11). In the given figure, \( \Large \triangle ABC \) is an equilateral triangle. O is the point of intersection of the medians. If AB = 6 cm, then OB is equal to
| A). \( \Large 3\sqrt{3}cm \) |
| B). \( \Large 2\sqrt{3}cm \) |
| C). \( \Large \sqrt{3}cm \) |
| D). \( \Large \frac{\sqrt{3}}{2}cm \) |
|
12). If an isosceles right triangle has an area 200 sq. cm, then area of a square drawn on hypotenuse is
| A). 400 sq. cm |
| B). \( \Large 400 \sqrt{2} cm \) |
| C). 800 sq. cm. |
| D). \( \Large 800 \sqrt{2} cm \) |
|
13). 
\( \Large \triangle ABC\ and\ PQR \) are congruent if
| A). \( \Large \angle ABC = \angle QPR \) and \( \Large \angle BCA = \angle QRP \) |
| B). \( \Large AB = PQ,\ AC=PR \) and \( \Large \angle ABC = \angle PQR \) |
| C). \( \Large AB= PQ,\ \angle ABC = \angle PQR \) and \( \Large \angle BAC = \angle PRQ \) |
| D). \( \Large BC = QR,\ AC = PR \) and \( \Large \angle ACB = \angle PRQ\) |
|
14). \( \Large \triangle \)PQR and \( \Large \triangle \)LMN are similar. If 3 PQ = LM and MN = 9 cm, then QR is equal to
| A). 3 cm |
| B). 6 cm |
| C). 9 cm |
| D). 12 cm |
|
15). If D, E, F are mid-points of the sides BC, CA and AB respectively of a triangle ABC, then which one of the following is not correctly matched?
| A). If G is centroid of the \( \Large \triangle ABC \), then AG : GD = 2 : 1 |
| B). If G is centroid of the \( \Large \triangle ABC \), then G is centroid of the \( \Large \triangle DEF \). |
| C). If \( \Large \ \angle A = 90 ^{\circ} \), then A is orthocentre of the \( \Large \triangle ABC \). |
| D). If \( \Large \ \angle A > 90 ^{\circ} \), then orthocentre of the \( \Large \triangle ABC \) lies inside the \( \Large \triangle ABC \). |
|
16). If lengths of two sides of a triangle are given, then its area is greater when
| A). both the sides are greater than the third |
| B). angle between sides is a right angle. |
| C). angle between sides is an obtuse angle. |
| D). angle between sides is an acute angle. |
|
17). Consider following statements relating to the congruency of two right-angled triangles.
1. Equality of two sides of one triangle with same two sides of the second makes the triangle congruent.
2. Equality of hypotenuse and a side of one triangle with the hypotenuse and a side of the second respectively makes the triangles congruent.
3. Equality of hypotenuse and an acute of triangle with the hypotenuse and an angle of the second respectively makes the triangles congruent.
Of these statements
| A). 1, 2 and 3 are correct |
| B). 1 and 2 are correct |
| C). 1 and 3 are correct |
| D). 2 and 3 are correct |
|
18). If \( \Large \triangle ABC \) is a right angled triangle with \( \Large \angle A = 90 ^{\circ} \), AN is perpendicular to BC, BC =12cm and AC = 6cm, then the ratio of \( \Large \frac{area\ of \ \triangle ANC}{area\ of\ \triangle ABC} \) is
| A). 1 : 2 |
| B). 1 : 3 |
| C). 1 : 4 |
| D). 1 : 8 |
|
19). In A PQR, the medians QM and RN intersect at O. PO meets QR in L. If OL is 2.5 cm, then PL is equal to
| A). 5 cm |
| B). 10 cm |
| C). 2.5 cm |
| D). 7.5 cm |
|
20). If side of an equilateral triangle is \( \Large 20 \sqrt{3} cm \), then numerical value of the radius of the circle circumscribing the triangle is
| A). 20 cm |
| B). \( \Large 20 \sqrt{3} cm \) |
| C). \( \Large 20 \pi cm \) |
| D). \( \Large \frac{20}{ \pi } cm \) |
|
