Questions covered in Standard

Review the question prompts below before starting the timed test. Try each problem independently, then use the interactive test to record your answers and review the worked solutions.

1. If $\left(\frac{1+i}{1-i}\right)^x = 1$, then the smallest positive integer value of $x$ is
2. How many words can be formed from the letters of the word 'DAUGHTER' so that the vowels always come together?
3. The coefficient of $x^6$ in the expansion of $(1+x)^{10}$ is
4. If the sum of $n$ terms of an A.P. is $3n^2 + 5n$, then which of its terms is 164?
5. The solution of the system of inequalities $2x - 3 < 7$ and $2x > -4$ is
6. Solve the quadratic equation $x^2 + 3x + 9 = 0$.
7. In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
8. Find the sum of all 2-digit numbers which when divided by 3 yield 1 as remainder.
9. Find the term independent of $x$ in the expansion of $(\frac{3}{2}x^2 - \frac{1}{3x})^6$.
10. Solve the system of inequalities graphically: $3x + 2y \le 12, x \ge 1, y \ge 2$.
11. If $\frac{a^n + b^n}{a^{n-1} + b^{n-1}}$ is the Arithmetic Mean between $a$ and $b$, then find the value of $n$.
12. Case Study: A manufacturer has 600 litres of a 12% solution of acid. How many litres of a 30% acid solution must be added to it so that acid content in the resulting mixture will be more than 15% but less than 18%?