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1
JEE Main 2021 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
If [x] be the greatest integer less than or equal to x,

then $$\sum\limits_{n = 8}^{100} {\left[ {{{{{( - 1)}^n}n} \over 2}} \right]} $$ is equal to :
A
0
B
4
C
$$-$$2
D
2
2
JEE Main 2021 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
The number of real solutions of the equation, x2 $$-$$ |x| $$-$$ 12 = 0 is :
A
2
B
3
C
1
D
4
3
JEE Main 2021 (Online) 25th July Morning Shift
MCQ (Single Correct Answer)
+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
4
JEE Main 2021 (Online) 22th July Evening Shift
MCQ (Single Correct Answer)
+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)
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