JEE Questions for Maths Equations And Inequalities Quiz 4 - MCQExams.com

If α and β are the roots of the equation χ2 - pχ + r = 0 and α/2, 2β are the roots of the equation χ2 - qχ + r = 0. Then, the value of r is
  • 2/9 (p - q) (2q - p)
  • 2/9 (q- p) (2p - q)
  • 2/9 (q - 2p) (2q - p)
  • 2/9 (2p - q) (2q - p)
If one root of the quadratic equation aχ2 + bχ + c = 0 is equal to nth power of the other root, then the value of (acn)1/(n+1) + (aχnc)1/(n+1) is equal to
  • b
  • - b
  • 1/ (bχn+1)
  • - (1/bχn+1)
If α and β are the roots of χ2 + 5χ + 4 = 0, then the equation, whose roots are (α+ 2)/2 and (β+2)/2, is
  • 9χ2 + 3χ + 2 = 0
  • 9χ2 - 3χ - 2 = 0
  • 9χ2 + 3χ - 2 = 0
  • 9χ2 - 3χ + 2 = 0
If sec α and cosec α are the roots of the equation χ2 + pχ + q = 0
  • p2 = p + 2q
  • q2 = p + 2q
  • p2 = q(q +2)
  • q2 =p(p + 2)
  • p2 = q(q - 2)
If α and β are the roots of the equation χ2 + pχ + q = 0 and the sum
Maths-Equations and Inequalities-27294.png
  • log(χ2 + pχ + q)
  • log(χ2 - pχ + q)
  • log(1 + pχ + qχ2)
  • log(1 - pχ + qχ2)
  • log(χ2 qχ + q)
If α and αχ2, are the roots of χ2 + χ + 1 = 0, then the equation, whose roots are α31 and α62 , is
  • χ2 - χ + 1 = 0
  • χ2 + χ - 1 = 0
  • χ2 + χ + 1 = 0
  • χ60 + χ30 + 1 = 0
If α and β are the roots of the equation lχ2 + mχ + n = 0, then the equation, whose roots are α3β and αβ3 , is
  • l4χ2 - nl(m2 - 2nl)χ + n4 = 0
  • l4χ2 + nl(m2 - 2nl)χ + n4 = 0
  • l4χ2 + nl(m2 - 2nl)χ - n4 = 0
  • l4χ2 - nl(m2 + 2nl)χ+ n4 = 0
If one root is square of the other root of the equation χ2 + pχ + q = 0, then the relation bewteen p and q is
  • p3 - (3p - 1)q + q2 = 0
  • p3 - q(3p ++ q2 = 0
  • p3 + q(3p -+ q2 = 0
  • p3 - q(3p -+ q2 = 0
If α ,β and γ are the roots of χ3 - 2χ2 + 3χ - 4 = 0, then the value of α2β2+ β2 γ2 + γ2α2
  • - 7
  • - 5
  • - 3
  • 0
If α and β are the roots of the equation aχ2 + bχ + c = 0, then the equation, whose roots are 2α + 3β and 3α + 2β, is
  • acχ2 + (a + c)bχ- (a + c)2 = 0
  • acχ2 - (a + c)bχ- (a + c)2 = 0
  • abχ2 - (a + b)cχ- (a + c)2 = 0
  • None of these
If the difference between the roots of χ2 + aχ - b = 0 is equal to the difference between the roots of χ2 - pχ + q = 0, then a2 - p2 in terms of b and q is equal
  • -4(b + q)
  • 4(b + q)
  • 4(b - q)
  • 4(q - b)
If α ,β and γ are the roots of the equation χ3 - 7χ + 7 = 0, then
Maths-Equations and Inequalities-27302.png
  • 7/3
  • 3/7
  • 4/7
  • 7/4
If the roots of the quadratic equation χ2 + pχ + q = 0 are tan 300 and tan 150 respectively, then the value of 2 + q - p is
  • 3
  • 0
  • 1
  • 2
If α ,β and γ are the roots of the equation 2χ3 + 3χ2 + 6χ+ 1 = 0, the α2 + β2 +γ2 is equal to
  • - (15/40)
  • 15/4
  • 9/4
  • 4
If α1 , α2 , and α3 are the roots of the equation χ4 + (2 √3)χ2 + 2 + √3 = 0, then the value of (1 - α1) (1 - α2) (1 - α3) (i- 1 - α4) is
  • 1
  • 4
  • 2 + √3
  • 5
  • 0
If a, b, and c are in geometric progression and the roots of the equation aχ2 + 2bχ + c = 0 are α , β and those of cχ2 + 2bχ + a = 0 are γ, δ, then
  • α ≠ β ≠ γ ≠ δ
  • α ≠ β and γ ≠ δ
  • aα = aβ = cγ = cδ
  • α = β and γ ≠ δ
  • α ≠ β and γ - δ
If α ,and β are the roots of the equation 6 χ2 - 5χ + 1 = 0, then the value of tan -1 α + tan-1 β is
  • 0
  • π/4
  • 1
  • /2
If ω and ω2 are the two imaginary cube roots of unity, then the equation, whose roots are aω317 and aω382, is
  • χ2 + a2χ + a2 = 0
  • χ2 + a2χ + a = 0
  • χ2 - aχ + a2 = 0
  • χ2 - a2χ + a = 0
If α ≠ β and a2 = 5α - 3, β2 = 5β - 3, then the equation having α/β and β/α as its roots is
  • 3χ2 + 19χ + 3 = 0
  • 3χ2 - 19χ + 3 = 0
  • 3χ2 - 19χ - 3 = 0
  • 3χ2 + 16χ + 1 = 0
The quadratic equation, whose roots are sin2 180 and cos2 360 , is
  • 16χ2 - 12χ + 1 = 0
  • 16χ2 + 12χ + 1 = 0
  • 16χ2 - 12χ - 1 = 0
  • 16χ2 + 10χ + 1 = 0
If a , c ≠ 0 and α, β are the roots of the equation aχ2 + bχ + c = 0, then the quadratic equation with 1/α and 1/β as its roots, is
  • χ2/a + χ/b + 1/c = 0
  • cχ2/bχ + a = 0
  • bχ2 + cχ + a = 0
  • aχ2 + cχ + b = 0
If sin θ + cos θ = h, then the quadratic equation having sin θ and cos θ as its roots, is
  • χ2 - hχ + (h2 -= 0
  • 2χ2 - 2hχ + (h2 -= 0
  • χ2 - hχ + 2(h2 -= 0
  • χ2 - 2hχ + (h2 -= 0
Let α and β be the roots of the equation aχ2 + bχ + c = 0 and ∆ = b2 - 4ac . If α + β, α2 + β2 and α3 + β3 are in GP, then
  • ∆ ≠ 0
  • b/∆ = 0
  • c∆ = 0
  • bc ≠ 0
Let α and β are the roots of equation 2χ2 - (p + 1)χ + (p -= 0. If α - β = αβ, then what is the value of p ?
  • 1
  • 2
  • 3
  • - 2
If the sum of two roots of χ3 + pχ2 - qχ + r = 0 is zero, then pq is equal to
  • - r
  • r
  • 2r
  • - 2r
If α and β are the roots of the equation pχ2 + qχ + r = 0, p ≠ 0. If p, q and r are in AP and 1/α + 1/β = 4, then the value of |α -β|is
  • √61/9
  • 2√17/9
  • √34/9
  • 2√13/9
The value of χ such that 32χ - 2(3χ+2) + 81 = 0 is
  • 1
  • 2
  • 3
  • 4
  • 5
The equation whose roots are the squares of the roots of the equation 2χ2 + 3χ + 1 = 0, is
  • 4χ2 + 5χ + 1 = 0
  • 4χ2 - χ + 1 = 0
  • 4χ2 - 5χ - 1 = 0
  • 4χ2 - 5χ + 1 = 0
In ∆ABC, tan A and tan B are the roots of pq(χ2 += r2χ. Then ∆ABC is
  • a right angled triangle
  • an cute angled triangle
  • an obtuse angled triangle
  • an equilateral triangle
If α and β are the roots of the quadratic equation χ2 + pχ + q = 0, then the values of α3 + β3 and α4 + α2β2 + β4 are respectively
  • 3pq - p3 and p4 -3p2q + 3q2
  • -p(3q - pand (p2 - q) (p2 + 3q)
  • pq - 4 and p4 - q4
  • 3pq - p3 and (p2 - q)(p2 - 3q)
The number of solution(s) of the equation
Maths-Equations and Inequalities-27322.png
  • 2
  • 0
  • 3
  • 1
The real number K for which the equation, 2χ3 + 3χ + k = 0 has two distinct real roots in [0,1]
  • lies between 1 and 2
  • lies between 2 and 3
  • lies between - 1 and 0
  • does not exist
The number of integral values of b, which the equation χ2 + bχ - 16 has integral roots , is
  • 2
  • 3
  • 4
  • 5
  • 6
If a, b and c are real numbers, such that a + 2b + 4c = 0. Then, the equation aχ2 + bχ + c = 0
  • has both the roots compplex
  • has its roots lying within - 1 < χ < 0
  • has one of roots equal to 1/2
  • has its roots lying within 2 < χ < 6
If one of the roots of 2χ2 - cχ + 3 = 0 is 3 and another equation 2χ2 - cχ + d = 0 has equal roots, where c and d are real numbers, then d is equal to
  • 3
  • 49/8
  • 8/49
  • - 3
The number of real values of χ which satisfy the equation
Maths-Equations and Inequalities-27327.png
  • 2
  • 1
  • infinite
  • Zero
The quadratic equations χ2 + 15 |χ| + 14 = 0 has
  • only positive solutions
  • only negative solutions
  • no solution
  • both positive and negative solutions
If (3/+ (7/is a solution of the equation aχ2 - 6χ + b = 0, where a and b are real numbers, then the value of a + b is
  • 10
  • 22
  • 30
  • 29
  • 31
The solution of the equation
Maths-Equations and Inequalities-27331.png
  • 3 ± 2√2
  • ± 1
  • ± 3√3 , ± 2√2
  • ± 7 , ± √3
  • ± 3 , ± √7
The equation 3/4 (log2 χ)2 + log2 χ - (5/= log χ√2 has
  • atleast one real solution
  • exactly three real solutions
  • exactly one irrational sloution
  • complex roots
If the roots of the quadratic equation χ2 - 4χ - log3 a = 0 are real, then the least value of a is
  • 81
  • 1/81
  • 1/64
  • None of these
If p, q and r are positive and are in AP, then the roots of the quadratic equation pχ2 + qχ + r = 0 are complex for

  • Maths-Equations and Inequalities-27335.png
  • 2)
    Maths-Equations and Inequalities-27336.png
  • all p and r
  • no p and r
If the equation (a + 1)χ2 - (a + 2)χ + (a += 0 has roots equal in magnitude but opposite in sign, then the roots of the equation are
  • ± a
  • ± (1/a
  • ± (3/2)a
  • ± 2a
If the difference between the roots of the equation χ2 + aχ + 1 = 0 is less than √5, then the set of possible values of a is
  • (- 3 , 3 )
  • (- 3 ,∞ )
  • (3 , ∞ )
  • (- ∞, - 3)
If (sin a)χ2 + (sin a)χ + (1 - cos a) = 0, then the value of a for which roots of this equation are real and distinct, is
  • (0 , 2 tan-1 1/4 )
  • (0 , 2π/3)
  • (0 , π)
  • (0 , 2π)
If bχ2 ≥ 4ac for the equation aχ4 + bχ2 + c = 0, then all the roots of the equation will be real positive, 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
Both the roots of the equation (χ - a) ( χ - b) + (χ - b) (χ - c) + (χ - c) (χ - a) = 0 are always
  • positive
  • negative
  • real
  • imaginary
The solution of the equation 2 χ3 - χ2 - 22 χ - 24 = 0 when two of the roots are in the ratio 3 : 4, is
  • 3, 4, (1/2)
  • -(3/, - 2, 4

  • Maths-Equations and Inequalities-27343.png

  • Maths-Equations and Inequalities-27344.png
If χ2/3 - 7χ1/3 + 10 = 0, then the value ox χ is
  • 125
  • 8
  • ∅
  • 125, 8
If a, b and c are the sides of ∆ABC such that a ≠ b ≠ c and χ2 -2(a + b + c )χ + 3⋋(a + b + ca ) = 0 has real roots, then
  • ⋋ < (4/3)
  • ⋋ > (5/3)

  • Maths-Equations and Inequalities-27347.png

  • Maths-Equations and Inequalities-27348.png
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