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Theory of Equations Model Question Paper

12th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
    5 x 1 = 5
  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. A polynomial equation in x of degree n always has

    (a)

    n distinct roots

    (b)

    n real roots

    (c)

    n imaginary roots

    (d)

    at most one root

  3. 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

  4. 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

  5. If (2+√3)x2-2x+1+(2-√3)x2-2x-1=\(\frac { 2 }{ 2-\sqrt { 3 } } \) then x=

    (a)

    0,2

    (b)

    0,1

    (c)

    0,3

    (d)

    0, √3

  6. 5 x 2 = 10
  7. Show that the equation 2x2−6x+7=0 cannot be satisfied by any real values of x.

  8. If x2+2(k+2)x+9k=0 has equal roots, find k.

  9. Examine for the rational roots of x8-3x+1=0

  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. Form a polynomial equation with integer coefficients with \(\sqrt { \frac { \sqrt { 2 } }{ \sqrt { 3 } } } \) as a root.

  15. Find the number .of real solu,tlons of sin (ex) -5x + 5-x

  16. Solve: 2x+2x-1+2x-2=7x+7x-1+7x-2

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

  18. 4 x 5 = 20
  19. Form the equation whose roots are the squares of the roots of the cubic equation x3+ax2+bx+c = 0.

  20. Find a polynomial equation of minimum degree with rational coefficients, having \(\sqrt{5}\)\(\sqrt{3}\) as a root.

  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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