Q.1
By what least number should 4320 be multiplied so as to obtain a number which a perfect cube ?
Q.2
If $$x = \sqrt 3 {\text{ + }}\sqrt 2 {\text{,}}$$   then the value of $${x^3} - \frac{1}{{{x^3}}}$$   is?
Q.3
The Value of ($$\sqrt {6} $$ + $$\sqrt {10} $$ - $$\sqrt {21} $$ - $$\sqrt {35} $$) × ($$\sqrt {6} $$ - $$\sqrt {10} $$ + $$\sqrt {21}$$ - $$\sqrt {35} $$) = ?
Q.4
If a - b = 3 and a2 + b2 = 29, find the value of ab = ?
Q.5
What is the value of $$\frac{{\sqrt {24} + \sqrt {216} }}{{\sqrt {96} }} = ?$$
Q.6
A body of 7300 troops is formed of 4 battalions so that $$\frac{1}{2}$$ of the first, $$\frac{2}{3}$$ of the second, $$\frac{3}{4}$$ of the third and $$\frac{4}{5}$$ of the fourth are all composed of the same number of men. How many men are there in the second battalion?
Q.7
$${\text{If }}\left[ {4 - \frac{5}{{1 + \frac{1}{{3 + \frac{1}{{2 + \frac{1}{4}}}}}}}} \right]$$    part of a journey takes ten minutes, then to complete $$\frac{3}{5}$$th of that journey, it will take = ?
Q.8
A teacher wants to arrange his students in an equal number of rows and columns. If there are 1369 students, the number of students in the last row are ?
Q.9
The value of $$\frac{{{{\left( {x - y} \right)}^3} + {{\left( {y - z} \right)}^3} + {{\left( {z - x} \right)}^3}}}{{{{\left( {{x^2} - {y^2}} \right)}^3} + {{\left( {{y^2} - {z^2}} \right)}^3} + {{\left( {{z^2} - {x^2}} \right)}^3}}}$$       is = ?
Q.10
$${\text{If }}\left( {{n^r} - tn + \frac{1}{4}} \right)$$     be a perfect square, then the values of t are = ?
Q.11
The number of pairs of natural numbers the difference of whose squares is 45 will be ?
Q.12
If $$\root 3 \of {{3^n}} {\text{ = 27,}}$$   then the value of n is = ?
Q.13
Simplify : $$\sqrt {3 + \frac{{33}}{{64}}} \div $$   $$\sqrt {9 + \frac{1}{7}} \times $$   $$2\sqrt {3\frac{1}{9}} $$   = ?
Q.14
$$\frac{{{{\left( {3\frac{2}{3}} \right)}^2} - {{\left( {2\frac{1}{2}} \right)}^2}}}{{{{\left( {4\frac{3}{4}} \right)}^2} - {{\left( {3\frac{1}{3}} \right)}^2}}}$$   $$ \div $$ $$\frac{{3\frac{2}{3} - 2\frac{1}{2}}}{{4\frac{3}{4} - 3\frac{1}{3}}}$$   = ?
Q.15
$$\sqrt {\frac{{4\frac{1}{7} - 2\frac{1}{4}}}{{3\frac{1}{2} + 1\frac{1}{7}}} \div \frac{1}{{2 + \frac{1}{{2 + \frac{1}{{5 - \frac{1}{5}}}}}}}} $$     is equal to = ?
Q.16
The cost of 5 pendants and 8 chains is Rs. 145785. What would be the cost of 15 pendants and 24 chains ?
Q.17
$$\frac{1}{{1 + {2^{a - b}}}} + \frac{1}{{1 + {2^{b - a}}}}$$     is equal to = ?
Q.18
The value of $${\text{3}}\frac{1}{2} - $$ $$\left[ {2\frac{1}{4} \div \left\{ {1\frac{1}{4} - \frac{1}{2}\left( {1\frac{1}{2} - \frac{1}{3} - \frac{1}{6}} \right)} \right\}} \right]$$       = ?
Q.19
If x = a + m, y = b + m, z = c + m, then the value of $$\frac{{{x^2} + {y^2} + {z^2} - yz - zx - xy}}{{{a^2} + {b^2} + {c^2} - ab - bc - ca}}$$       is = ?
Q.20
$$\left( {\frac{{785 \times 785 \times 785 + 435 \times 435 \times 435}}{{785 \times 785 + 435 \times 435 - 785 \times 435}}} \right)$$       simplifies to = ?
Q.21
The lowest temperature in the night in a city is one third more than $$\frac{1}{2}$$ the highest during the day. Sum of the lowest temperature and the highest temperature is 100 degrees. Then what is the lowest temperature?
Q.22
A millionaire bought a lot of hats $$\frac{1}{4}$$ of which were brown. The millionaire sold $$\frac{2}{3}$$ of the including $$\frac{4}{5}$$ of the brown hats. What fraction of the unsold hats were brown ?
Q.23
The simplified value of $$\frac{{\left( {1 + \frac{1}{{1 + \frac{1}{{100}}}}} \right)\left( {1 + \frac{1}{{1 + \frac{1}{{100}}}}} \right) - \left( {1 - \frac{1}{{1 + \frac{1}{{100}}}}} \right)\left( {1 - \frac{1}{{1 + \frac{1}{{100}}}}} \right)}}{{\left( {1 + \frac{1}{{1 + \frac{1}{{100}}}}} \right) + \left( {1 - \frac{1}{{1 + \frac{1}{{100}}}}} \right)}} = ?$$
Q.24
The simplification of $$\left( {\frac{{75983 \times 75983 - 45983 \times 45983}}{{30000}}} \right)$$       yields the result = ?
Q.25
The value of $${\text{5}}\frac{1}{3} \div 1\frac{2}{9} \times \frac{1}{4}$$   $$\left( {10 + \frac{3}{{1 - \frac{1}{5}}}} \right)$$ &nbsp = ?
Q.26
What is $$\frac{{\frac{7}{8} \times \frac{7}{8} + \frac{5}{6} \times \frac{5}{6} + \frac{7}{8} \times \frac{5}{3}}}{{\frac{7}{8} \times \frac{7}{8} - \frac{5}{6} \times \frac{5}{6}}}$$     equal to ?
Q.27
$$\frac{{{{\left( {469 + 174} \right)}^2} - {{\left( {469 - 174} \right)}^2}}}{{469 \times 174}} $$      = ?
0 h : 0 m : 1 s