1
JEE Main 2021 (Online) 31st August Evening Shift
+4
-1
The sum of the roots of the equation

$$x + 1 - 2{\log _2}(3 + {2^x}) + 2{\log _4}(10 - {2^{ - x}}) = 0$$, is :
A
log2 14
B
log2 11
C
log2 12
D
log2 13
2
JEE Main 2021 (Online) 31st August Morning Shift
+4
-1
cosec18$$^\circ$$ is a root of the equation :
A
x2 + 2x $$-$$ 4 = 0
B
4x2 + 2x $$-$$ 1 = 0
C
x2 $$-$$ 2x + 4 = 0
D
x2 $$-$$ 2x $$-$$ 4 = 0
3
JEE Main 2021 (Online) 27th August Evening Shift
+4
-1
The set of all values of K > $$-$$1, for which the equation $${(3{x^2} + 4x + 3)^2} - (k + 1)(3{x^2} + 4x + 3)(3{x^2} + 4x + 2) + k{(3{x^2} + 4x + 2)^2} = 0$$ has real roots, is :
A
$$\left( {1,{5 \over 2}} \right]$$
B
[2, 3)
C
$$\left[ { - {1 \over 2},1} \right)$$
D
$$\left( {{1 \over 2},{3 \over 2}} \right] - \{ 1\}$$
4
JEE Main 2021 (Online) 27th July Evening Shift
+4
-1
Let $$\alpha = \mathop {\max }\limits_{x \in R} \{ {8^{2\sin 3x}}{.4^{4\cos 3x}}\}$$ and $$\beta = \mathop {\min }\limits_{x \in R} \{ {8^{2\sin 3x}}{.4^{4\cos 3x}}\}$$. If $$8{x^2} + bx + c = 0$$ is a quadratic equation whose roots are $$\alpha$$1/5 and $$\beta$$1/5, then the value of c $$-$$ b is equal to :
A
42
B
47
C
43
D
50
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