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Theory of Equations Model Question Paper 1

12th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
    5 x 1 = 5
  1. According to the rational root theorem, which number is not possible rational root of 4x7+2x4-10x3-5?

    (a)

    -1

    (b)

    \(\frac { 5 }{ 4 } \)

    (c)

    \(\frac { 4 }{ 5 } \)

    (d)

    5

  2. 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

  3. 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

  4. Let a > 0, b > 0, c >0. h n both th root of th quatlon ax2+b+C= 0 are

    (a)

    real and negative

    (b)

    real and positive

    (c)

    rational numb rs

    (d)

    none

  5. If ∝, β, ૪ are the roots of the equation x3-3x+11=0, then ∝+β+૪ is __________.

    (a)

    0

    (b)

    3

    (c)

    -11

    (d)

    -3

  6. 5 x 2 = 10
  7. Find a polynomial equation of minimum degree with rational coefficients, having 2-\(\sqrt{3}\)i as a root.

  8. Show that the equation 2x2−6x+7=0 cannot be satisfied by any real values of x.

  9. Show that the equation x9-5x5+4x4+2x2+1=0 has atleast 6 imaginary solutions.

  10. Find value of a for which the sum of the squares of the equation x2 - (a- 2) x - a-1=0 assumes the least value.

  11. Find x If \(x=\sqrt { 2+\sqrt { 2+\sqrt { 2+....+upto\infty } } } \)

  12. 5 x 3 = 15
  13. Find the sum of the squares of the roots of ax4+bx3+cx2+dx+e = 0.

  14. Find the condition that the roots of x3+ax2+bx+c = 0 are in the ratio p:q:r.

  15. Solve the equation 9x-36x2+44x-16=0 if the roots form an arithmetic progression.

  16. Find the number of positive integral solutions of (pairs of positive integers satisfying) x2 - y2 =353702.

  17. Solve: \({ (5+2\sqrt { 6 } ) }^{ { x }^{ 2 }-3 }+{ (5-2\sqrt { 6 } ) }^{ { x }^{ 2 }-3 }=10\)

  18. 4 x 5 = 20
  19. Solve the equation (x-2)(x-7)(x-3)(x+2)+19=0

  20. Solve the equation (2x-)(6x-1)(3x-2)(x-12)-7=0

  21. If a, b, c, d and p are distinct non-zero real numbers such that (a2+b2+c2) p2-2 (ab+bc+cd) p+(b2+c2+d2)≤ 0 the n. Prove that a,b,c,d are in G.P and ad=bc

  22. Solve: (2x2 - 3x + 1) (2x2 + 5x + 1) = 9x2.

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