61. If $${\left( {a + \frac{1}{a}} \right)^2} = 3{\text{,}}$$ then find the value of $${a^{30}}$$ + $${a^{24}}$$ + $${a^{18}}$$ + $${a^{12}}$$ + $${a^6}$$ + $$1$$ = ?
62. If x : y = 3 : 5 and x - y = -2, then the value of x + y is?
63. If x = 1 + $$\sqrt 2 $$ + $$\sqrt 3 $$ and y = 1 + $$\sqrt 2 $$ - $$\sqrt 3 {\text{,}}$$ then the value of $$\frac{{{x^2} + 4xy + {y^2}}}{{x + y}}$$ is?
64. If $$x + \frac{1}{x} = 3{\text{,}}$$ where $$x \ne 0{\text{,}}$$ then the value of $$\frac{{{x^4} + 3{x^3} + 5{x^2} + 3x + 1}}{{{x^4} + 1}}$$ = ?
65. If p(x + y)2 = 5 and q(x - y)2 = 3, then the simplified value of p2(x + y)2 + 4pqxy - q2(x - y)2 is?
66. If α and β are the roots of equation x2 + αx + β = 0 then find α3 + β3 = ?
67. If $${x^2} + \frac{1}{{{x^2}}} = 1{\text{,}}$$ then the value of $${x^{102}}$$ $$ + $$ $${x^{96}}$$ $$ + $$ $${x^{90}}$$ $$ + $$ $${x^{84}}$$ $$ + $$ $${x^{78}}$$ $$ + $$ $${x^{72}}$$ $$ + $$ $$5$$ is?
68. Find the value of a and b if (x - 1) and (x + 1) are factors of x4 + ax3 - 3x2 + 2x + b = ?
69. Find the minimum value of x which the expression x3 - 7x2 + 11x - 5 ≥ 0.
70. If a + b + c = 26 and ab + bc + ca = 109, find the value of a2 + b2 + c2 = ?
Read More Section(Algebra)
Each Section contains maximum 100 MCQs question on Algebra. To get more questions visit other sections.