1
JEE Main 2020 (Online) 4th September Morning Slot
+4
-1
Let [t] denote the greatest integer $$\le$$ t. Then the equation in x,
[x]2 + 2[x+2] - 7 = 0 has :
A
no integral solution.
B
exactly two solutions.
C
exactly four integral solutions.
D
infinitely many solutions.
2
JEE Main 2020 (Online) 4th September Morning Slot
+4
-1
Let $$\alpha$$ and $$\beta$$ be the roots of x2 - 3x + p=0 and $$\gamma$$ and $$\delta$$ be the roots of x2 - 6x + q = 0. If $$\alpha, \beta, \gamma, \delta$$ form a geometric progression.Then ratio (2q + p) : (2q - p) is:
A
9 : 7
B
5 : 3
C
3 : 1
D
33 :31
3
JEE Main 2020 (Online) 3rd September Evening Slot
+4
-1
The set of all real values of $$\lambda$$ for which the quadratic equations,
($$\lambda$$2 + 1)x2 – 4$$\lambda$$x + 2 = 0 always have exactly one root in the interval (0, 1) is :
A
(–3, –1)
B
(2, 4]
C
(0, 2)
D
(1, 3]
4
JEE Main 2020 (Online) 3rd September Morning Slot
+4
-1
If $$\alpha$$ and $$\beta$$ are the roots of the equation
x2 + px + 2 = 0 and $${1 \over \alpha }$$ and $${1 \over \beta }$$ are the
roots of the equation 2x2 + 2qx + 1 = 0, then
$$\left( {\alpha - {1 \over \alpha }} \right)\left( {\beta - {1 \over \beta }} \right)\left( {\alpha + {1 \over \beta }} \right)\left( {\beta + {1 \over \alpha }} \right)$$ is equal to :
A
$${9 \over 4}\left( {9 - {q^2}} \right)$$
B
$${9 \over 4}\left( {9 + {q^2}} \right)$$
C
$${9 \over 4}\left( {9 - {p^2}} \right)$$
D
$${9 \over 4}\left( {9 + {p^2}} \right)$$
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