Let p and q be real numbers such that p ≠ 0, p 3 ≠ q and p 3 ≠ - q. If α and β are non - zero complex numbers satisfying α + β = - p and α 3 + β 3 = q, then a quadratic equation having α/β and α/β as its roots is

(p3 + q)χ2 - (p3 - 2q)χ + (p3 + q ) = 0

(p3 + q)χ2 - (p3 + 2q)χ + (p3 + q ) = 0

(p3 - q)χ2 - (5p3 - 2q)χ + (p3 - q ) = 0

(p3 - q)χ2 - (5p3 + 2q)χ + (p3 - q ) = 0

JEE Questions for Maths Equations And Inequalities Quiz 1

log₄ 2 - log₁₆ 2 + log 2 - ... is equal to

0%
e2
0%
loge 2 + 1
0%
loge 3 - 2
0%
1 - loge 2

x, y, z are +ve real numbers and x + y + z = 1/2 then

0%
0%
2)
0%
0%
none of these

Maths-Equations and Inequalities-27032.png

0%
x > y
0%
x < y
0%
x = y
0%
None of these

The equation x + 2y + 2z = 1 and 2x + 4y + 4z = 9 have

0%
Only two solutions
0%
Only one solution
0%
Infinite number of solutions
0%
None of these.

Given that, a, b ϵ {0,1,2...9} with a + b ≠ 0 and
Maths-Equations and Inequalities-27035.png

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

Maths-Equations and Inequalities-27037.png

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

Maths-Equations and Inequalities-27039.png

0%
7
0%
4
0%
2
0%
1

Maths-Equations and Inequalities-27041.png

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

Maths-Equations and Inequalities-27043.png

0%
√2 -3
0%
2 + √2
0%
2 - √2
0%
6 - 2√2

Maths-Equations and Inequalities-27045.png

0%
254
0%
192
0%
292
0%
66
0%
62

Solution of the equation
Maths-Equations and Inequalities-27047.png

0%
3
0%
2
0%
3/2
0%
2/3

The number of digits in 20 ³⁰¹
Maths-Equations and Inequalities-27049.png

0%
602
0%
301
0%
392
0%
391

If x, y and z are real and different and u = x² + 4y² + 9z² – 6yz – 3zx – 2xy, then u is always.

0%
non negative
0%
zero
0%
non positive
0%
none of these

Maths-Equations and Inequalities-27052.png

0%
are real and negative
0%
have negative real parts
0%
both (a) and (b)
0%
none of these

If (x,y) is the solution of the following equations (2x)^log2 = (3y)^log3 and 3^logx = 2^logy , then x is equal to

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

Maths-Equations and Inequalities-27055.png

0%
1
0%
2
0%
0
0%
- 1

The sequence
Maths-Equations and Inequalities-27057.png

0%
a GP
0%
an AP
0%
a HP
0%
both a GP and a HP

If log₃ 2, log₃ (2^x -and log₃ (2^x - 7/are in AP, then x is equal to

0%
8
0%
3
0%
- 8
0%
- 3

The approximate value of ∛28 is

0%
3.0037
0%
3.037
0%
3.0086
0%
3.37

Both the roots of the equation (x – b) (x – c) + (x – a) (x – c) + (x – a) (x – b) = 0 are always

0%
positive
0%
real
0%
negative
0%
none of these.

The value of log ₂ 20 . log₂ 80 - log₂ 5 . log₂ 320 is

0%
5
0%
6
0%
7
0%
8
0%
10

If log₅ log₅ log₂ χ = 0, then the value of χ is

0%
32
0%
125
0%
625
0%
25

The number of solutions of log ₄ ( χ -= log₂ ( χ - 3 )

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

Maths-Equations and Inequalities-27065.png

0%
10
0%
2
0%
– 0.01
0%
none of these.

If a, b, c are distinct positive numbers each being different form 1 such that (log_b a . log_c a -log_a a) + (log_a b . log_c b - log_b b) + (log_a c . log_b c - log_c c) = 0, then abc is equal to

0%
0
0%
e
0%
1
0%
2
0%
3

Maths-Equations and Inequalities-27068.png

0%
a = b
0%
a = b/2
0%
2a = b
0%
a = b/3

If a^x = b^y = c^z = d^w, then the values of
Maths-Equations and Inequalities-27070.png

0%
loga(bcd)
0%
loga (abc)
0%
logb(cda)
0%
logc(dab)

Maths-Equations and Inequalities-27072.png

0%
0
0%
1
0%
- 1
0%
2

The solution set of the equation
Maths-Equations and Inequalities-27074.png

0%
{4, 1/4}
0%
{2,1/2}
0%
{1,2}
0%
{8,1/8}

The value of
Maths-Equations and Inequalities-27076.png

0%
0
0%
1
0%
2
0%
100!

If a, b, c ≠ 0 and belong to the set {0,1,2,3...9}, then
Maths-Equations and Inequalities-27078.png

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

The value of a, so that the sum of squares of the root of the equations χ² - (a -χ - a + 1 = 0 assume the least value, is

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

Let f(χ )=2χ² + 5χ + 1. If we write f(χ ) as
f(χ ) = [a (χ +(χ —+ b (χ -(χ -+ c(χ - 1)(χ + 1)] for real numbers a,b and c, then

0%
there are infinite numbers of choices for a, b and c
0%
only one choice for a but infinite numbers of choices for b and c
0%
exactly one choice for each of a, b and c
0%
more than one but finite number of choices for a, b and c

If α and β are the roots of the equation aχ ² + bx + c = 0 and S_n = αⁿ + βⁿ and a S_n+1 + b S _n + c S _n-1 is equal to

0%
0
0%
abc
0%
a + b + c
0%
None of these

If the roots of the equation aχ² + bχ + c = 0 are of the form
Maths-Equations and Inequalities-27083.png

0%
b2 - 4ac
0%
b2 - 2 ac
0%
2b2 - ac
0%

If (x² + px +is a factor of (ax³ + bx + c), then

0%
a2 + c2 = – ab
0%
a2 – c2 = – ab
0%
a2 – c2 = ab
0%
none of these

If α , β and γ are the roots of the equation χ³ + 4χ + 2 = 0, then α³ + β³ + γ³ is equal to

0%
2
0%
6
0%
- 2
0%
- 6

If the product of the roots of the equation χ² - 2 √2kχ + 2e^2logk - 1 = 0 is 31, then the roots of the equation are real for k, is equal to

0%
- 4
0%
1
0%
4
0%
0

Let p and q be real numbers such that p ≠ 0, p³ ≠ q and p³ ≠ - q. If α and β are non - zero complex numbers satisfying α + β = - p and α³ + β³ = q, then a quadratic equation having α/β and α/β as its roots is

0%
(p3 + q)χ2 - (p3 + 2q)χ + (p3 + q ) = 0
0%
(p3 + q)χ2 - (p3 - 2q)χ + (p3 + q ) = 0
0%
(p3 - q)χ2 - (5p3 - 2q)χ + (p3 - q ) = 0
0%
(p3 - q)χ2 - (5p3 + 2q)χ + (p3 - q ) = 0

If χ² + pχ + q = 0 has the roots α and β, then the value of (α - β)² is

0%
p2 - 4q
0%
(p2 - 4q)2
0%
p2 + 4q
0%
(p2 + 4q)2

If the roots of the equation χ² - bχ + c = 0 are two consecutive integers, then b² - 4c is equal to

0%
- 1
0%
0
0%
1
0%
2
0%
3

If α and β are the roots of the quadratic equation ⋋(χ² - χ) + χ + 5 = 0 and ⋋₁, ⋋₂ are two values ⋋ obtained from
Maths-Equations and Inequalities-27092.png

0%
4192
0%
4144
0%
4096
0%
4048

If 2 - r is a root of the equation aχ² + 12χ² + b = 0(where,a and b are real), then the value of ab is

0%
45
0%
15
0%
- 15
0%
- 45
0%
25

If α and β are the roots of χ² - 2χ + 4 = 0, then thevalue of α⁶ + β⁶ is

0%
32
0%
64
0%
128
0%
256

If α ,β and γ are the roots of χ³ + 4χ + 1 = 0, then the equation, whose roots are
Maths-Equations and Inequalities-27096.png

0%
χ3 - 4χ - 1 = 0
0%
χ3 - 4χ + 1 = 0
0%
χ3 + 4χ - 1 = 0
0%
χ3 + 4χ + 1 = 0

The number of real solutions of the equation | x |² – 3 | x | + 2 = 0 is

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

If α ,β and γ are such that α + β + γ = 2, α² + β² + γ² = 6, α³ + β³ + γ³ = 8 then α⁴ + β⁴ + γ⁴ is equal to

0%
7
0%
12
0%
18
0%
36

Let the two numbers have arithmetic mean 9 and geometric mean 4. Then, these numbers are the roots of the quadratic equation

0%
χ2 - 18χ - 16 = 0
0%
χ2 - 18χ +16 = 0
0%
χ2 + 18χ - 16 = 0
0%
χ2 + 18χ + 16 = 0

If α and β are the roots of the equations χ² - (1 + n² )χ+ 1/2(1 + n² + n⁴) = 0, then α² + β² is equal to

0%
n2
0%
- n2
0%
n4
0%
- n4

If α and β are the roots of χ² - 2χ cos ∅ + 1 = 0, then the equation, whose roots are αⁿ + βⁿ

0%
χ2 - 2 χcos n∅ - 1 = 0
0%
χ2 - 2 χcos n∅ + 1 = 0
0%
χ2 - 2 χsin n∅ + 1 = 0
0%
χ2 + 2 χsin n∅ - 1 = 0

JEE Questions for Maths Equations And Inequalities Quiz 1 - MCQExams.com

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Practice Maths Quiz Questions and Answers

JEE Questions for Maths Equations And Inequalities Quiz 1 - MCQExams.com

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Practice Maths Quiz Questions and Answers

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