = \frac{{5 + \sqrt {10} }}{{\sqrt 5 + \sqrt 2 }} \cr & = \frac{{\sqrt 5 \left( {\sqrt 5 + \sqrt 2 } \right)}}{{\sqrt 5 + \sqrt 2 }} \cr & = \sqrt 5 \cr} $$
16.
The square root of ÃÂÃÂ ÃÂÃÂ is = ?
Show Answer
Solution:
$$\frac{{{{\left( {0.75} \right)}^3}}}{{1 - 0.75}}$$ $${\text{ + }}$$$$\left[ {0.75 + {{\left( {0.75} \right)}^2} + 1} \right]$$ $$ = \frac{{{{\left( {0.75} \right)}^2} \times 0.75}}{{0.25}}$$ $${\text{ + }}$$ $$\left[ {0.75 + 0.5625 + 1} \right]$$ $$ = 0.5625 \times 3 \,\, + $$ $$\left[ {0.75 + 0.5625 + 1} \right]$$ $$\eqalign{ & = 1.6875 + 2.3125 \cr & = 4 \cr} $$ Square root of 4 = 2
17.
If ÃÂÃÂ ÃÂÃÂ then what will be the value of ÃÂÃÂ ÃÂÃÂ = ?
(A) 13.41
(B) 20.46
(C) 21.66
(D) 22.35
Show Answer
Solution:
$$\eqalign{ & \Rightarrow 3\sqrt 5 + \sqrt {125} = 17.88 \cr & \Rightarrow {\text{ }}3\sqrt 5 + \sqrt {25 \times 5} = 17.88 \cr & \Rightarrow {\text{ }}3\sqrt 5 + 5\sqrt 5 = 17.88 \cr & \Rightarrow {\text{ }}8\sqrt 5 = 17.88 \cr & \Rightarrow \sqrt 5 = 2.235 \cr & \therefore \sqrt {80} + 6\sqrt 5 \cr & = \sqrt {16 \times 5} + 6\sqrt 5 \cr & = 4\sqrt 5 + 6\sqrt 5 \cr & = 10\sqrt 5 \cr & = \left( {10 \times 2.235} \right) \cr & = 22.35 \cr} $$
18.
(A) 1367631
(B) 111
(C) 1366731
(D) 1367
Show Answer
Solution:
$$\eqalign{ & {\text{Let,}} \cr & {\text{ }}99 \times 21 - \root 3 \of x = 1968 \cr & {\text{Then,}} \cr & \Leftrightarrow 2079 - \root 3 \of x = 1968 \cr & \Leftrightarrow \root 3 \of x = 2079 - 1968 \cr & \Leftrightarrow \root 3 \of x = 111 \cr & \Leftrightarrow x = {\left( {111} \right)^3} \cr & \Leftrightarrow x = 1367631 \cr} $$
19.
The square root of 123454321 is = ?
(A) 111111
(B) 12341
(C) 11111
(D) 11211
Show Answer
Solution:
$$\therefore \sqrt {123454321} = 11111$$
20.
One-fourth of the sum of prime numbers, greater than 4 but less than 16, is the square of = ?
Show Answer
Solution:
Sum of prime numbers greater than 4 but less than 16 $$\eqalign{ & = \left( {5 + 7 + 11 + 13} \right) \cr & = 36 \cr & \therefore \frac{1}{4} \times 36 \cr & = 9 \cr & = {3^2} \cr} $$