#### 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.