Q.1
If $$\frac{{m - 3{a^3}}}{{{b^3} + {c^3}}}$$  $$+$$ $$\frac{{m - 3{b^3}}}{{{c^3} + {a^3}}}$$  $$+$$ $$\frac{{m - 3{c^3}}}{{{a^3} + {b^3}}}$$   = 9, then the value of m is?
Q.2
If $$a + \frac{1}{a} + 1 = 0\left( {a \ne 0} \right){\text{,}}$$     then the value of $$\left( {{a^4} - a} \right)\,{\text{is?}}$$
Q.3
$$\frac{{\frac{1}{3}.\frac{1}{3}.\frac{1}{3} + \frac{1}{4}.\frac{1}{4}.\frac{1}{4} - 3.\frac{1}{3}.\frac{1}{4}.\frac{1}{5} + \frac{1}{5}.\frac{1}{5}.\frac{1}{5}}}{{\frac{1}{3}.\frac{1}{3} + \frac{1}{4}.\frac{1}{4} + \frac{1}{5}.\frac{1}{5} - \left( {\frac{1}{3}.\frac{1}{4} + \frac{1}{4}.\frac{1}{5} + \frac{1}{5}.\frac{1}{3}} \right)}}{\text{ is?}}$$
Q.4
If 0.13 × p2 = 13, then p is equal to?
Q.5
If (125)x = 3125, then the value of x is?
Q.6
If a2x+2 = 1, where is a positive real number other than 1, then x is equal to?
Q.7
If $${\left( {a + \frac{1}{a}} \right)^2} = 3{\text{,}}$$    then find the value of $${a^{30}}$$ + $${a^{24}}$$ + $${a^{18}}$$ + $${a^{12}}$$ + $${a^6}$$ + $$1$$ = ?
Q.8
If $$\left( {\sqrt a + \sqrt b } \right)$$   = 15 and $$\left( {\sqrt a - \sqrt b } \right)$$   = 3, then the value of $$\frac{{\sqrt {ab} }}{4}$$  is?
Q.9
If $$a + \frac{1}{a} = 3,$$   then the value of $${a^3} + \frac{1}{{{a^3}}}$$  is?
Q.10
If α and β are the roots of equation x2 + αx + β = 0 then find α3 + β3 = ?
Q.11
If a2 = b + c, b2 = a + c, c2 = b + a, then what will be the value of $$\frac{1}{{a + 1}}$$  + $$\frac{1}{{b + 1}}$$  + $$\frac{1}{{c + 1}}$$ ?
Q.12
If $$x = 7 - 4\sqrt 3 {\text{,}}$$    then $$\sqrt x {\text{ + }}\frac{1}{{\sqrt x }}$$   is equal to?
Q.13
If x : y = 3 : 4, then (7x + 3y) : (7x - 3y) is equal to?
Q.14
For what value (s) of a is $$x + \frac{1}{4}\sqrt x + {a^2}$$    a perfect square?
Q.15
If x : y = 3 : 5 and x - y = -2, then the value of x + y is?
Q.16
If x = 1 + $$\sqrt 2 $$  + $$\sqrt 3 $$  and y = 1 + $$\sqrt 2 $$  - $$\sqrt 3 {\text{,}}$$  then the value of $$\frac{{{x^2} + 4xy + {y^2}}}{{x + y}}$$   is?
Q.17
If $$x + \frac{1}{x} = 3{\text{,}}$$   where $$x \ne 0{\text{,}}$$  then the value of $$\frac{{{x^4} + 3{x^3} + 5{x^2} + 3x + 1}}{{{x^4} + 1}}$$     = ?
Q.18
If $$x = \sqrt {a\root 3 \of {ab\sqrt {a\root 3 \of {ab} } } } .... \propto $$      then the value of x is?
Q.19
If $${x^2} + \frac{1}{{{x^2}}} = 1{\text{,}}$$   then the value of $${x^{102}}$$ $$ + $$ $${x^{96}}$$ $$ + $$ $${x^{90}}$$ $$ + $$ $${x^{84}}$$ $$ + $$ $${x^{78}}$$ $$ + $$ $${x^{72}}$$ $$ + $$ $$5$$ is?
Q.20
Find the value of a and b if (x - 1) and (x + 1) are factors of x4 + ax3 - 3x2 + 2x + b = ?
Q.21
If $$a + b = 2c,$$   find $$\frac{a}{{a - c}}$$  + $$\frac{c}{{b - c}}$$   = ?
Q.22
If $$\frac{a}{b} = \frac{1}{2},$$   find the value of the expression $$\frac{{\left( {2a - 5b} \right)}}{{\left( {5a + 3b} \right)}}$$   = ?
Q.23
The simplified value of following is: $$\left( {\frac{3}{{15}}{a^5}{b^6}{c^3} \times \frac{5}{9}a{b^5}{c^4}} \right)$$     $$ ÷ $$ $$\frac{{10}}{{27}}{a^2}b{c^3}$$
Q.24
If x = 5, then the value of the expression $${x^2} - 2 + \frac{1}{{{x^2}}}$$   is?
Q.25
If $$\frac{x}{y}{\text{ = }}\frac{{a + 2}}{{a - 2}}{\text{,}}$$   then the value of $$\frac{{{x^2} - {y^2}}}{{{x^2} + {y^2}}}$$   = ?
Q.26
If p(x + y)2 = 5 and q(x - y)2 = 3, then the simplified value of p2(x + y)2 + 4pqxy - q2(x - y)2 is?
Q.27
If x + y + z = 6 and xy + yz + zx = 10, then the value of x3 + y3 + z3 - 3xyz is?
Q.28
If $$\frac{{x + 1}}{{x - 1}} = \frac{a}{b}$$   and $$\frac{{1 - y}}{{1 + y}} = \frac{b}{a}{\text{,}}$$   then the value of $$\frac{{x - y}}{{1 + xy}}$$   is?
Q.29
If 999x + 888y = 1332 and 888x + 999y = 555, then the value of x + y is?
Q.30
If a2 + b2 + c2 = ab + bc + ca, then the value of $$\frac{{a + c}}{b}$$  is?
0 h : 0 m : 1 s