61). What is equals to \( cosec(75^{\circ} + \theta) - sec(15^{\circ} - \theta) - tan(55^{\circ} + \theta) + cot(35^{\circ} - \theta) \)
| A). -1 |
| B). 0 |
| C). 1 |
| D). 3/2 |
|
62). If \( \sin \theta + 2 \cos \theta = 1\), where \( \large 0 < \theta < \frac{\pi}{2} \), then what is \( 2 \sin \theta -\cos \theta\) equal to ?
| A). \( -1\) |
| B). \( \Large \frac{1}{2} \) |
| C). \( 2\) |
| D). \( 1\) |
|
63). If \( \tan 8 \theta = \cot 2\theta \), where \( \large 0 < 8 \theta < \frac{\pi}{2} \), then what is the value of \( \tan 5\theta \)?
| A). \( \Large \frac{1}{\sqrt{3}} \) |
| B). \( 1\) |
| C). \( \sqrt{3}\) |
| D). \( 0\) |
|
64). A square is inscribed in a circle of diameter 2a and another square is circumscribing the circle. The difference between the areas of the outer and inner squares is
| A). \( a^{2}\) |
| B). \(2a^{2} \) |
| C). \( 3a^{2}\) |
| D). \( 4a^{2}\) |
|
65). The area of a sector of a circle of radius \( 36 cm\) is \( 72\pi cm^{2}\)The length of the corresponding arc of the sector is
| A). \( \pi cm\) |
| B). \( 2\pi cm\) |
| C). \( 3\pi cm\) |
| D). \( 4\pi cm\) |
|
66). A cone of radius r cm and height h cm is divided into two parts by drawing a plane through the middle point of its height and parallel to the base. What is the ratio of the volume of the original cone to the volume of the smaller cone?
| A). 4 : 1 |
| B). 8 : 1 |
| C). 2 : 1 |
| D). 6 : 1 |
|
67). Which one of the following is a Pythagorean triple in which one side differs from the hypotenuse by two units ?
| A). \( \left(2n + 1,4n,2n^{2} + 2n\right)\) |
| B). \( \left( 2n, 4n, n^{2}+1\right)\) |
| C). \( \left( 2n^{2},2n,2n+1\right)\) |
| D). \( \left( 2n,n^{2}-1,n^{2}+1\right)\) |
|
68). A cube has each edge 2 cm and a cuboid is 1 cm long, 2 cm wide and 3 cm high. The paint in a certain container is sufficient to paint an area equal to \( 54 cm^{2}\)
Which one of the following is correct?
| A). Both cube and cuboid can be painted |
| B). Only cube can be painted |
| C). Only cuboid can be painted |
| D). Neither cube nor cuboid can be painted |
|
69). ABC is a triangle right-angled at A where AB = 6 cm and AC = 8 cm. Semicircles are drawn (outside the triangle) on AB, AC and BC as diameters which enclose areas x, y and z square units respectively. What is \( x+y-z\) equal to?
| A). \( 48 cm^{2}\) |
| B). \( 32 cm^{2}\) |
| C). 0 |
| D). None of these |
|
70). The three sides of a triangle are 15, 25 and \( x\) units. Which one of the following is correct?
| A). \(10\)<\( x\)<\( 40\) |
| B). \(10\)\( \le\)\( x\)\( \le\)\( 40\) |
| C). \(10\)\( \le\)\( x\)<\( 40\) |
| D). \(10\)<\( x\)\( \le\)\( 40\) |
|
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