31). Find the sum of \( \Large 15^{3}+16^{3}+....+50^{3} \)
| A). 1614600 |
| B). 1614660 |
| C). 1614670 |
| D). 1615676 |
|
32). Find the square root of \( \Large x^{4}+2x^{2}y^{2}+y^{4} \)
| A). \( \Large x^{2}+y^{2} \) |
| B). \( \Large \left(x+y\right)^{2} \) |
| C). \( \Large x^{2}-y^{2} \) |
| D). None of these |
|
33). Find the square root of \( \Large \left(a^{2}-1\right) \left(a^{2}-2a-3\right) \left(a^{2}-4a+3\right) \)
| A). \( \Large \left(a+1\right) \left(a-1\right) \left(a-3\right) \) |
| B). \( \Large \left(a-1\right) \left(a+3\right) \left(a+1\right) \) |
| C). \( \Large \left(a-1\right) \left(a+1\right) \) |
| D). None of these |
|
34). Which of the following is correct. The squares root of \( \Large 25x^{4}+30x^{3}+19x^{2}+6x+1 \)
| A). \( \Large 5x^{2}-3x-1 \) |
| B). \( \Large 5x^{2}+3x+1 \) |
| C). \( \Large 5x^{2}+6x+1 \) |
| D). \( \Large 5x^{2}-6x+1 \) |
|
35). If \( \Large 25x^{4}+20x^{3}-26x^{2}+ax+b \) is a perfect square, find the value of a and b
| A). a = 12, c = 9 |
| B). a = 12, b = 9 |
| C). a = -12, b = 9 |
| D). a = 6, b = 9 |
|
36). Solve: \( \Large x^{2}-121-0 \), find the value of x.
| A). 11, -11 |
| B). 6, 15 |
| C). 11, 11 |
| D). 12, 11 |
|
37). In a rectangle, the length of the rectangle is 10 mts more than the breadth. If the area of the rectangle is \( \Large 144 m^{2} \), then its perimeter is
| A). 52 mts. |
| B). 54 mts. |
| C). 18 mts. |
| D). 36 mts. |
|
38). Using the formula find the roots of the equation \( \Large 3x^{2}-4x+1=0 \)
| A). \( \Large -1, \frac{1}{3} \) |
| B). \( \Large 1, \frac{1}{3} \) |
| C). \( \Large 2, \frac{2}{3} \) |
| D). 3, 1 |
|
39). If \( \Large \alpha \) and \( \Large \beta \) are the roots of the equation \( \Large x^{2}-7x+12=0 \), then find the value of \( \Large \alpha ^{2}+ \beta ^{2} \)
| A). 25 |
| B). 24 |
| C). 49 |
| D). 12 |
|
40). The sum of the squares of two consecutive even number is 100. Then the numbers are
| A). 4, 6 |
| B). 6, 8 |
| C). 8, 10 |
| D). 10, 12 |
|
