JEE Questions for Maths Equations And Inequalities Quiz 2

If α, β and γ are the roots of the equation χ³ - 8 χ + 8 = 0, then ∑a² and ∑ 1/αβ are respectively

0%
0 and - 16
0%
16 and 18
0%
- 16 and 0
0%
16 and and 0

If α and β are the roots of the equation aχ² + bχ + c = 0, αβ = 3, and a, b, c are in AP, then α + β is equal to

0%
- 4
0%
1
0%
4
0%
- 2

If α and β are the roots of the equation χ² + aχ + b = 0, then
Maths-Equations and Inequalities-27105.png

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0%
2)
0%
0%

If α and β are the roots of the equation aχ² + bχ + c = 0 and pχ² + qχ + r = 0 has roots
Maths-Equations and Inequalities-27111.png

0%
a + 2b
0%
a + b + c
0%
ab + bc + ca
0%
abc

If α and β are the roots of the equation χ² - 7χ + 1 = 0, then the value of
Maths-Equations and Inequalities-27113.png

0%
45
0%
47
0%
49
0%
50
0%
51

If α ,β and γ are the roots of χ³ + bχ + c = 0, then α²β +αβ² + β² γ + βγ² + γ² α + γα²

0%
c
0%
- c
0%
- 3c
0%
3c

The condition that χ³ - pχ² + qχ - r = 0 may have two of its roots equal in magnitude but of opposite sign, is

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r = pq
0%
r = 2p3 + pq
0%
r = p2 q
0%
None of these

If 3p² = 5p + 2 and 3q² = 5q + 2, where p ≠ q, then the equation, whose roots are 3p - 2q and 3q - 2p, is

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3χ2 - 5χ - 100 = 0
0%
5χ2 + 3χ + 100 = 0
0%
3χ2 - 5χ + 100 = 0
0%
5χ2 - 3χ - 100 = 0

If α and β are the roots of the equation χ² - 6χ + a = 0 and satisfy the relation 3α + 2β = 16, then the value of α is

0%
- 8
0%
8
0%
- 16
0%
9
0%
None of these

If α ,β and γ are the roots of χ³ + 2χ² - 3χ - 1 = 0, then α^-2 + β^-2 + γ^-2 is equal to

0%
12
0%
13
0%
14
0%
15

Maths-Equations and Inequalities-27120.png

0%
χ2 - 4 = 0
0%
χ2 - 4χ + 6 = 0
0%
χ2 - 5χ + 4 = 0
0%
χ3 - 3χ + 2 = 0

If α ,β and γ are the roots of the equation χ³ - 3χ² + χ + 5 = 0, then y = ∑α² + αβγ satisfies the equation

0%
y3 + y + 2 = 0
0%
y3 - y2 - y - 2 = 0
0%
y3 + 3y2 - y - 3 = 0
0%
y3 + 4y2 5y + 20 = 0

The sum of the roots of the equation is aχ² + bχ + c = 0 is equal to the sum of the reciprocal of their squares, then bc² , ca² , ab² will be in

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

If 9√χ = √12 + √147, then the value of χ is

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

solve the equation χ² - √3χ + 1 = 0

0%
χ = (-√3 ± 2i)/2
0%
χ = (-√3 ± i)/2
0%
χ = (-√3 ± i)
0%
χ = (-√3 ± i)/2

The number of real solutions of the equation sin e^χ = 5^χ + 5^-χ is

0%
1
0%
0
0%
2
0%
None of these

If a, b and c are in arithmetic progression, then the roots of the equation aχ² - 2b χ + c = 0 are

0%
1 and c/a
0%
2)
0%
0%

The value of α for which the equation 2χ² + 2√6χ + a = 0 has equal roots, is

0%
3
0%
4
0%
2
0%
√3
0%
√2

Two towns A and B are 60 km apart. A school is to be built to serve 150 students in town A and 50 students in town B. If the total distance to be travelled by all 200 students is to be as small as possible, then the school should be built at

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town B
0%
45 km from town A
0%
town A
0%
45 km from town B

If χ satisfies |χ² - 3χ + 2|+ |χ - 1| = χ - 3 , then

0%
χ ϵ ∅
0%
χ ϵ [1 , 2]
0%
χ ϵ [3 , ∞)
0%
χ ϵ (- ∞, ∞)

The roots of the equation (χ - a) (χ - a - 1)+ (χ - a -(χ - a - 2)+ (χ - a) (χ - a -= 0 a ϵ r are always

0%
equal
0%
imaginary
0%
real and distinct
0%
rational and equal

If f(χ) = χ² + aχ + b, where a , b ϵ R. If f(χ) = 0 has all its roots imaginary, then the roots f(χ) + f ' '(χ) = 0 are

0%
real and distinct
0%
imaginary
0%
equal
0%
rational and equal

The number of real roots of the equation
Maths-Equations and Inequalities-27136.png

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

If a + b + c = 0, then the roots of the equation 4aχ² + 3bχ + 2c = 0 are

0%
equal
0%
imaginary
0%
real
0%
None of these

The roots of equation χ³ - 6χ + 9 = 0 is

0%
-6
0%
-9
0%
6
0%
-3

The equation χ² - 3|χ| + 2 = 0 has

0%
no real root
0%
one real root
0%
two real roots
0%
four real roots

A value of K for which the quadratic equation χ² - 2χ (1 + 3K) + 7(2K += 0 has equal roots, is

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

If p, q, r are any real numbers, then

0%
max (p, q) < max (p, q, r)
0%
2)
0%
max (p, q) < min (p, q, r)
0%
none of these

If p, q and r real and p q, then the roots of the equation (p - q)χ² + 5(p + q)χ - 2(p - q) = r are

0%
real and equal
0%
unequal and rational
0%
unequal and irrational
0%
nothing can be said -

The number of real roots of the equation
Maths-Equations and Inequalities-27145.png

0%
0
0%
2
0%
4
0%
6

If (1 - p) is a root of quadratic equation χ² + pχ + (1 - p) = 0, then its roots are

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

If e^{cos χ} - e^{-cos χ} = 4, then the value of cos χ is

0%
log(2 + √5)
0%
- log(2 + √5)
0%
log( - 2 + √5)
0%
None of the above

The number of real solutions of the equation
Maths-Equations and Inequalities-27149.png

0%
0
0%
1
0%
2
0%
None of these

If 1, 2, 3 and 4 are the roots of the equation χ⁴ + aχ³ + bχ² + cχ + d = 0, then a + 2b + c is equal to

0%
- 25
0%
0
0%
10
0%
24

The maximum number of real roots of the equation χ²ⁿ - 1 = 0 is

0%
2
0%
3
0%
n
0%
2n

The roots of the equation(q - r) χ² + (r - p)χ + (p - q) = 0 are

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

The roots of the equation χ³ - 3χ² - 6χ + 8 = 0 are in arithmetic progression, then the roots of the equation are

0%
3, 4 , 5
0%
4, 7, 10
0%
- 2, 1, 4
0%
1, 4, 7

The polynomial (aχ² + bχ + c) (aχ² - dχ - c), ac ≠0 has

0%
four real roots
0%
atleast two real roots
0%
atmost two real roots
0%
no real roots

The roots of the equation χ³ - 3χ - 2 = 0 are

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

If one of the roots of equation χ² + aχ + 3 = 0 is 3 and one of the roots of the equation χ² + aχ + b = 0 is three times the other root, then the value of b is