JEE Questions for Maths Equations And Inequalities Quiz 10 - MCQExams.com

All the value of m for which both roots of the equation x2 – 2mx + m2 – 1 = 0 are greater than –2 but less than 4, lie in the interval
  • –2 < m < 0
  • m > 3
  • –1 < m < 3
  • 1 < m < 4
Roots of the equations 2x2 – 5x + 1 = 0, and x2 + 5x + 2 = 0
  • Reciprocal and same sign
  • Reciprocal and of opposite signs
  • Equal in product
  • None of the above
If a + b + c = 0, a ≠ 0, a, b, c ϵ Q, then both the roots of the equation ax2 + bx + c = 0 are
  • Rational
  • Non real
  • Irrational
  • Zero
The expression x2 + 2bx + c has the positive value if

  • Maths-Equations and Inequalities-28097.png
  • 2)
    Maths-Equations and Inequalities-28098.png

  • Maths-Equations and Inequalities-28099.png

  • Maths-Equations and Inequalities-28100.png

Maths-Equations and Inequalities-28102.png
  • a = 0
  • b = 0
  • c = 0
  • none of these

Maths-Equations and Inequalities-28104.png

  • Maths-Equations and Inequalities-28105.png
  • 2)
    Maths-Equations and Inequalities-28106.png

  • Maths-Equations and Inequalities-28107.png

  • Maths-Equations and Inequalities-28108.png
If the roots of equations x2 + a2 = 8x + 6a are real, then

  • Maths-Equations and Inequalities-28110.png
  • 2)
    Maths-Equations and Inequalities-28111.png

  • Maths-Equations and Inequalities-28112.png

  • Maths-Equations and Inequalities-28113.png
Let p, q ϵ {1, 2, 3, 4}. The number of equations of the form px2 + qx + 1 = 0 having real roots is
  • 15
  • 9
  • 7
  • 8
The value of k for which the equation (k – 2)x2 + 8x + k + 4 = 0 has both roots real, distinct and negative
  • 0
  • 2
  • 3
  • –4

Maths-Equations and Inequalities-28117.png
  • complex
  • real and unequal
  • real and equal
  • one real and one imaginary

Maths-Equations and Inequalities-28119.png
  • 2l = m + n
  • 2m = n + l
  • m = n + l
  • l = m + n
The least integer k which makes the roots of the equation x2 + 5x + k = 0 imaginary is
  • 4
  • 5
  • 6
  • 7

Maths-Equations and Inequalities-28122.png
  • 2
  • 0
  • 1
  • 3
If sinA, sinB, cosA are in GP then roots of x2 + 2xcotB + 1 = 0 are always
  • Real
  • Imaginary
  • Greater than 1
  • Equal
The number of solutions of the equation |x| = x – 10 is
  • Two
  • Infinite
  • No solution
  • One

Maths-Equations and Inequalities-28126.png
  • Imaginary
  • Real, rational and equal
  • Real, irrational and unequal
  • Real, rational and unequal

Maths-Equations and Inequalities-28128.png

  • Maths-Equations and Inequalities-28129.png
  • 2)
    Maths-Equations and Inequalities-28130.png

  • Maths-Equations and Inequalities-28131.png

  • Maths-Equations and Inequalities-28132.png

Maths-Equations and Inequalities-28134.png

  • Maths-Equations and Inequalities-28135.png
  • 2)
    Maths-Equations and Inequalities-28136.png

  • Maths-Equations and Inequalities-28137.png

  • Maths-Equations and Inequalities-28138.png

Maths-Equations and Inequalities-28140.png
  • (–4, 7)
  • (4, 7)
  • (4, –7)
  • (–4, –7)
If α and β and γ are the roots of the equation x2 + 6x + λ = 0 and 3α + 2β = –20, then λ
  • –8
  • –16
  • 16
  • None of these

Maths-Equations and Inequalities-28143.png
  • b
  • –b
  • 1 – b
  • b – 1
If the ration of the roots of the equation ax2 + bx + c = 0 be p : q then

  • Maths-Equations and Inequalities-28145.png
  • 2)
    Maths-Equations and Inequalities-28146.png

  • Maths-Equations and Inequalities-28147.png
  • None of these
If the sum of the roots of the equation ax2 + bx + c = 0 be equal to the sum of their squares, then
  • a(a + b) = 2bc
  • c(a + c) = 2ab
  • b(a + b) = 2ac
  • b(a + b) = ac

Maths-Equations and Inequalities-28150.png
  • Zero
  • One
  • Two
  • Four

Maths-Equations and Inequalities-28152.png

  • Maths-Equations and Inequalities-28153.png
  • 2)
    Maths-Equations and Inequalities-28154.png

  • Maths-Equations and Inequalities-28155.png

  • Maths-Equations and Inequalities-28156.png
The quadratic equation in t, such that A.M. of its roots is A and G.M is G, is

  • Maths-Equations and Inequalities-28158.png
  • 2)
    Maths-Equations and Inequalities-28159.png

  • Maths-Equations and Inequalities-28160.png
  • None of these
If the difference of the roots of x2 – px + 8 = 0 be 2, then the value of p is
  • ±2
  • ±4
  • ±6
  • ±8

Maths-Equations and Inequalities-28163.png

  • Maths-Equations and Inequalities-28164.png
  • 2)
    Maths-Equations and Inequalities-28165.png

  • Maths-Equations and Inequalities-28166.png

  • Maths-Equations and Inequalities-28167.png
The quadratic equation with real coefficient whose one root is 7 + 5i, will be

  • Maths-Equations and Inequalities-28169.png
  • 2)
    Maths-Equations and Inequalities-28170.png

  • Maths-Equations and Inequalities-28171.png

  • Maths-Equations and Inequalities-28172.png

Maths-Equations and Inequalities-28174.png
  • Real and equal
  • Unequal and rational
  • Unequal and irrational
  • Nothing can be said

Maths-Equations and Inequalities-28176.png

  • Maths-Equations and Inequalities-28177.png
  • 2)
    Maths-Equations and Inequalities-28178.png
  • 0

  • Maths-Equations and Inequalities-28179.png

Maths-Equations and Inequalities-28181.png

  • Maths-Equations and Inequalities-28182.png
  • 2)
    Maths-Equations and Inequalities-28183.png

  • Maths-Equations and Inequalities-28184.png

  • Maths-Equations and Inequalities-28185.png

Maths-Equations and Inequalities-28187.png

  • Maths-Equations and Inequalities-28188.png
  • 2)
    Maths-Equations and Inequalities-28189.png

  • Maths-Equations and Inequalities-28190.png

  • Maths-Equations and Inequalities-28191.png
If the sum of the roots of the equation x2 + px + q = 0 is three times their difference, then which one of the following is true?

  • Maths-Equations and Inequalities-28193.png
  • 2)
    Maths-Equations and Inequalities-28194.png

  • Maths-Equations and Inequalities-28195.png

  • Maths-Equations and Inequalities-28196.png

Maths-Equations and Inequalities-28198.png
  • 0
  • 1
  • 2
  • 3
If b2 ≥ 4ac for the equation ax4 + bx2 + c = 0, then all the roots of the equation will be real, if
  • b > 0, a < 0, c > 0
  • b < 0, a > 0, c > 0
  • b > 0, a > 0, c > 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
  • 42
  • 24
  • 12
  • 21

Maths-Equations and Inequalities-28202.png
  • 0
  • 2
  • 4
  • 6
If α, β are the roots of the quadratic equation x2 + bx – c = 0, then the equation whose roots are b and c is

  • Maths-Equations and Inequalities-28204.png
  • 2)
    Maths-Equations and Inequalities-28205.png

  • Maths-Equations and Inequalities-28206.png

  • Maths-Equations and Inequalities-28207.png
Roots of the equation x2 + bx – c = 0 (b, c >are
  • Both positive
  • Both negative
  • Of opposite sign
  • None of these
If p and q are roots of x2 + px + q == 0, then
  • p = 1, q = –2
  • p = –2, q = 1
  • p = 1, q = 0
  • p = –2, q = 0

Maths-Equations and Inequalities-28211.png
  • –4
  • –1
  • 4
  • –2

Maths-Equations and Inequalities-28213.png
  • 1
  • 2
  • 3
  • –2

Maths-Equations and Inequalities-28215.png
  • 16
  • 32
  • 64
  • None of these

Maths-Equations and Inequalities-28217.png

  • Maths-Equations and Inequalities-28218.png
  • 2)
    Maths-Equations and Inequalities-28219.png

  • Maths-Equations and Inequalities-28220.png

  • Maths-Equations and Inequalities-28221.png

Maths-Equations and Inequalities-28223.png

  • Maths-Equations and Inequalities-28224.png
  • 2)
    Maths-Equations and Inequalities-28225.png

  • Maths-Equations and Inequalities-28226.png
  • None of these
If one of the roots of equation x2 + ax + 3 = 0 is 3 and one of the roots of the equation x2 + ax + b is three times the other root, then the value of b is equal to
  • 3
  • 4
  • 2
  • 1
If the roots of equation x2 + px + q = 0 differ by 1, then

  • Maths-Equations and Inequalities-28229.png
  • 2)
    Maths-Equations and Inequalities-28230.png

  • Maths-Equations and Inequalities-28231.png
  • None of these

Maths-Equations and Inequalities-28233.png

  • Maths-Equations and Inequalities-28234.png
  • 2)
    Maths-Equations and Inequalities-28235.png

  • Maths-Equations and Inequalities-28236.png

  • Maths-Equations and Inequalities-28237.png
The values of p for which one root of the equation x2 – 30x + p = 0 is the square of the other, are
  • 125 only
  • 125 and –216
  • 125 and 215
  • 216 only
0:0:1


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