51). If A and B are complementary angles, then the value of \( \Large Sin A cos B + cos A sin B - tan A tan B + 2sec^{2}A - 2cot^{2}B is : \)
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52). A, O, B are three points on a line segment and C is a point not lying on AOB. If ∠ AOC = 40° and OX , OY are the internal and external bisectors of ∠ AOC respectively, then ∠ BOY is :
| A). 70° |
| B). 80° |
| C). 72° |
| D). 68° |
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53). If 4x =sec ϴ and \( \Large \frac{4}{x} \) = tan ϴ, the \( \Large 8 \left(x^{2} - \frac{1}{x^{2}}\right) \) is :
| A). \( \Large \frac{1}{16} \) |
| B). \( \Large \frac{1}{8} \) |
| C). \( \Large \frac{1}{2} \) |
| D). \( \Large \frac{1}{4} \) |
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54). In the following figure, O is the centre of the circle and XO is perpendicular to OY. If the area of the triangle XOY is 32, then the area of the circle is :
| A). \( \Large 64 \pi \) |
| B). \( \Large 256 \pi \) |
| C). \( \Large 16 \pi \) |
| D). \( \Large 32 \pi \) |
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55). The side BC of ∆ ABC is produced to D. If ∠ ACD = 108° and ∠ B= \( \Large \frac{1}{2} \)∠ A,then ∠ A is:
| A). 36° |
| B). 72° |
| C). 108° |
| D). 59° |
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56). Two circles of radii 4 cm and 9 cm respectively touch each other externally at a point and a common tangent touches them at the points P and Q respectively. Then the area of a square with one side PQ is :
| A). 97 sq cm |
| B). 194 sq cm |
| C). 72 sq cm |
| D). 144 sq cm |
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57). If the length of the side PQ of the rhombus PQRS is 6 cm and ∠PQR = 120°, then the length, of QS, in cm is :
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58). If \( \Large x^{4} +\frac{1}{x^{4}=23} \), then the value \( \Large \left(x - \frac{1}{x}\right) \) will be :
| A). 7 |
| B). -7 |
| C). -3 |
| D). 3 |
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59). If\( \Large x + \frac{1}{x} \), the value of \( \Large x^{5}+\frac{1}{x^{5}} \) is :
| A). 123 |
| B). 126 |
| C). 113 |
| D). 129 |
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60). If the average of39, 48, 51, 63, 75, 83, x and 69 is 60 then the value of x is :
| A). 52 |
| B). 53 |
| C). 50 |
| D). 51 |
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