JEE Questions for Maths Equations And Inequalities Quiz 6 - MCQExams.com


Maths-Equations and Inequalities-27440.png
  • - 2 > χ > - 1
  • - 2 ≥ χ ≥ - 1
  • - 2 < χ < - 1
  • - 2 < χ ≤ - 1
Number of integral solutions of
Maths-Equations and Inequalities-27442.png
  • 0
  • 1
  • 2
  • 3
  • 4
If r is a real number that |r| < 1 and if a = 5(1 - r), then
  • 0 < a < 5
  • - 5 < a < 5
  • 0 < a < 10
  • 0 ≤ a < 10
  • - 10 < a < 10
The set of values of χ for which the inequalities χ2 - 3χ - 10 < 0, 10χ - χ2 - 16 > 0 hold simultaneously, is
  • (- 2, 5)
  • (2, 8)
  • (- 2, 8)
  • (2, 5 )
The set of all χ satisfying the inequality
Maths-Equations and Inequalities-27446.png

  • Maths-Equations and Inequalities-27447.png
  • 2)
    Maths-Equations and Inequalities-27448.png

  • Maths-Equations and Inequalities-27449.png

  • Maths-Equations and Inequalities-27450.png

  • Maths-Equations and Inequalities-27451.png
The set of values of χ satisfying 2 ≤ |χ - 3|< 4 is
  • (- 1, 1] ∪ [5, 7)
  • - 4 ≤ χ ≤ 2
  • - 1 < χ < 7 or χ ≥ 5
  • χ < 7 or χ ≥ 5
  • -∞ < χ ≤ 1 or 5 ≤ χ < ∞
If one root of the equation χ2 (1 - 3i)χ - 2(1 + i) = 0 is - 1 + i, then the other root is
  • -1 - i
  • (-1 - i)/2
  • i
  • 2i

Maths-Equations and Inequalities-27455.png
  • (2, ∞)
  • (-∞, 2)
  • (-∞, ∞)
  • (4, ∞)
If the equation 2aχ2 - 3bχ + 4c = 0 and 3χ2 - 4χ + 5 = 0 have a common root, then (a + b)/ (b + c) is equal to (a, b, c ϵ R)
  • 1/2
  • 3/35
  • 34/31
  • 29/23
  • None of these
(b + c )(c + a)(a + b) is greater than
  • abc
  • 2abc
  • 4abc
  • 8abc
If a, b, c are +ve, then a2 + b2 + c2 is
  • > a + b + c
  • > ab + bc + ca
  • < a + b + c
  • < ab + bc + ca
If x > 0, y > 0 and x2 + y2 = 8 [x ∈ R], then
  • x + y ≥ 4
  • x + y ≤ 4
  • x + y = 1
  • none of these.
Minimum value of bcx + cay + abz when xyz = abc is
  • abc
  • 2 abc
  • 3 abc
  • none of these
If a root of the equation x2 + px + 12 = 0 is 4 while the roots of the equation x2 + px + q = 0 are same, then the value of q will be
  • 4
  • 4/49
  • 49/4
  • None of these

Maths-Equations and Inequalities-27463.png
  • X is an irrational number
  • 2 < x < 3
  • x = 3
  • none of these
The roots of the quadratic equation 2x2 + 3x + 1 = 0, are
  • Irrational
  • Rational
  • Imaginary
  • None of these

Maths-Equations and Inequalities-27465.png
  • Real and unequal
  • Rational and equal
  • Irrational and equal
  • Irrational and unequal
If the roots of 4x2 + px + 9 = 0 are equal, then absolute value of p is
  • 144
  • 13
  • –12
  • ±12
The values of k for which the quadratic equation, kx2 + 1 = kx + 3x – 11x2 has real and roots are
  • –11, –3
  • 5, 7
  • 5, –7
  • None of these

Maths-Equations and Inequalities-27467.png

  • Maths-Equations and Inequalities-27468.png
  • 0

  • Maths-Equations and Inequalities-27469.png

  • Maths-Equations and Inequalities-27470.png
For what value of k will be equation x2 – (3k – 1)x + 2k2 + 2k = 11 have equal roots?
  • 5
  • 9
  • Both of a and b
  • 0
The quadratic equation x2 + 15|x| + 14 = 0 has
  • Only positive solutions
  • Only negative solutions
  • No solution
  • Both positive and negative solutions

Maths-Equations and Inequalities-27473.png
  • 0
  • 5
  • 1/6
  • 6
If the sum of the roots of the equation λx2 + 2x + 3 λ = 0 be equal to their product then λ =
  • 4
  • –4
  • 6
  • None of these

Maths-Equations and Inequalities-27476.png

  • Maths-Equations and Inequalities-27477.png
  • 0

  • Maths-Equations and Inequalities-27478.png
  • None of these
If the product of roots of the equation, mx2 + 6x + (2m –= 0, is –1, then the value of m will be
  • 1
  • –1
  • 1/3
  • –1/3

Maths-Equations and Inequalities-27481.png

  • Maths-Equations and Inequalities-27482.png
  • 2)
    Maths-Equations and Inequalities-27483.png

  • Maths-Equations and Inequalities-27484.png

  • Maths-Equations and Inequalities-27485.png

Maths-Equations and Inequalities-27487.png
  • –8
  • 8
  • –16
  • 9
What is the sum of the squares of roots of x2 – 3x + 1 = 0?
  • 5
  • 7
  • 9
  • 10

Maths-Equations and Inequalities-27490.png

  • Maths-Equations and Inequalities-27491.png
  • 2)
    Maths-Equations and Inequalities-27492.png

  • Maths-Equations and Inequalities-27493.png

  • Maths-Equations and Inequalities-27494.png
Product of real roots of the equation t2x2 + |x| + 9 = 0
  • Is always positive
  • Is always negative
  • Does not exist
  • None of these
If x be real, the latest value of x2 – 6x + 10 is
  • 1
  • 2
  • 3
  • 10
If sin α and cos α are the roots of the equation pχ2 + qχ + r = 0, then
  • p2 + q2 - 2pr = 0
  • p2 - q2 + 2pr = 0
  • p2 - q2 - 2pr = 0
  • p2 + q2 + 2pr = 0
In ∆ PQR, ∠R = π/2. If tan (P/and tan (Q/are the roots of aχ2 + bχ + c = 0 , a ≠ 0, then
  • b = a + c
  • b = c
  • c = a + b
  • a = B + c
Let α and β be real and z be a complex number. If z2 + αz + β = 0 has two distinct roots on the line Re(z) = 1, then it is necessary that
  • β ϵ (-1, 0)
  • |β| = 1
  • β ϵ (1, ∞)
  • β ϵ (0 , 1)
If (χ - 1)(χ2 - 5χ +< (χ - 1), then χ belongs to
  • (1,∪ (3, ∞)
  • ( -∞,∪ (2, 3)
  • (2, 3)
  • None of the above
The greatest value of x + y + z for possible values of x, y, z such that x3 + y3 + z3 = 1 is
  • 21/3
  • 31/3
  • 32/3
  • 34/3
The least value of a + b + c + d + e + f + g + h for possible values of a, b, c, d,e, f, g, and h satisfying the condition a2/3 + b2/3 + c2/3 + d2/3 + e2/3 + f2/3 + g2/3 + h2/3 = 4 is

  • Maths-Equations and Inequalities-27503.png
  • 2)
    Maths-Equations and Inequalities-27504.png

  • Maths-Equations and Inequalities-27505.png

  • Maths-Equations and Inequalities-27506.png

Maths-Equations and Inequalities-27508.png
  • < 9
  • > 9
  • > 0
  • > 24
If a2 + b2 + c2 = x2 + y2 + z2 = 1, then ax + by + cz is
  • > 1
  • < 1
  • > 0
  • < 0

Maths-Equations and Inequalities-27511.png

  • Maths-Equations and Inequalities-27512.png
  • 2)
    Maths-Equations and Inequalities-27513.png

  • Maths-Equations and Inequalities-27514.png
  • None of these
If a, b, c be +ve and unequal, then
  • > 1
  • < 1
  • > 6
  • < 6
If a be any real number, then
Maths-Equations and Inequalities-27517.png

  • Maths-Equations and Inequalities-27518.png
  • 2)
    Maths-Equations and Inequalities-27519.png

  • Maths-Equations and Inequalities-27520.png

  • Maths-Equations and Inequalities-27521.png
If a, b, c are lengths of the sides of a triangle, then (a + b + c)3 is

  • Maths-Equations and Inequalities-27523.png
  • 2)
    Maths-Equations and Inequalities-27524.png

  • Maths-Equations and Inequalities-27525.png
  • none of these

Maths-Equations and Inequalities-27527.png

  • Maths-Equations and Inequalities-27528.png
  • 2)
    Maths-Equations and Inequalities-27529.png

  • Maths-Equations and Inequalities-27530.png
  • none of these

Maths-Equations and Inequalities-27532.png
  • > 2(a + b + c)
  • > a + b + c
  • > ab + bc + ca
  • none of these
If a, b, c be +ve and in H.P., then an cn is
  • > bn
  • > 2bn
  • < bn
  • < 2bn
If a > 0, b > 0 and a + b = 1. Then a1/3 + b1/3 is
  • > 22/3
  • < 22/3
  • > 42/3
  • < 42/3

Maths-Equations and Inequalities-27536.png

  • Maths-Equations and Inequalities-27537.png
  • 2)
    Maths-Equations and Inequalities-27538.png

  • Maths-Equations and Inequalities-27539.png

  • Maths-Equations and Inequalities-27540.png
If a, b, c are +ve real numbers, then
Maths-Equations and Inequalities-27542.png

  • Maths-Equations and Inequalities-27543.png
  • 2)
    Maths-Equations and Inequalities-27544.png

  • Maths-Equations and Inequalities-27545.png
  • none of these
0:0:1


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