JEE Questions for Maths Equations And Inequalities Quiz 12 - MCQExams.com

If a, b and c are in geometric progression and the roots of the equations ax² + 2bx + c = 0 are α and β and those of cx² + 2bx + a = 0 are γ and δ, then

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2)
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0%

The sum of all real roots of the equation |x – 2|² + |x – 2| – 2 = 0 is

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7
0%
4
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1
0%
5

Maths-Equations and Inequalities-28404.png

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2)
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0%

Maths-Equations and Inequalities-28410.png

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Four real roots
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Two real roots
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Four imaginary roots
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None of the above

Maths-Equations and Inequalities-28412.png

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Positive
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Negative
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Real
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Imaginary

Maths-Equations and Inequalities-28414.png

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AP
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GP
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HP
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None of these

Maths-Equations and Inequalities-28416.png

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2
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3
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0
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1

Maths-Equations and Inequalities-28418.png

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2)
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0%

Maths-Equations and Inequalities-28424.png

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At least one real solution
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Exactly three real solutions
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Exactly one irrational solution
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All of the above

Maths-Equations and Inequalities-28426.png

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Are real and negative
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Have negative real parts
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Are rational numbers
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None of the above

Maths-Equations and Inequalities-28428.png

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2)
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If x² + 2x + 2xy + my – 3 has two rational factors, then the value of m will be

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–6, –2
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–6, 2
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6, –2
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6, 2

If a and b are odd integers, then the roots of the equation 2ax² + (2a + b)x + b = 0, a ≠ 0 will be

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Rational
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Irrational
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Non – real
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Equal

Maths-Equations and Inequalities-28436.png

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1
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4
0%
0%
5

Maths-Equations and Inequalities-28439.png

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Real roots
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Purely imaginary roots
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Imaginary roots
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None of the above

The expression y = ax² + bx + c has always the same sign as c if

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4ac < b2
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4ac > b2
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ac < b2
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ac > b2

Maths-Equations and Inequalities-28442.png

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2)
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0%

Maths-Equations and Inequalities-28448.png

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–6, –4
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–6, 5
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–6, 4
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6, –4

Maths-Equations and Inequalities-28450.png

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1
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–1
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2
0%
–2

Maths-Equations and Inequalities-28452.png

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2)
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0%
None of these

Maths-Equations and Inequalities-28457.png

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0%
2)
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0%
None of the above

Maths-Equations and Inequalities-28462.png

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0%
2)
0%
0%
None of these

Maths-Equations and Inequalities-28467.png

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0%
2)
0%
0%
None of these

Maths-Equations and Inequalities-28472.png

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0 and –16
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16 and 8
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–16 and 0
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16 and 0

Maths-Equations and Inequalities-28474.png

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2)
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0%

Maths-Equations and Inequalities-28480.png

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0%
2)
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0%

Maths-Equations and Inequalities-28486.png

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2)
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None of these

Maths-Equations and Inequalities-28491.png

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2)
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If one root of ax² + bx + c = 0 be square of the other, then the value of b³ + ac² + a²c is

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3abc
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–3abc
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0
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None of these

Maths-Equations and Inequalities-28498.png

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a, c
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b, c
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a, b
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a + c, b + c

If the sum of the roots of the quadratic equation ax² + bx + c = 0 is equal to the sum of the squares of their reciprocals, then a/b, b/a, c/b are in

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A.P
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G.P
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H.P
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None of these

Maths-Equations and Inequalities-28501.png

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0%
2)
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0%

Maths-Equations and Inequalities-28507.png

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2)
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0%

Maths-Equations and Inequalities-28513.png

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–2
0%
–1
0%
1
0%
2

If the roots of the equation x² + 2mx + m² – 2m + 6 = 0 are same, then the value of m will be

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3
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0
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2
0%
–1

If the roots of the equation ax² + bx + c = 0 are l and 2l, then

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2)
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The sum of the roots of a equation is 2 and sum of their cubes is 98, then the equation is

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2)
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The roots of the equation x² + ax + b = 0 are p and q, then the equation whose roots are p²q and pq² will be

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2)
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0%

Maths-Equations and Inequalities-28531.png

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2)
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0%

Maths-Equations and Inequalities-28537.png

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1
0%
64
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8
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None of these

The quadratic equation whose roots are three times the roots of 3ax² + 3bx + c = 0 is

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ax2 + 3bx + 3c = 0
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ax2+ 3bx + c = 0
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9ax2 + 9bx + c = 0
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ax2 + bx + 3c = 0

Maths-Equations and Inequalities-28540.png

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Negative
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None of these
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Zero
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Positive

Maths-Equations and Inequalities-28542.png

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2)
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None of these

If the ratio of the roots of ax² + 2bx + c = 0 is same as the ratio of the roots of px² + 2qx + r = 0, then

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2)
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None of these

Maths-Equations and Inequalities-28551.png

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0
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1
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0%

Maths-Equations and Inequalities-28555.png

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2)
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0%

Maths-Equations and Inequalities-28562.png

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2)
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Maths-Equations and Inequalities-28568.png

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2)
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0%

Maths-Equations and Inequalities-28574.png

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2)
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0%

Maths-Equations and Inequalities-28580.png

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2
0%
–2
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1
0%
–1

0:0:1

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