Q.1
If a + b + c = 9 (where a, b, c are real numbers) then the minimum value of a2 + b2 + c2 is?
Q.2
If a2 + b2 + 4c2 = 2(a + b - 2c) - 3 and a, b, c are real, then the value of (a2 + b2 + c2) is?
Q.3
If (x - a)(x - b) = 1 and a - b + 5 = 0, then the value of $${\left( {x - a} \right)^3}$$   - $$\frac{1}{{{{\left( {x - a} \right)}^3}}}\,{\text{}}$$  is?
Q.4
If x2 - 3x + 1 = 0, then the value of $${x^2} + x + \frac{1}{x} + \frac{1}{{{x^2}}}$$    is?
Q.5
If a2 + b2 = 5ab, then the value of $$\left( {\frac{{{a^2}}}{{{b^2}}}{\text{ + }}\frac{{{b^2}}}{{{a^2}}}} \right)$$   is?
Q.6
If $$x = \frac{{\sqrt 5 + 1}}{{\sqrt 5 - 1}}$$   and $${\text{y}} = \frac{{\sqrt 5 - 1}}{{\sqrt 5 + 1}}{\text{,}}$$   then the value of $$\frac{{{x^2} + xy + {y^2}}}{{{x^2} - xy + {y^2}}}$$   is?
Q.7
If x4 + 2x3 + ax2 + bx + 9 is a perfect square where a and b are positive real numbers, then the value of a and b is?
Q.8
If $${x^2} + \frac{1}{5}x + {a^2}$$   is a perfect square, then a is?
Q.9
If (x - 1) and (x + 3) are the factors of x2 + k1x + k2 then-
Q.10
If $$\frac{{x - {a^2}}}{{b + c}}$$   + $$\frac{{x - {b^2}}}{{c + a}}$$   + $$\frac{{x - {c^2}}}{{a + b}}$$   = 4(a + b + c), then x = ?
Q.11
If $$\frac{a}{b} = \frac{4}{5}$$   and $$\frac{b}{c} = \frac{{15}}{{16}}{\text{,}}$$   then $$\frac{{18{c^2} - 7{a^2}}}{{45{c^2} + 20{a^2}}}$$   is equal to?
Q.12
If $$x + \frac{1}{x} \ne 0$$   and $${x^3} + \frac{1}{{{x^3}}} = 0{\text{,}}$$   then the value $${\left( {x + \frac{1}{x}} \right)^4}$$   is?
Q.13
If $$x + \frac{1}{x} = 2$$   then $${x^2} + \frac{1}{{{x^2}}}$$   is equal to?
Q.14
If $${\left( {{\text{ }}a + \frac{1}{a}} \right)^2} = 3{\text{,}}$$    then the value of a18 + a12 + a6 + 1 is?
Q.15
If xy + yz + zx = 0, then $$\left( {\frac{1}{{{x^2} - yz}} + \frac{1}{{{y^2} - zx}} + \frac{1}{{{z^2} - xy}}} \right)$$       $$\left( {x,y,z \ne 0} \right) = ?$$
Q.16
When a number x is divided by a divisor it is seen that the divisor = 4 times the quotient = double of remainder. If the remainder is 80, then the value of x is?
Q.17
If a2 + b2 + c2 = 16, x2 + y2 + z2 = 25 and ax + by + cz = 20 then the value of $$\frac{{a + b + c}}{{x + y + z}}$$   = ?
Q.18
If $$\frac{{5x}}{{2{x^2} + 5x + 1}} = \frac{1}{3},$$     then the value of $$\left( {x + \frac{1}{{2x}}} \right) = \,?$$
Q.19
If $$x \ne 0,$$   $$y \ne 0$$   and $$z \ne 0$$   and $$\frac{1}{{{x^2}}}$$  + $$\frac{1}{{{y^2}}}$$  + $$\frac{1}{{{z^2}}}$$  = $$\frac{1}{{xy}}$$  + $$\frac{1}{{yz}}$$  + $$\frac{1}{{zx}}$$  then the relation among x, y, z is?
Q.20
If a = 2, b = -3, then the value of 27a3 - 54a2b + 36ab2 - 8b3 is?
Q.21
If $${a^3} + \frac{1}{{{a^3}}} = 2{\text{,}}$$   then the value of $$\frac{{{a^2} + 1}}{a}$$  is (a positive number) ?
Q.22
If $${x^2} + {y^2} = 29$$   and xy = 10 where x > 0, y > 0, x > y, then the value of $$\frac{{x + y}}{{x - y}}$$   is?
Q.23
If $${p^2} + {q^2} = 7pq{\text{,}}$$    then the value of $$\frac{p}{q}{\text{ + }}\frac{q}{p}$$   is equal to?
Q.24
If $$2x + \frac{2}{{9x}} = 4{\text{,}}$$   then the value of $$27{x^3} + \frac{1}{{27{x^3}}}$$   is?
Q.25
If $$\frac{{{\text{ }}{x^2} + 1}}{{{x^2}}} = 2{\text{,}}$$   then the value of $$\frac{{x - 1}}{x}$$  is?
Q.26
If x + y = √3 and x - y = √2, then the value of 8xy(x2 + y2) is?
Q.27
If $$\left( {x + \frac{1}{x}} \right)$$   : $$\left( {x - \frac{1}{x}} \right)$$  = 5 : 3 the value of x is/are ?
Q.28
If p = 99, then the value of p(p2 + 3p + 3) is?
Q.29
If $$\frac{1}{p} + \frac{1}{q}$$  = $$\frac{1}{{p + q}}{\text{,}}$$   then the value of p3 - q3 is?
Q.30
If ab = 21 and $$\frac{{{{\left( {a + b} \right)}^2}}}{{{{\left( {a - b} \right)}^2}}}$$   = $$\frac{{25}}{4}{\text{,}}$$  then the value of a2 + b2 + 3ab is?
0 h : 0 m : 1 s