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Theory of Equations 3 Mark Creative Question Paper With Answer Key

12th Standard

    Reg.No. :
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Maths

Time : 00:30:00 Hrs
Total Marks : 33

     3 Marks

    11 x 3 = 33
  1. Find the number of real solutions of sin (ex) -5x + 5-x

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

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

  4. Solve: (x-1)4+(x-5)= 82

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

  6. Solve \(x^{4}-4 x^{2}+8 x+35=0\), given \(2+i \sqrt{3}\) is a root.

  7. Solve \(x^{4}-5 x^{3}+4 x^{2}+8 x-8=0\), given that one of the roots is \(1-\sqrt{5} \) .

  8. Solve \(27 x^{3}+42 x^{2}-28 x-8=0\), given that its roots are in geometric progression.

  9. Solve the equation \(15 x^{3}-23 x^{2}+9 x-1=0\) whose roots are in harmonic progression

  10. Calculate the sum of the cubes of the roots of \(x^{4}+2 x+3=0\)

  11. lf \(\alpha, \beta, \gamma\) are the roots of the equation \(x^{3}+a x^{2}+b x+c=0\). Form the equation whose roots are \(\alpha \beta, \beta \gamma, \gamma \alpha .\)

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