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

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. Classify each element of \(\left\{ \sqrt { 7 } ,\frac { -1 }{ 4 } ,0,3.14,4,\frac { 22 }{ 7 } \right\} \) as a member of N, Q, R, -Q or Z.

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

  4. Are there two distinct irrational numbers such that their difference is a rational number? Justify.

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

  6. Find a positive number small than \(\frac { 1 }{ { 2 }^{ 1000 } } \). Justify.

  7. Simplify by rationalising the denominator \(\frac { 7+\sqrt { 6 } }{ 3-\sqrt { 2 } } \)

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

  9. Compute \({ log }_{ 9 }^{ 27 }-{ log }_{ 27 }^{ 9 }\)

  10. Solve logx + logx + logx = 11

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