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JEE Questions for Maths Equations And Inequalities Quiz 10 - MCQExams.com
JEE
Maths
Equations And Inequalities
Quiz 10
All the value of m for which both roots of the equation x
2
– 2mx + m
2
– 1 = 0 are greater than –2 but less than 4, lie in the interval
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0%
–2 < m < 0
0%
m > 3
0%
–1 < m < 3
0%
1 < m < 4
Roots of the equations 2x
2
– 5x + 1 = 0, and x
2
+ 5x + 2 = 0
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0%
Reciprocal and same sign
0%
Reciprocal and of opposite signs
0%
Equal in product
0%
None of the above
If a + b + c = 0, a ≠ 0, a, b, c ϵ Q, then both the roots of the equation ax
2
+ bx + c = 0 are
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0%
Rational
0%
Non real
0%
Irrational
0%
Zero
The expression x
2
+ 2bx + c has the positive value if
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0%
0%
2)
0%
0%
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0%
a = 0
0%
b = 0
0%
c = 0
0%
none of these
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0%
0%
2)
0%
0%
If the roots of equations x
2
+ a
2
= 8x + 6a are real, then
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0%
0%
2)
0%
0%
Let p, q ϵ {1, 2, 3, 4}. The number of equations of the form px
2
+ qx + 1 = 0 having real roots is
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0%
15
0%
9
0%
7
0%
8
The value of k for which the equation (k – 2)x
2
+ 8x + k + 4 = 0 has both roots real, distinct and negative
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0%
0
0%
2
0%
3
0%
–4
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0%
complex
0%
real and unequal
0%
real and equal
0%
one real and one imaginary
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0%
2l = m + n
0%
2m = n + l
0%
m = n + l
0%
l = m + n
The least integer k which makes the roots of the equation x
2
+ 5x + k = 0 imaginary is
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0%
4
0%
5
0%
6
0%
7
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0%
2
0%
0
0%
1
0%
3
If sinA, sinB, cosA are in GP then roots of x
2
+ 2xcotB + 1 = 0 are always
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0%
Real
0%
Imaginary
0%
Greater than 1
0%
Equal
The number of solutions of the equation |x| = x – 10 is
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0%
Two
0%
Infinite
0%
No solution
0%
One
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0%
Imaginary
0%
Real, rational and equal
0%
Real, irrational and unequal
0%
Real, rational and unequal
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0%
0%
2)
0%
0%
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0%
0%
2)
0%
0%
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0%
(–4, 7)
0%
(4, 7)
0%
(4, –7)
0%
(–4, –7)
If α and β and γ are the roots of the equation x
2
+ 6x + λ = 0 and 3α + 2β = –20, then λ
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0%
–8
0%
–16
0%
16
0%
None of these
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0%
b
0%
–b
0%
1 – b
0%
b – 1
If the ration of the roots of the equation ax
2
+ bx + c = 0 be p : q then
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0%
0%
2)
0%
0%
None of these
If the sum of the roots of the equation ax
2
+ bx + c = 0 be equal to the sum of their squares, then
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0%
a(a + b) = 2bc
0%
c(a + c) = 2ab
0%
b(a + b) = 2ac
0%
b(a + b) = ac
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0%
Zero
0%
One
0%
Two
0%
Four
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0%
0%
2)
0%
0%
The quadratic equation in t, such that A.M. of its roots is A and G.M is G, is
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0%
0%
2)
0%
0%
None of these
If the difference of the roots of x
2
– px + 8 = 0 be 2, then the value of p is
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0%
±2
0%
±4
0%
±6
0%
±8
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0%
0%
2)
0%
0%
The quadratic equation with real coefficient whose one root is 7 + 5i, will be
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0%
0%
2)
0%
0%
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0%
Real and equal
0%
Unequal and rational
0%
Unequal and irrational
0%
Nothing can be said
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0%
0%
2)
0%
0
0%
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0%
0%
2)
0%
0%
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0%
0%
2)
0%
0%
If the sum of the roots of the equation x
2
+ px + q = 0 is three times their difference, then which one of the following is true?
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0%
0%
2)
0%
0%
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0%
0
0%
1
0%
2
0%
3
If b
2
≥ 4ac for the equation ax
4
+ bx
2
+ c = 0, then all the roots of the equation will be real, if
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0%
b > 0, a < 0, c > 0
0%
b < 0, a > 0, c > 0
0%
b > 0, a > 0, c > 0
0%
b > 0, a > 0, c < 0
A two digit number is four times the sum and three times the product of its digits. The number is
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0%
42
0%
24
0%
12
0%
21
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0%
0
0%
2
0%
4
0%
6
If α, β are the roots of the quadratic equation x
2
+ bx – c = 0, then the equation whose roots are b and c is
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0%
0%
2)
0%
0%
Roots of the equation x
2
+ bx – c = 0 (b, c >are
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0%
Both positive
0%
Both negative
0%
Of opposite sign
0%
None of these
If p and q are roots of x
2
+ px + q == 0, then
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0%
p = 1, q = –2
0%
p = –2, q = 1
0%
p = 1, q = 0
0%
p = –2, q = 0
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0%
–4
0%
–1
0%
4
0%
–2
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0%
1
0%
2
0%
3
0%
–2
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0%
16
0%
32
0%
64
0%
None of these
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0%
0%
2)
0%
0%
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0%
0%
2)
0%
0%
None of these
If one of the roots of equation x
2
+ ax + 3 = 0 is 3 and one of the roots of the equation x
2
+ ax + b is three times the other root, then the value of b is equal to
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0%
3
0%
4
0%
2
0%
1
If the roots of equation x
2
+ px + q = 0 differ by 1, then
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0%
0%
2)
0%
0%
None of these
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0%
0%
2)
0%
0%
The values of p for which one root of the equation x
2
– 30x + p = 0 is the square of the other, are
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0%
125 only
0%
125 and –216
0%
125 and 215
0%
216 only
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