1
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
$$\left( {{1 \over 2},{3 \over 2}} \right] - \{ 1\}$$
2
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
3
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
Let $$\alpha$$, $$\beta$$ be two roots of the

equation x2 + (20)1/4x + (5)1/2 = 0. Then $$\alpha$$8 + $$\beta$$8 is equal to
A
10
B
100
C
50
D
160
4
JEE Main 2021 (Online) 25th July Evening Shift
+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
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