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12th Standard Maths Theory of Equations English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021

12th Standard

    Reg.No. :
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Maths

Time : 00:10:00 Hrs
Total Marks : 10

    Answer all the questions

    10 x 1 = 10
  1. If f and g are polynomials of degrees m and n respectively, and if h(x) =(f 0 g)(x), then the degree of h is

    (a)

    mn

    (b)

    m+n

    (c)

    mn

    (d)

    nm

  2. The polynomial x3-kx2+9x has three real zeros if and only if, k satisfies

    (a)

    |k|≤6

    (b)

    k=0

    (c)

    |k|>6

    (d)

    |k|≥6

  3. If x3+12x2+10ax+1999 definitely has a positive zero, if and only if

    (a)

    a≥0

    (b)

    a>0

    (c)

    a<0

    (d)

    a≤0

  4. The number of positive zeros of the polynomial \(\overset { n }{ \underset { j=0 }{ \Sigma } } { n }_{ C_{ r } }\)(-1)rxr is

    (a)

    0

    (b)

    n

    (c)

    < n

    (d)

    r

  5. The quadratic equation whose roots are ∝ and β is

    (a)

    (x - ∝)(x -β) =0

    (b)

    (x - ∝)(x + β) =0

    (c)

    ∝+β=\(\frac{b}{a}\)

    (d)

    ∝.β=\(\frac{-c}{a}\)

  6. If x is real and \(\frac { { x }^{ 2 }-x+1 }{ { x }^{ 2 }+x+1 } \) then

    (a)

    \(\frac{1}{3}\) ≤k≤

    (b)

    k≥5

    (c)

    k≤0

    (d)

    none

  7. The equation \(\sqrt { x+1 } -\sqrt { x-1 } =\sqrt { 4x-1 } \) has

    (a)

    no solution

    (b)

    one solution

    (c)

    two solution

    (d)

    more than one solution

  8. For real x, the equation \(\left| \frac { x }{ x-1 } \right| +|x|=\frac { { x }^{ 2 } }{ |x-1| } \) has

    (a)

    one solution

    (b)

    two solution

    (c)

    at least two solution

    (d)

    no solution

  9. If ∝, β,૪ are the roots of 9x3-7x+6=0, then ∝ β ૪ is __________

    (a)

    \(\frac{-7}{9}\)

    (b)

    \(\frac{7}{9}\)

    (c)

    0

    (d)

    \(\frac{-2}{3}\)

  10. If ax2 + bx + c = 0, a, b, c E R has no real zeros, and if a + b + c < 0, then __________

    (a)

    c>0

    (b)

    c<0

    (c)

    c=0

    (d)

    c≥0

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