11). Area of the shaded portion in the given figure is \( \Large \left(x = \frac{22}{7}\right) \) 
| A). 42 sq. cm |
| B). 48 sq. cm |
| C). 76 sq. cm |
| D). 152 sq. cm |
|
12). A circle A has a radius of 3 cm, two circles B and C have a radius each equal to diameter of the circle A. The radius of a circle D which has an area equal to the total area of A, B and C, is
| A). 9 cm |
| B). 12 cm |
| C). 15 cm |
| D). 18 cm |
|
13). If straight line \( \Large y = x+c \) is a tangent to the circle \( \Large x^{2}+y^{2}=1 \), then c is equal to
| A). \( \Large \pm \sqrt{2} \) |
| B). \( \Large \pm 2 \) |
| C). \( \Large \pm 1 \) |
| D). \( \Large \pm 3 \) |
|
14). The equation, \( \Large ax^{2}+2hxy+b^{2}+2gx+2fy+c=0 \) represents a circle if
| A). \( \Large h^{2} = ab \) |
| B). \( \Large a = b \) |
| C). \( \Large h^{2}+ab = 0 \) |
| D). \( \Large a = b\ and\ h = 0 \) |
|
15). Consider following statements relating to the chords and arcs of a circle :
1. Equal chords are equidistant from the centre.
2. Between two arcs, the one that subtends a larger angle at the centre is larger.
3. If two arcs are of the same length, so are the chords joining their extremities.
Of these statements :
| A). 1 and 2 are correct |
| B). 2 and 3 are correct |
| C). 1 and 3 are correct |
| D). 1, 2 and 3 are correct |
|
16). Sum of the diamters of two circles is 35 cm and difference of their circumferences is 22 cm. Then area of the smaller circle will be
| A). 121 sq. cm |
| B). 144 sq. m |
| C). 154 sq. cm |
| D). 308 sq. m |
|
17). The area of the given figure is 
| A). \( \Large \frac{3}{4} \pi r^{2} \) |
| B). \( \Large \frac{1}{4} \pi r^{2} \) |
| C). \( \Large \pi r^{2} \) |
| D). \( \Large 3 \pi r^{2} \) |
|
18). Chords AB and CD of a circle intersect at O. If AO = 8 cms, BO = 9 cms and CO = 2 DO, then length of DO (in cms) is
| A). 5.67 approx. |
| B). 5 |
| C). 6 |
| D). 6.17 (approx) |
|
19). If A, B be points of contact of the tangents drawn to a circle C with centre O and radius r cm from a point P Outside C, then which one of the following is correct ?
| A). If M is mid-point of AB, then OM + MP > OP. |
| B). If M is mid-point of AB, then AMP is an acute angled triangle. |
| C). If M is mid-point of AB, then AM is perpendicular to OP. |
| D). Either \( \Large \triangle AOP \) is obtuse-angled or \( \Large \triangle BOP \) is obtuse-angled. |
|
20). If C be a circle with centre O and radius 5 cm, then locus of mid-points of equal chords of C each of length 6 cm is a
| A). concentric circle whose radius is 7 cm. |
| B). concentric circle whose radius is 4 cm. |
| C). straight line parallel to some chord of length of 6 cm. |
| D). straight line perpendicular to some chord of length of 6 cm. |
|
