JEE Main 2021 (Online) 22th July Evening Shift | Quadratic Equation and Inequalities Question 76 | Mathematics

Let [x] denote the greatest integer less than or equal to x. Then, the values of x$$\in$$R satisfying the equation $${[{e^x}]^2} + [{e^x} + 1] - 3 = 0$$ lie in the interval :

$$\left[ {0,{1 \over e}} \right)$$

[log_e2, log_e3)

[1, e)

[0, log_e2)

JEE Main 2021 (Online) 20th July Morning Shift

MCQ (Single Correct Answer)

-1

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 + $$\sqrt 3 $$