Q.1
If a2 + b2 = 2 and c2 + d2 = 1, then the value of (ad - bc)2 + (ac - bd)2 is?
Q.2
If x varies inversely as (y2 - 1) and x is equal to 24 when y = 10, then the value of x when y = 5 is?
Q.3
If x2 + y2 + 2x + 1 = 0, then the value of x31 + y35 is?
Q.4
If a = 2.361, b = 3.263, and c = 5.624, then the value of a3 + b3 - c3 + 3abc is?
Q.5
If $$x = \frac{{4ab}}{{a + b}}{\text{ }}a \ne b,$$     the value of $$\frac{{x + 2a}}{{x - 2a}}$$   + $$\frac{{x + 2b}}{{x - 2b}}$$   is?
Q.6
If $$m + \frac{1}{{m - 2}} = 4{\text{,}}$$    find the value of $${\left( {m - 2} \right)^2}{\text{ + }}\frac{1}{{{{\left( {m - 2} \right)}^2}}}$$     is?
Q.7
If a, b, c are real and a2 + b2 + c2 = 2(a - b - c) -3, then the value of 2a - 3b + 4c is?
Q.8
If (3a + 1)2 + (b - 1)2 + (2c - 3)2 = 0 then the value of (3a + b + 2c) is equal to?
Q.9
If $$\frac{p}{a}$$ + $$\frac{q}{b}$$ + $$\frac{r}{c}$$ = 1 and $$\frac{a}{p}$$ + $$\frac{b}{q}$$ + $$\frac{c}{r}$$ = 0 where p, q, r and a, b, c are non - zero, then value of $$\frac{{{p^2}}}{{{a^2}}}$$ + $$\frac{{{q^2}}}{{{b^2}}}$$ + $$\frac{{{r^2}}}{{{c^2}}}$$ = ?
Q.10
If $${x^2} + \frac{1}{{{x^2}}} = 66{\text{,}}$$    then the value of $$\frac{{{x^2} - 1 + 2x}}{x}$$   = ?
Q.11
If a2 + a + 1 = 0, then the value of a9 is?
Q.12
If x = -2k and y = 1 - 3k, then for what value of k, will be x = y?
Q.13
If $$x + \frac{1}{x} = 5{\text{,}}$$   then $${x^6}{\text{ + }}\frac{1}{{{x^6}}}$$   is?
Q.14
If $$x$$ = $$\sqrt 3 - \frac{1}{{\sqrt 3 }}$$   and $$y$$ = $$\sqrt 3 + \frac{1}{{\sqrt 3 }}$$   then the value of $$\frac{{{x^2}}}{y} + \frac{{{y^2}}}{x}$$  is?
Q.15
If a + b + c + d = 4, then find the value of $$\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)\left( {1 - c} \right)}}$$     + $$\frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)\left( {1 - d} \right)}}$$     + $$\frac{1}{{\left( {1 - c} \right)\left( {1 - d} \right)\left( {1 - a} \right)}}$$     + $$\frac{1}{{\left( {1 - d} \right)\left( {1 - a} \right)\left( {1 - b} \right)}}$$     is?
Q.16
If a2 + b2 + 2b + 4a + 5 = 0, then the value of $$\frac{{a - b}}{{a + b}}\,{\text{is?}}$$
Q.17
The value of the expression $$\frac{{{{\left( {a - b} \right)}^2}}}{{\left( {b - c} \right)\left( {c - a} \right)}} + $$   $$\frac{{{{\left( {b - c} \right)}^2}}}{{\left( {a - b} \right)\left( {c - a} \right)}} + $$    $$\frac{{{{\left( {c - a} \right)}^2}}}{{\left( {a - b} \right)\left( {b - c} \right)}}$$   = ?
Q.18
If x is a rational number and $$\frac{{{{\left( {x + 1} \right)}^3} - {{\left( {x - 1} \right)}^3}}}{{{{\left( {x + 1} \right)}^2} - {{\left( {x - 1} \right)}^2}}}$$     = 2, then the sum of numerator and denominator of x is?
Q.19
If $$x = \sqrt 5 + 2{\text{,}}$$   then the value of $$\frac{{2{x^2} - 3x - 2}}{{3{x^2} - 4x - 3}}$$   is equal to?
Q.20
If $${a^{\frac{1}{3}}} + {b^{\frac{1}{3}}} + {c^{\frac{1}{3}}} = 0,$$     then a relation among a, b, c is?
Q.21
If $$x - \frac{1}{x} = 1{\text{,}}$$   then the value of $$\frac{{{x^4} - \frac{1}{{{x^2}}}}}{{3{x^2} + 5x - 3}}$$   = ?
Q.22
If $$a\left( {2 + \sqrt 3 } \right)$$   = $$b\left( {2 - \sqrt 3 } \right)$$   = 1, then the value of $$\frac{1}{{{a^2} + 1}}$$  + $$\frac{1}{{{b^2} + 1}}$$  = ?
Q.23
If $$a = 2 + \sqrt 3 {\text{,}}$$   then the value of $$\left( {{a^2} + \frac{1}{{{a^2}}}} \right) = \,?$$
Q.24
If x2 + y2 + 1 = 2x, then the value of x3 + y5 is?
Q.25
If x(x - 3) = -1, then the value of x3(x3 - 18) is?
Q.26
If x2 - 3x + 1 = 0, then the value of $$\frac{{{x^6} + {x^4} + {x^2} + 1}}{{{x^3}}}$$     will be?
Q.27
If x + y = 15, then the value of (x - 10)3 + (y - 5)3 is?
Q.28
If $$a = \frac{{{b^2}}}{{b - a}}{\text{,}}$$   then the value of a3 + b3 is?
Q.29
The graph of 2x + 1 = 0 and 3y - 9 = 0 intersect at the point?
Q.30
If x = -1, then the value of $$\frac{1}{{{x^{99}}}}$$  + $$\frac{1}{{{x^{98}}}}$$  + $$\frac{1}{{{x^{97}}}}$$  + $$\frac{1}{{{x^{96}}}}$$  + $$\frac{1}{{{x^{95}}}}$$  + $$\frac{1}{{{x^{94}}}}$$  + $$\frac{1}{x}$$  - 1 is?
0 h : 0 m : 1 s