Q.1
If 2s = a + b + c, then the value of s(s - c) + (s - a) (s - b) is?
Q.2
If $$x + \frac{1}{x} = 2{\text{,}}$$   then the value of $${x^{12}} - \frac{1}{{{x^{12}}}}$$   is?
Q.3
If $$\frac{{144}}{{0.144}} = \frac{{14.4}}{x}{\text{,}}$$    then the value of x is?
Q.4
If x2 = y + z, y2 = z + x, z2 = x + y, then the value of $$\frac{1}{{x + 1}}$$   + $$\frac{1}{{y + 1}}$$   + $$\frac{1}{{z + 1}} = \,?$$
Q.5
If a + b + c = 0, then the value of $$\left( {\frac{{a + b}}{c} + \frac{{b + c}}{a} + \frac{{c + a}}{b}} \right)$$    $$\left( {\frac{a}{{b + c}} + \frac{b}{{c + a}} + \frac{c}{{a + b}}} \right) = \,?$$
Q.6
If 5x + 9y = 5 and 125x3 + 729y3 = 120, then the value of the product of x and y is?
Q.7
If $$2 + x\sqrt 3 $$   = $$\frac{1}{{2 + \sqrt 3 }}{\text{,}}$$   then the simplest value of x is?
Q.8
When xm is multiplied by xn, product is 1. The relation between m and n is?
Q.9
If $$x + \left( {\frac{1}{x}} \right) = 2{\text{,}}$$   then the value of $${x^7}{\text{ + }}\left( {\frac{1}{{{x^5}}}} \right)$$   is?
Q.10
If $$x + \frac{1}{x} = 99{\text{,}}$$   find the value of   $$\frac{{100x}}{{2{x^2} + 2 + 102x}}$$    is?
Q.11
If $$\frac{{4x - 3}}{x}$$   + $$\frac{{4y - 3}}{y}$$   + $$\frac{{4z - 3}}{z} = 0{\text{,}}$$   then the value of $$\frac{1}{x} + \frac{1}{y} + \frac{1}{z}$$   is?
Q.12
a = $$\sqrt 6 \,$$ - $$\sqrt 5 $$ , b = $$\sqrt 5 \,$$ - 2, c = 2 - $$\sqrt 3 $$  then point out the correct alternative among the four alternatives given below ?
Q.13
If a : b = 2 : 3 and b : c = 4 : 5, find a2 : b2 : bc = ?
Q.14
If $$x = 5 - \sqrt {21} {\text{,}}$$   then the value of $$\frac{{\sqrt x }}{{\sqrt {32 - 2x} - \sqrt {21} }}$$    is?
Q.15
If $${3^{x + 3}} + 7 = 250{\text{,}}$$    then x is equal to?
Q.16
If $$\frac{1}{4} \times $$ $$\frac{2}{6} \times $$ $$\frac{3}{8} \times $$ $$\frac{4}{{10}} \times $$ $$\frac{5}{{12}} \times $$ . . . . . $$ \times \frac{{31}}{{64}}$$ $$ = \frac{1}{{{2^x}}}$$   then the value of x is?
Q.17
If a, b, c are non - zero $$a + \frac{1}{b} = 1$$   and $$b + \frac{1}{c} = 1,$$   then the value of abc is?
Q.18
x2 + y2 + z2 = 2(x + z - 1), then the value of x3 + y3 + z3 = ?
Q.19
If $$x + \frac{1}{x} = 1,$$   then the value of $$\frac{2}{{{x^2} - x + 2}} = \,?$$
Q.20
If $$x = \frac{{\sqrt 5 - \sqrt 3 }}{{\sqrt 5 + \sqrt 3 }}$$   and $$y = \frac{{\sqrt 5 + \sqrt 3 }}{{\sqrt 5 - \sqrt 3 }}$$   then the value of $$\frac{{{x^2} + xy + {y^2}}}{{{x^2} - xy + {y^2}}} = ?$$
Q.21
If a * b = 2a - 3b + ab, then 3 * 5 + 5 * 3 is equal to?
Q.22
If $$\frac{{xy}}{{x + y}} = a,$$   $$\frac{{xz}}{{x + z}} = b$$   and $$\frac{{yz}}{{y + z}} = c{\text{,}}$$   where a, b, c are all non - zero numbers, then x equals to?
Q.23
If x and y are positive real numbers and xy = 8, then the minimum value of 2x + y is?
Q.24
The value of $${\left( {{x^{b + c}}} \right)^{b - c}}$$   $$ \times $$ $${\left( {{x^{c + a}}} \right)^{c - a}}$$   $$ \times $$ $${\left( {{x^{a + b}}} \right)^{a - b}}$$ &nbsp is?
Q.25
If $$\frac{x}{a} = \frac{1}{a} - \frac{1}{x}{\text{,}}$$   then the value of x - x2 is?
Q.26
If $$x = 3 + 2\sqrt 2 {\text{,}}$$    then the value of $$\left( {\sqrt x - \frac{1}{{\sqrt x }}} \right){\text{ is?}}$$
Q.27
If p = 999, then the value of $$\root 3 \of {p\left( {{p^2} + 3p + 3} \right) + 1} {\text{ is?}}$$
Q.28
Simplified value of $$\left[ {\,\left( {1 + \frac{1}{{10 + \frac{1}{{10}}}}} \right)\,\left( {1 + \frac{1}{{10 + \frac{1}{{10}}}}} \right)\,\, - \,\,\left( {1 - \frac{1}{{10 + \frac{1}{{10}}}}} \right)\,\left( {1 - \frac{1}{{10 + \frac{1}{{10}}}}} \right)\,} \right]$$              $$ ÷ $$  $$\left[ {\,\left( {1 + \frac{1}{{10 + \frac{1}{{10}}}}} \right)\,\, + \,\,\left( {1 - \frac{1}{{10 + \frac{1}{{10}}}}} \right)\,} \right]$$       = ?
Q.29
If 1 < x < 2, then the value of $$\sqrt {{{\left( {x - 1} \right)}^2}} {\text{ + }}\sqrt {{{\left( {3 - x} \right)}^2}} {\text{ is?}}$$
Q.30
If a * b = a + b + ab, then 3 * 4 - 2 * 3 is equal to?
0 h : 0 m : 1 s