Q2. The three sides of a triangle measure 6 cm, 8 cm and 10 cm respectively. A rectangle equal in area to the triangle has a length of 8 cm. The perimeter of the rectangle is:
(a) 11 cm
(b) 22 cm
(c) 16 cm
(d) None of these
Q3. A rectangular enclosure 40 m × 36 m has a horse tethered to a corner with a rope of 14 m in length. What is the ratio of the respective areas it can graze, if it is outside the enclosure and if it is inside the enclosure?
(a) 2 : 1
(b) 2 : 3
(c) 1 : 4
(d) 3 : 1
Q4. A quadrilateral is inscribed in a circle. If an angle is inscribed in each of the segments outside the quadrilateral, then what is the sum of the four angles?
(a) 270°
(b) 360°
(c) 540°
(d) 720°
Q6. The volume of spheres are proportional to the cubes of their radii. Two spheres of the same material weigh 6.3 kg and 2.7 kg and the radius of the smaller one is 2 cm. If the two were melted down and formed into a single sphere, what would be its radius(approx..)?
(a) 4 cm
(b) 4.3 cm
(c) 3 cm
(d) 2.6 cm
Q7. There are two regular polygons with the number of sides in the ratio of 4 : 5 and the interior angles in the ratio of 25 : 26. The number of sides in the first polygon are
(a) 8
(b) 10
(c) 12
(d) 15
Q9. In a triangle ABC, BC is produced to D so that CD = AC. If ∠BAD = 111° and ∠ACB = 80°, then the measure of ∠ABC is:
(a) 31°
(b) 33°
(c) 35°
(d) 29°
Q10. Two circles of an equal radii are drawn, without any overlap, in a semicircle of radius 2 cm. If these are the largest possible circles that the semicircle can accommodate, what is the radius (in cm) of each of the circles?
(a) 0.414
(b) 0.828
(c) 0.172
(d) 0.586
Q11. PQRS is trapezium, in which PQ is parallel to RS, and PQ = 3 (RS). The diagonal of the trapezium intersect each other at X, then the ratio of ∆PXQ and ∆RXS is
(a) 6 : 1
(b) 3 : 1
(c) 9 : 1
(d) 7 : 1
Q12. Let ABCDEF be a regular hexagon. What is the ratio of the area of the triangle ACE to that of the hexagon ABCDEF?
(a) 1/3
(b) 1/2
(c) 2/3
(d) 5/6
Q15. Four horses are tied on the four corners of a square field of 14 m length so that each horse can touch just the other two horses. They were able to graze in the area accessible to them for 11 days. For how many days in the ungrazed area sufficient for them?
(a) 3 days
(b) 4 days
(c) 5 days
(d) 2 days
