Basic Algebra Three Marks Questions

11th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
    10 x 3 = 30
  1. Solve the quadratic equation 52x-5x+3+125=5x.

  2. Solve \(\sqrt [ 8 ]{{{x}\over{x+3}} } -\sqrt{{{x+3}\over{x}}}=2.\)

  3. A factory kept increasing its out-put by the same percentage every year. Find the percentage, if it is known that the output has doubled in the last two years.

  4. Find the value of log2 \(\left({{\sqrt [ 3 ]{4 } }\over{4^2\sqrt{8}}} \right).\)

  5. Find x if \({{1}\over{2}}\) log10 \((11+4\sqrt{7})\) = log10 (2+x).

  6. Solve 23x<100 when (i) x is a natural number (ii) x is an integer.

  7. Prove that \(log2+16log\frac { 16 }{ 15 } +12log\frac { 25 }{ 24 } +7log\frac { 81 }{ 80 } =1\)

  8. A plumber can be paid according to the following schemes: In the first scheme he will be paid rupees 500 plus rupees 70 per hour, and in the second scheme he will pay rupees 120 per hour. If he works x hours then for what value of x does the first scheme give better wages?

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

  10. Find a quadratic polynomial f(x) such that, f(0)=1; f(-2)=0 and f(1)=0.

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