1
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
The number of real roots of the equation $${e^{6x}} - {e^{4x}} - 2{e^{3x}} - 12{e^{2x}} + {e^x} + 1 = 0$$ is :
A
2
B
4
C
6
D
1
2
JEE Main 2021 (Online) 22th July Evening Shift
+4
-1
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 :
A
$$\left[ {0,{1 \over e}} \right)$$
B
[loge2, loge3)
C
[1, e)
D
[0, loge2)
3
JEE Main 2021 (Online) 20th July Morning Shift
+4
-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 :
A
56 $$\times$$ 325
B
56 $$\times$$ 324
C
52 $$\times$$ 324
D
28 $$\times$$ 325
4
JEE Main 2021 (Online) 18th March Morning Shift
+4
-1
The value of $$3 + {1 \over {4 + {1 \over {3 + {1 \over {4 + {1 \over {3 + ....\infty }}}}}}}}$$ is equal to
A
1.5 + $$\sqrt 3$$
B
2 + $$\sqrt 3$$
C
3 + 2$$\sqrt 3$$
D
4 + $$\sqrt 3$$
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