61). If (x-2) and (x+3) are the factors of the equation x2 + \( \large k_{1} \) x + \( \large k_{2} \) = 0, then what are the values of \( \large k_{1} \) and \( \large k_{2} \) ?
| A). \( \large k_{1} \)=6,\( \large k_{2} \)=-1 |
| B). \( \large k_{1} \)=1,\( \large k_{2} \)=-6 |
| C). \( \large k_{1} \)=1,\( \large k_{2} \)=6 |
| D). \( \large k_{1} \)=-6,\( \large k_{2} \) =1 |
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62). If (x-y)= 7. then what is the value of\( \large (x-15)^{3} \)-\( \large (y-8)^{3} \) ?
| A). 0 |
| B). 343 |
| C). 392 |
| D). 2863 |
|
63). If x-y-\( \large \sqrt{18} \) = -1 and x+y-3 \( \large \sqrt{2} \) = 1 then What is the value of 12xy(x2-y2)?
| A). 0 |
| B). 1 |
| C). 512\( \large \sqrt{2} \) |
| D). 612\( \large \sqrt{2} \) |
|
64). If \( \Large \frac{p}{q} \)=\( \Large \frac{r}{s} \)=\( \Large \frac{t}{u} \)=\( \large \sqrt{5} \), then what is the value of \( \Large \left[ \left(\frac{3p^{2} + 4r^{2} + 5t^{2}}{3q^{2} + 4s^{2} + 5u^{2}}\right) \right] \)
| A). \( \Large \frac{1}{5} \) |
| B). 5 |
| C). 25 |
| D). 60 |
|
65). In triangle ABC, a lie is drawn from the vertex A to a point D on BC. If BC =9cm and DC = 3cm, then what is the ratio of the areas of triangle ABD and triangle ADC respetively?
| A). 1:1 |
| B). 2:1 |
| C). 3:1 |
| D). 4:1 |
|
66). PQR is a right angled triangle in which \( \Large \angle{R} = 90^{o}, \)If \( \Large Rs \perp PQ \), PR = 3cm and RQ = 4cm, then what is the value of RS (in cm) ?
| A). \( \Large \frac{12}{5} \) cm |
| B). \( \Large \frac{36}{5} \) cm |
| C). 5cm |
| D). 2.5cm |
|
67). In triangle POR, A is the point of intersection of all the altitudes an B is the point of intersection of all the angle bisector of the triangle. If \( \Large \angle{PBR} = 105^{o} \), then what is the value of \( \Large \angle {PAR} \) ( in degree)?
| A). \( \Large 60^{o} \) |
| B). \( \Large 100^{o} \) |
| C). \( \Large 105^{o} \) |
| D). none of the above |
|
68). If there are four lines in a plane, then what cannot be the number of points of intersection of these lines?
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69). What is the simplified value of cosec 2A + cot 2A?
| A). sec A |
| B). sec ( \( \Large \frac{A}{2} \) ) |
| C). cot A |
| D). \( \large cot^{2} \) A |
|
70). If \( \Large A = 30^{o}, B = 60^{o} \ and \ C = 135^{o} \), then what is the value of \( \large sin^{3} \)+ \( \large cos^{3} \)+\( \large tan^{3} \)- 3 sin A cos B tan C?
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