E 1 : a + b + c = 0 , if 1 is root of aχ 2 + bχ + c = 0, E 2 : b 2 - a 2 = 2ac, if sin θ and cos θ are the roots of aχ 2 + bχ + c = 0, which of the following is correct ?

E1 is incorrect E2 is incorrect

JEE Questions for Maths Equations And Inequalities Quiz 5

If f(χ) = 2χ³ + mχ² - 13χ + n and 2, 3 are the roots of the equation f(χ) = 0, then the values of m and n are

0%
-5 , - 30
0%
-5 , 30
0%
5 , 30
0%
None of these

The difference between two roots of the equation χ³ - 13χ² + 15χ + 189 = 0 is 2. Then, the roots of the equation are

0%
-3, 7, 9
0%
-3, - 7, - 9
0%
-3, - 5, 7
0%
-3, -7, 9

If the cube roots of unity are 1, ω and ω² then the roots of the equation(χ - 1)³ + 8 = 0, are

0%
- 1, 1 + 2ω , 1 + 2ω2
0%
- 1, 1- 2ω, 1 - 2ω2
0%
- 1, - 1, - 1,
0%
- 1, - 1 + 2ω, - 1 - 2ω2

If sin A, sin B and cos A are in GP, then the roots of χ² + 2χ cot B + 1 = 0 are always

0%
real
0%
imaginary
0%
greater than 1
0%
equal

The roots of the equation χ⁴ - 2χ³ + χ = 380 are

0%
0%
2)
0%
0%

let a, b be the solutions of χ² + pχ + 1 = 0 and c, d be the solutions of χ² + qχ + 1 = 0. If (a - c) (b - c) and (a + d) (b + d) are the solutions of χ² + αχ + β = 0, then β equals

0%
P + q
0%
p - q
0%
p2 + q2
0%
q2 - p2

The solution set of the equation pqχ² - (p + q)² χ + (p + q)² = 0 is

0%
0%
2)
0%
0%
0%

The coefficients of χ in the quadratic equation χ² + bχ + c = 0 was taken as 17 in place of 13, its roots were found to be - 2 and -15. The correct roots of the original equation are

0%
- 10, - 3
0%
- 9, - 4
0%
- 8, - 5
0%
- 7, - 6

E₁ : a + b + c = 0 , if 1 is root of aχ² + bχ + c = 0, E₂ : b² - a² = 2ac, if sin θ and cos θ are the roots of aχ² + bχ + c = 0, which of the following is correct ?

0%
E1 is correct E2 is correct
0%
E1 is correct E2 is incorrect
0%
E1 is incorrect E2 is correct
0%
E1 is incorrect E2 is incorrect

If a, b and c are distinct positive real numbers in AP, then the roots of the equation aχ² + 2bχ + c = 0 are

0%
imaginary
0%
rational and equal
0%
rational and distinct
0%
irrational

If a = cos(2π/+ i sin(2π/7), then the quadratic equation whose roots are α = a + a² + a⁴ and β = a³ + a⁵ + a⁶, is

0%
χ2 - χ + 2 = 0
0%
χ2 + 2χ + 2 = 0
0%
χ2 + χ + 2 = 0
0%
χ2 + χ - 2 = 0

If the roots of the equation ⋋² +8⋋ + μ² + 6μ = 0 are real, then μ lies between

0%
- 2 and 8
0%
- 3 and 6
0%
- 8 and 2
0%
- 6 and 3

Let p and q be real numbers. If α is the root of χ² + 3p² χ + 5q² = 0, β is the root of χ² + 9p²χ + 15q² = 0 and 0 < α< β, then the equation χ² + 6p²χ + 10q² = 0 has root γ that always satisfies

0%
0%
β < γ
0%
0%
α < β < γ

If the equations x² + 2χ + 3 = 0 and aχ² + bχ + c = 0; a, b, c ∈ R, have a common root, then a : b : c is equal to

0%
1: 2 : 3
0%
3 : 2 : 1
0%
1 : 3 : 2
0%
3 : 1 : 2

Let a, b and c be real numbers, a ≠ 0, if α ≠0. If α is a root of a²x² + bx + c = 0, β is a root of a²χ² - bχ - c = 0 and 0 < α< β. Then, the equation a²χ² + 2bχ - c = 0 has a root γ that always satisfies

0%
γ = a
0%
α < β < γ
0%
α < γ < β
0%

A value of b for which the equations χ² + bχ - 1 = 0, χ² + χ + b = 0 have one root in common, is

0%
- √2
0%
- i√3
0%
i√5
0%
√2

If α and β are the roots of the equation aχ² + bχ + c = 0, then the equation whose roots are k/α and k/β is

0%
cχ2 + kbχ + k2a = 0
0%
cχ2 + k2bχ + ka = 0
0%
kcχ2 + bχ + k2a = 0
0%
k2cχ2 + bχ + ka = 0

If both the roots of the equation χ² - 6aχ + 2 – 2a + 9a² = 0 exceed 3, then

0%
a < ½
0%
a > ½
0%
a < 1
0%
a > 11/9

If the roots of the equation bχ² + cχ + a = 0 is imaginary, then for all real values of χ, the expression 3b² χ² + 6bcχ + 2c² is

0%
greater than 4ab
0%
less than 4ab
0%
greater than – 4ab
0%
less than – 4ab

If a, b and c are in GP, then the equation aχ² + 2bχ + c = 0 and dχ² + 2eχ + f = 0 have a common root, if d/a, e/b and f/c are in

0%
AP
0%
HP
0%
GP
0%
None of these

If ax² + bχ + c = 0 and 2χ² + 3χ + 4 = 0 have a common root, where a, b, c ∈ N (set of natural numbers), then the least value of a + b + c is

0%
13
0%
11
0%
7
0%
9

Maths-Equations and Inequalities-27383.png

0%
a = -1, b =1
0%
a = 1, b = - 1
0%
a = 5, b = 9
0%
a = 9, b = 5

The quadratic equations χ² - 6χ + a = 0 χ² - cχ + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then, the common root is

0%
2
0%
1
0%
4
0%
3

Let a, b and c be real. If aχ² + bχ + c = 0 has two real roots α and β where α < - 1 and β > 1 , then
Maths-Equations and Inequalities-27386.png

0%
< 0
0%
> 0
0%
≤ 0
0%
None of these

All the values of m for which both roots of the equation χ² - 2mχ + m² - 1 = 0 are greater than - 2 but less than 4 lie in the interval

0%
m > 3
0%
- 1 < m < 3
0%
1 < m < 4
0%
- 2 < m < 0

The values of k, for which the equations χ² - kχ - 21 = 0 and χ² - 3kχ + 35 = 0 will have a common roots, is

0%
K = ± 4
0%
K = ± 1
0%
K = ± 3
0%
K = 0

If the both the root of the quadratic equation χ² - 2kχ + k² + k - 5 = 0 are less than 5, then k lies in the interval

0%
(4, 5)
0%
(- ∞, 4)
0%
(6, ∞)
0%
(5, 6)

If χ is real, then the value of
Maths-Equations and Inequalities-27391.png

0%
0%
2)
0%
0%
None of these

If a real value of fraction f of a real variable χ is such that
Maths-Equations and Inequalities-27396.png

0%
0%
2)
0%
1 - χ
0%
None of these

Maths-Equations and Inequalities-27400.png

0%
0%
2)
0%
0%

Th partial fraction of
Maths-Equations and Inequalities-27406.png

0%
0%
2)
0%
0%
None of these

The number of solutions of the inequation |χ - 2| + |χ + 2|< 4 is

0%
1
0%
2
0%
4
0%
0
0%
3

Solve the inequality 2χ - 5 ≤ (4χ - 7)/3

0%
χ ϵ (- ∞ , 4)
0%
χ ϵ (- ∞ , 4]
0%
χ ϵ (- ∞ , 8]
0%
χ ϵ (- ∞ ,- 4]

Solve the inequality 3χ + 2 > - 16, 2χ - 3 ≤ 11.

0%
(- 6, 7]
0%
[ -6, 7)
0%
(- 6, 7)
0%
[- 6, 7]

If χ, y and z are three positive real numbers, then minimum values of
Maths-Equations and Inequalities-27414.png

0%
1
0%
2
0%
3
0%
6

The minimum value of the sum of real numbers a^-5, a^-4 , 3a^-3, 1, a⁸ and a¹⁰ with a > 0 is

0%
9
0%
8
0%
2
0%
1

If |2χ - 3| < |χ + 5|, then χ lies in the interval

0%
(- 3, 5)
0%
(5, 9)
0%
0%
0%

The solution set of the inequality
Maths-Equations and Inequalities-27421.png

0%
(- ∞ , 2)
0%
(- 2, ∞)
0%
(∞ , ∞)
0%
(2 , ∞)

If a, b > o satisfy a³ + b³ = a - b, then

0%
a2 + b2 > 1
0%
a2 - b < 0
0%
a2 + b2 = 1
0%
a2 +ab + b2 < 1

If 3 ≤ 3t - 18 ≤ 18, then which one of the following is correct ?

0%
15 ≤ 2t + 1≤ 20
0%
8 ≤ t < 12
0%
8 ≤ t + 1≤ 13
0%
21 ≤ 3t ≤ 24
0%
t ≤ 7 or t ≥ 12

The minimum of f(χ) = |3χ - |+ 7 is

0%
0
0%
6
0%
7
0%
8

The solution set of the inequation
Maths-Equations and Inequalities-27426.png

0%
(- ∞, -∪ (3,∞)
0%
(- ∞, - 10 ) ∪ (2,∞)
0%
(- 100, -∪ (1,∞)
0%
(- 5,∪ (3,7)
0%
(0,∪ (- 1, 0)

If log₁₀ (χ³ + y³ ) - log₁₀(χ² + y² - χy) ≤ 2, then the maximum value of χy,
Maths-Equations and Inequalities-27428.png

0%
2500
0%
3000
0%
1200
0%
3500

If a, b and c are sides of a triangle, then
Maths-Equations and Inequalities-27430.png

0%
[1 , 2]
0%
[2, 3]
0%
[3, 4]
0%
[1, 3]

If χ² + 4aχ + 2 > 0 for all values of χ, then a lies in the interval

0%
(- 2, 4)
0%
(1 , 2)
0%
(-√2, √2)
0%
0%
(-4, 2)

The largest interval for which χ¹² - χ⁹ + χ⁴ - χ + 1 > 0 is

0%
- 4 < χ < 0
0%
0 < χ < 1
0%
- 100 < χ < 100
0%
- ∞ < χ < ∞

If a, b, c > 0 and abc = 1, then the value of a + b + c + ab + bc + ca lies in the interval

0%
(∞, - 6)
0%
(- 6, 0)
0%
(0, 6)
0%
(6, ∞)

The number of positive integers satisfying the inequality ⁿ⁺¹C_n-2 - ⁿ⁺¹C_n-1 ≤ 50, is

0%
9
0%
8
0%
7
0%
6

If a, b and c > 0, then the minimum value of
Maths-Equations and Inequalities-27437.png

0%
1
0%
3/2
0%
2
0%
5/2

If χ² + 2χ + n > 10 for all real numbers χ, then which of the following conditions is correct ?

0%
n < 11
0%
n = 10
0%
n = 11
0%
n > 11
0%
n < - 11

JEE Questions for Maths Equations And Inequalities Quiz 5 - MCQExams.com

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Practice Maths Quiz Questions and Answers

JEE Questions for Maths Equations And Inequalities Quiz 5 - MCQExams.com

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Practice Maths Quiz Questions and Answers

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