Q.1
Find the minimum value of x which the expression x3 - 7x2 + 11x - 5 ≥ 0.
Q.2
If a + b + c = 26 and ab + bc + ca = 109, find the value of a2 + b2 + c2 = ?
Q.3
If for a non - zero x, 3x2 + 5x + 3 = 0, then the value of $${x^3} + \frac{1}{{{x^3}}}$$   is?
Q.4
If $$x - \frac{1}{x} = 2{\text{,}}$$   then the value of the following is $${x^3} - \frac{1}{{{x^3}}}$$   = ?
Q.5
If $$a = \frac{{\sqrt 3 - \sqrt 2 }}{{\sqrt 3 + \sqrt 2 }}$$    and $$b = \frac{{\sqrt 3 + \sqrt 2 }}{{\sqrt 3 - \sqrt 2 }}{\text{,}}$$    then the value of $$\frac{{{a^2}}}{b}$$  + $$\frac{{{b^2}}}{a}$$  = ?
Q.6
If $$\frac{a}{b} = \frac{{25}}{6}{\text{,}}$$   then the value of $$\frac{{{a^2} - {b^2}}}{{{a^2} + {b^2}}}$$   is?
Q.7
If 2, 0 is a solution of the linear equation 2x + 3y = k, then the value of k is?
Q.8
If x = 2, y = 1 and z = -3, then x3 + y3 + z3 - 3xyz is equal to?
Q.9
The sum of $$\frac{1}{{x + y}}$$  and $$\frac{1}{{x - y}}$$  is?
Q.10
If x + y = 2a, then the value of $$\frac{a}{{x - a}}$$  $$ + $$ $$\frac{a}{{y - a}}$$  is?
Q.11
If x(x + y + z) = 20, y = (x + y + z) = 30 & z(x + y + z) = 50, then the value of 2(x + y + z) is?
Q.12
If a2 + b2 + c2 = 2(a - b - c) -3, then the value of a + b + c is?
Q.13
If x + y = 4, x2 + y2 = 14 and x > y. Then the correct value of x and y is?
Q.14
If a2 + b2 + c2 - ab - bc - ca = 0 then a : b : c is?
Q.15
If a + b = 1, find the value of a3 + b3 - ab - (a2 - b2)2 = ?
Q.16
If x = z = 225 and y = 226, then the value of x3 + y3 + z3 - 3xyz = ?
Q.17
If $${x^2} + x = 5{\text{,}}$$   then the value of $${\left( {x + 3} \right)^3} + \frac{1}{{{{\left( {x + 3} \right)}^3}}} = ?$$
Q.18
If $${\text{ }}x - \sqrt 3 - \sqrt 2 = 0$$    and $$y - \sqrt 3 + \sqrt 2 {\text{,}}$$    then the value of $$\left( {{x^3} - 20\sqrt 2 } \right) - $$   $$\left( {{y^3} + 2\sqrt 2 } \right)?$$
Q.19
3(a2 + b2 + c2) = (a + b + c)2 then the relation between a, b and c is ?
Q.20
$$\frac{{m - {a^2}}}{{{b^2} + {c^2}}}$$   + $$\frac{{m - {b^2}}}{{{c^2} + {a^2}}}$$   + $$\frac{{m - {c^2}}}{{{a^2} + {b^2}}}$$   = 3, then the value of m is?
Q.21
If m - 5n = 2, then the value of (m3 - 125n3 - 30mn) is?
Q.22
The minimum value of (x - 2)(x - 9) is?
Q.23
If $$\sqrt x = \sqrt 3 - \sqrt 5 {\text{,}}$$    then the value of x2 - 16x + 6 is?
Q.24
If $$x + \frac{1}{x} = 1{\text{,}}$$   then the value of $$\frac{{{x^2} + 3x + 1}}{{{x^2} + 7x + 1}}$$   is?
Q.25
If x = a(b - c), y = b(c - a), z = c(a - b), then the value of $${\left( {\frac{x}{a}} \right)^3}$$  + $${\left( {\frac{y}{b}} \right)^3}$$  + $${\left( {\frac{z}{c}} \right)^3}$$   is?
Q.26
If $$a - \frac{1}{{a - 3}} = 5{\text{,}}$$   then the value of $${\left( {a - 3} \right)^3}$$   - $$\frac{1}{{{{\left( {a - 3} \right)}^3}}} = ?$$
Q.27
(3x - 2y) : (2x + 3y) = 5 : 6, then one of the value of $${\left( {\frac{{\root 3 \of x + \root 3 \of y }}{{\root 3 \of x - \root 3 \of y }}} \right)^2}$$   is?
Q.28
If m = -4, n = -2,then the value of m3 - 3m2 + 3m + 3n + 3n2 + n3 is?
Q.29
If x = 332, y = 333, z = 335, then the value of x3 + y3 + z3 - 3xyz is?
Q.30
If $$m = \sqrt {5 + \sqrt {5 + \sqrt {5.....} } } $$      and $$n = \sqrt {5 - \sqrt {5 - \sqrt {5.....} } } $$      then among the following the relation between m & n holds is?
0 h : 0 m : 1 s