Q.1
If $$\left( {2 + \sqrt 3 } \right)a$$   = $$\left( {2 - \sqrt 3 } \right)b$$   = 1 then the value of $$\frac{1}{a}$$ + $$\frac{1}{b}$$ is?
Q.2
If $$a + \frac{1}{b}$$  = $$b + \frac{1}{c}$$  = $$c + \frac{1}{a}$$ $$\left( {a \ne b \ne c} \right)$$   then the value of abc is?
Q.3
For what value of k the expression $$p + \frac{1}{4} + \sqrt p + {k^2}$$     is perfect square?
Q.4
If $$\frac{{b - c}}{a}$$  + $$\frac{{a + c}}{b}$$  + $$\frac{{a - b}}{c}$$  = 1 and a - b + c ≠ 0 then which one of the following relations is true ?
Q.5
The reciprocal of $$x + \frac{1}{x}$$  is?
Q.6
If $$x + \frac{1}{x} = 2{\text{,}}$$   then the value of $$\left( {{x^2} + \frac{1}{{{x^2}}}} \right)\left( {{x^3} + \frac{1}{{{x^3}}}} \right)$$     is?
Q.7
If the equation 2x2 - 7x + 12 = 0 has two roots $$\alpha$$ and $$\beta$$, then the value of $$\frac{\alpha }{\beta }{\text{ + }}\frac{\beta }{\alpha }\,{\text{is?}}$$
Q.8
If $$\frac{1}{{\root 3 \of 4 + \root 3 \of 2 + 1}}$$    = $$a\root 3 \of 4 $$  + $$b\root 3 \of 2 $$  + c and a, b, c are rational numbers then a + b + c is equal to?
Q.9
If $$x = \root 3 \of {2 + \sqrt 3 } {\text{,}}$$    then the value of $${x^3}{\text{ + }}\frac{1}{{{x^3}}}$$   is?
Q.10
The simplest form of the expression $$\frac{{{p^2} - p}}{{2{p^3} + {p^2}}}$$   + $$\frac{{{p^2} - 1}}{{{p^2} + 3p}}$$   + $$\frac{{{p^2}}}{{p + 1}}$$ &nbsp = ?
Q.11
If $$\frac{x}{y} = \frac{4}{5}{\text{,}}$$   then the value of $$\left( {\frac{4}{7} + \frac{{2y - x}}{{2y + x}}} \right)$$   is?
Q.12
If a + b = 12, ab = 22, then (a2 + b2) is equal to?
Q.13
If $$2x + \frac{2}{x} = 3{\text{,}}$$   then the value of $${x^3} + \frac{1}{{{x^3}}} + 2$$   is?
Q.14
If a + b + c = 15 and a2 + b2 + c2 = 83 then the value of a3 + b3 + c3 - 3abc = ?
Q.15
If $$x > 1$$  and $${x^2} + \frac{1}{{{x^2}}} = 83,$$   then the $${x^3} - \frac{1}{{{x^3}}}\,{\text{is?}}$$
Q.16
If a, b, c are positive and a + b + c = 1, then the least value of $$\frac{1}{a}$$  + $$\frac{1}{b}$$  + $$\frac{1}{c}$$ is?
Q.17
If $${x^3} + \frac{3}{x}$$   = $$4\left( {{a^3} + {b^3}} \right)$$   and $$3x + \frac{1}{{{x^3}}}$$   = $$4\left( {{a^3} - {b^3}} \right){\text{,}}$$   then a2 - b2 is equal to?
Q.18
The term to be added to 121a2 + 64b2 to make a perfect square is?
Q.19
If $$x + \frac{1}{{x + 1}} = 1,$$    then $${\left( {x + 1} \right)^5}$$   + $$\frac{1}{{{{\left( {x + 1} \right)}^5}}}$$   equals?
Q.20
If a + b + c = 0, then a3 + b3 + c3 is equal to?
Q.21
If x = y = 333 and z = 334, then the value of x3 + y3 + z3 - 3xyz is?
Q.22
If $${\left( {a + \frac{1}{a}} \right)^2}\, = 3$$    then $${a^3} + \frac{1}{{{a^3}}} = ?$$
Q.23
If x + y + z = 6 and x2 + y2 + z2 = 20, then the value of x3 + y3 + z3 - 3xyz is?
Q.24
If x = a - b, y = b - c, z = c - a, then the numerical value of the algebraic expression x3 + y3 + z3 - 3xyz will be?
Q.25
If $$x = 3 + 2\sqrt 2 {\text{,}}$$   then the value of $${x^2}{\text{ + }}\frac{1}{{{x^2}}}{\text{ is?}}$$
Q.26
If $$x\left( {3 - \frac{2}{x}} \right) = \frac{3}{x}{\text{,}}$$    then the value of $${x^2}{\text{ + }}\frac{1}{{{x^2}}}$$   is?
Q.27
The simplified value of $$\left( {1 - \frac{{2xy}}{{{x^2} + {y^2}}}} \right)$$   $$ ÷ $$ $$\left( {\frac{{{x^3} - {y^3}}}{{x - y}} - 3xy} \right)$$    is?
Q.28
If x2 + y2 + 2x +1 = 0, then the value of x31 + y35 is?
Q.29
If a + b = 1, c + d = 1 and a - b = $$\frac{d}{c}{\text{,}}$$  then the value of c2 - d2 = ?
Q.30
If x = 3t, y = $$\frac{1}{2}$$(t + 1), then the value of t for which x = 2y is?
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