JEE Main 2021 (Online) 20th July Morning Shift | Quadratic Equation and Inequalities Question 82 | Mathematics

If $$\alpha$$ and $$\beta$$ are the distinct roots of the equation $${x^2} + {(3)^{1/4}}x + {3^{1/2}} = 0$$, then the value of $${\alpha ^{96}}({\alpha ^{12}} - 1) + {\beta ^{96}}({\beta ^{12}} - 1)$$ is equal to :

56 $$\times$$ 3²⁵

56 $$\times$$ 3²⁴

52 $$\times$$ 3²⁴

28 $$\times$$ 3²⁵

JEE Main 2021 (Online) 18th March Morning Shift

MCQ (Single Correct Answer)

-1

The value of $$3 + {1 \over {4 + {1 \over {3 + {1 \over {4 + {1 \over {3 + ....\infty }}}}}}}}$$ is equal to

1.5 + $$\sqrt 3 $$

2 + $$\sqrt 3 $$

3 + 2$$\sqrt 3 $$

4 + $$\sqrt 3 $$

JEE Main 2021 (Online) 17th March Morning Shift

MCQ (Single Correct Answer)

-1

The value of $$4 + {1 \over {5 + {1 \over {4 + {1 \over {5 + {1 \over {4 + ......\infty }}}}}}}}$$ is :

2 + $${2 \over 5}\sqrt {30} $$

2 + $${4 \over {\sqrt 5 }}\sqrt {30} $$

5 + $${2 \over 5}\sqrt {30} $$

4 + $${4 \over {\sqrt 5 }}\sqrt {30} $$

JEE Main 2021 (Online) 25th February Evening Shift

MCQ (Single Correct Answer)

-1

Let $$\alpha$$ and $$\beta$$ be the roots of x² $$-$$ 6x $$-$$ 2 = 0. If a_n = $$\alpha$$ⁿ $$-$$ $$\beta$$ⁿ for n $$ \ge $$ 1, then the value of $${{{a_{10}} - 2{a_8}} \over {3{a_9}}}$$ is :