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11th Standard English Medium Maths Subject Basic Algebra Book Back 3 Mark Questions with Solution Part - II

11th Standard

    Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 30

    3 Marks

    10 x 3 = 30
  1. If \(\left( { x }^{ \frac { 1 }{ 2 } }+{ x }^{ -\frac { 1 }{ 2 } } \right) ^{ 2 }=\frac { 9 }{ 2 } \), then find the value of \(\left( { x }^{ \frac { 1 }{ 2 } }-{ x }^{ -\frac { 1 }{ 2 } } \right) \)for x > 1

  2. Prove that \(\sqrt { 3 } \) is an irrational number. (Hint: Follow the method that we have used to prove \(\sqrt { 2 } \notin Q\))

  3. Find two irrational numbers such that their sum is a rational number. Can you find two irrational numbers whose product is a rational number

  4. Solve for x  \(\left| 3-\frac { 3 }{ 4 } x \right| \le \frac { 1 }{ 4 } \)

  5. Solve logx + logx + logx = 11

  6. If a2+b2 = 7ab. Show that log \(\ \frac { a+b }{ 3 } =\frac { 1 }{ 2 } \)  (log a + log b)

  7. Determine the region in the Plane determined by the inequalities.
    \(3x+5y\ge 45,\ x\ge 0,\ y\ge 0\)

  8. Solve the equation \(\sqrt{6-4x-x^2}=x+4\)

  9. Solve x = \(\sqrt{x+20}\) for x ∈ R

  10. Shade the region given by the inequality x ≥ 2.

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