Quadratic Equation JEE Main 2024 January Question Bank
Questions with Answer Keys MathonGo
Q1 - 2024 (01 Feb Shift 1)
Let S = {x ∈ R : (√3 + √2) x
+ (√3 − √2)
x
= 10} .
Then the number of elements in S is :
(1) 4
(2) 0
(3) 2
(4) 1
Q2 - 2024 (01 Feb Shift 2)
Let α and β be the roots of the equation px 2
+ qx− r = 0 , where p ≠ 0. If p, q and r be the consecutive terms
of a non-constant G.P and , then the value of (α − β) is :
1 1 3 2
+ =
α β 4
(1)
80
9
(2) 9
(3) 20
3
(4) 8
Q3 - 2024 (27 Jan Shift 2)
If α, β are the roots of the equation, x 2
− x − 1 = 0 and S n = 2023α
n
+ 2024β
n
, then
(1) 2 S 12 = S11 + S10
(2) S 12 = S11 + S10
(3) 2 S 11 = S12 + S10
(4) S 11 = S10 + S12
Q4 - 2024 (29 Jan Shift 2)
Let the set C = {(x, y) ∣ x
2
− 2
y
= 2023, x, y ∈ N} . Then ∑ (x,y)=C
(x + y) is equal to _____
Q5 - 2024 (30 Jan Shift 1)
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, Quadratic Equation JEE Main 2024 January Question Bank
Questions with Answer Keys MathonGo
Let α, β ∈ N be roots of equation x 2
− 70x + λ = 0 , where λ
2
,
λ
3
∉ N . If λ assumes the minimum possible
(√α−1+√β−1)(λ+35)
value, then |α−β|
is equal to:
Q6 - 2024 (30 Jan Shift 2)
The number of real solutions of the equation x (x 2
+ 3|x| + 5|x − 1| + 6|x − 2|) = 0 is_______.
Q7 - 2024 (31 Jan Shift 1)
For 0 < c < b < a, let (a + b − 2c)x 2
+ (b + c − 2a)x +(c + a − 2b) = 0 and α ≠ 1 be one of its root.
Then, among the two statements
(I) If α ∈ (−1, 0), then b cannot be the geometric mean of a and c
(II) If α ∈ (0, 1), then b may be the geometric mean of a and c
(1) Both (I) and (II) are true
(2) Neither (I) nor (II) is true
(3) Only (II) is true
(4) Only (I) is true
Q8 - 2024 (31 Jan Shift 1)
2
ax +2(a+1)x+9a+4
Let S be the set of positive integral values of a for which 2
x −8x+32
< 0, ∀x ∈ R .
Then, the number of elements in S is :
(1) 1
(2) 0
(3) ∞
(4) 3
Q9 - 2024 (31 Jan Shift 2)
The number of solutions, of the equation e sin x
− 2e
− sin x
= 2 is
(1) 2
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Questions with Answer Keys MathonGo
Q1 - 2024 (01 Feb Shift 1)
Let S = {x ∈ R : (√3 + √2) x
+ (√3 − √2)
x
= 10} .
Then the number of elements in S is :
(1) 4
(2) 0
(3) 2
(4) 1
Q2 - 2024 (01 Feb Shift 2)
Let α and β be the roots of the equation px 2
+ qx− r = 0 , where p ≠ 0. If p, q and r be the consecutive terms
of a non-constant G.P and , then the value of (α − β) is :
1 1 3 2
+ =
α β 4
(1)
80
9
(2) 9
(3) 20
3
(4) 8
Q3 - 2024 (27 Jan Shift 2)
If α, β are the roots of the equation, x 2
− x − 1 = 0 and S n = 2023α
n
+ 2024β
n
, then
(1) 2 S 12 = S11 + S10
(2) S 12 = S11 + S10
(3) 2 S 11 = S12 + S10
(4) S 11 = S10 + S12
Q4 - 2024 (29 Jan Shift 2)
Let the set C = {(x, y) ∣ x
2
− 2
y
= 2023, x, y ∈ N} . Then ∑ (x,y)=C
(x + y) is equal to _____
Q5 - 2024 (30 Jan Shift 1)
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, Quadratic Equation JEE Main 2024 January Question Bank
Questions with Answer Keys MathonGo
Let α, β ∈ N be roots of equation x 2
− 70x + λ = 0 , where λ
2
,
λ
3
∉ N . If λ assumes the minimum possible
(√α−1+√β−1)(λ+35)
value, then |α−β|
is equal to:
Q6 - 2024 (30 Jan Shift 2)
The number of real solutions of the equation x (x 2
+ 3|x| + 5|x − 1| + 6|x − 2|) = 0 is_______.
Q7 - 2024 (31 Jan Shift 1)
For 0 < c < b < a, let (a + b − 2c)x 2
+ (b + c − 2a)x +(c + a − 2b) = 0 and α ≠ 1 be one of its root.
Then, among the two statements
(I) If α ∈ (−1, 0), then b cannot be the geometric mean of a and c
(II) If α ∈ (0, 1), then b may be the geometric mean of a and c
(1) Both (I) and (II) are true
(2) Neither (I) nor (II) is true
(3) Only (II) is true
(4) Only (I) is true
Q8 - 2024 (31 Jan Shift 1)
2
ax +2(a+1)x+9a+4
Let S be the set of positive integral values of a for which 2
x −8x+32
< 0, ∀x ∈ R .
Then, the number of elements in S is :
(1) 1
(2) 0
(3) ∞
(4) 3
Q9 - 2024 (31 Jan Shift 2)
The number of solutions, of the equation e sin x
− 2e
− sin x
= 2 is
(1) 2
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Click here to download MARKS App
