TOD

Q1. A straight line parallel to the base BC of the triangle ABC intersects AB and AC at the points D and E respectively. If the area of the ∆ABE be 36 sq. cm. then the area of the ∆ACD is 

18 sq. cm
36 sq. cm
120 sq. cm
54 sq. cm
Solution:

Q2. Two circles with centre A and B and radius 2 units touch each other externally at ‘C’, A third circle with centre ‘C’ and radius ‘2’ units meets other two at D and E. Then the area of the quadrilateral ABDE is

2√2 sq. units
3√3 sq. units
3√2 sq. units
2√3 sq. units
Solution:

Q3. If the length of a side of the square is equal to that of the diameter of a circle, then the ratio of the area of the square and that of the circle (π=22/7)

14:11
7:11
11:14
11:7
Solution:

Q4. A playground is in the shape of a rectangle. A sum of Rs. 1,000 was spent to make the ground usable at the rate of 25 paise per sq. m. The breadth of the ground is 50 m. If the length of the ground is increased by 20 m. what will be the expenditure (in rupees) at the same rate per sq. m.?

1,250
1,000
1,500
2,250
Solution:

Q5. The height of an equilateral triangle is 4√3 cm. The ratio of the area of its circumcircle to that of its in-circle is

2:1
4:1
4:3
3:2
Solution:

Q6. ABCD is a parallelogram in which diagonals AC and BD intersect at O. If E, F G and H are the mid-points of AO, DO, CO and BO respectively, then the ratio of the perimeter of the quadrilateral EFGH to the perimeter of parallelogram ABCD is

1:4
2:3
1:2
1:3
Solution:

Q7.

19 cm
20 cm
28 cm
21 cm
Solution:

Q8. A hospital room is to accommodate 56 patients. It should be done in such a way that every patient gets 2.2 m² of floor and 8.8 m³ of space. If the length of the room is 14 cm, then breadth and the height of the room are respectively

8.8 m, 4 m
8.4 m, 4.2 m
8 m, 4 m
7.8 m, 4.2 m
Solution:

Q9. The lengths of two sides of a right angled triangle which contain the right angle are a and b, respectively. Three squares are drawn on the three sides of the triangle on the outer side. What is the total area of the triangle and the three squares?

2(a²+b² ) + ab
2(a²+b² ) + 2.5 ab
2(a²+b² ) + 0.5ab
2.5(a²+b² )
Solution:

Q10. A piece of wire 78 cm long is bent in the form of and isosceles triangle. If the ratio of one of the equal sides to the base is 5:3, then what is the length of the base?

16 cm
18 cm
20 cm
30 cm
Solution:

Q11. A square of side x is taken. A rectangle is cut out from this square such that on side of the rectangle is half that of the square and the other is 1/3rd of the first side of the rectangle. What is the area of the remaining portion?

(3/4) x²
(7/8) x²
(11/12) x²
(15/16) x²
Solution:

Q12. Consider a circle C of radius 6 cm with centre at O. What is the difference in the area of the circle C and the area of the sector of C subtending an angle of 80° at O?

26π cm²
16π cm²
28π cm²
30π cm²
Solution:

Q13. Find the area of the largest (or maximum sized) square that can be made inside a right angle triangle having sides 6 cm, 8 cm & 10 cm when one of vertices of the square coincide with the vertex of right angle of the triangle?

576/49 cm²
24 cm²
24/7 cm²
None of these
Solution:

Q14. PQRS is a diameter of a circle of radius 6 cm as shown in the figure above. The lengths PQ, QR and RS are equal. Semicircles are drawn on PQ and QS as diameters. What is the perimeters of the shaded region?

 
12 π cm
14 π cm
16 π cm
18 π cm
Solution:

Q15. The area of a rhombus is 150 cm². The length of one of its diagonals is 10cm. The length of the other diagonal is:

25 cm
30 cm
35 cm
40 cm
Solution:

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