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SECTION - A
Question numbers 1 to 10 carry 1 mark each. For each of the questions 1 to 10, four
alternative choices have been provided of which only one is correct. You have to
select the correct choice.
1. Which of the following is not a linear equation ?
(A) ax1by1c50 (B) 0x10y1c50
(C) 0x1by1c50 (D) ax10y1c50
2. Which of the following is a solution of the equation 4x13y516 ?
(A) (2, 3) (B) (1, 4) (C) (2, 4) (D) (1, 3)
3. In figure, PQRS is a rectangle. If RPQ 30∠ 5 8 then the value of (x 1 y) is
(A) 908 (B) 1208 (C) 1508 (D) 1808
4. Two polygons have the same area in figure :
(A) (a) (B) (b) (C) (c) (D) (d)
5. Two consecutive angles of a parallelogram are in the ratio 1 : 3, then the smaller angle
(A) 508 (B) 908 (C) 608 (D) 458
6. In figure, PQRS is a parallelogram in which ∠PSR 1255 8 , RQT∠ is equal to
(A) 758 (B) 658 (C) 558 (D) 1258
7. The diagonals of rhombus are 12 cm and 16 cm. The length of the side of rhombus is
(A) 10 cm (B) 12 cm (C) 16 cm (D) 8 cm
8. The length of the diagonal of the square is 10 cm. The area of the square is
(A) 20 cm2 (B) 100 cm2 (C) 50 cm2 (D) 70 cm2
9. The length of the longest pole that can be put in a room of dimensions
10 m 3 10 m 3 5 m.
(A) 15 m (B) 16 m (C) 10 m (D) 12 m
10. The range of the data 25.7, 16.3, 2.8, 21.7, 24.3, 22.7, 24.9 is
(A) 22 (B) 22.9 (C) 21.7 (D) 20.5
SECTION - B
Question numbers 11 to 18 carry 2 marks each
11. Find the mean of factors of 24.
12. The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the
cost of painting the walls of the room and ceiling at the rate of Rs. 50 per m2.
13. How many litres of water flow out through a pipe having an area of cross-section of
5 cm2 in one minute, if the speed of water in pipe is 30 cm/sec.
14. Two parallel chords of a circle whose diameter is 13 cm are respectively 5 cm and
12 cm. Find the distance between them if they lie on opposite sides of centre.
15. In a paralleloram, show that the angle bisectors of two adjacent angles intersect at
16. The angle between the two attitudes of parallelogram through the vertex of an obtuse
angle is 508. Find the angles of parallelogram.
D is the mid point of side BC of DABC and E is the mid point of AD, then show that
ar (BED) 5
17. Two congruent circles intersect each other at points A and B. Through A a line segment
PAQ is drawn so that P and Q lie on the two circles. Prove that BP 5 BQ.
18. Express y in terms x in equation 2x23y512. Find the points where the line represented
by this equation cuts x-axis and y-axis.
SECTION - C
Question numbers 19 to 28 carry 3 marks each
19. Draw the graph of two lines whose equations are 3x22y1650 and x12y2650 on
the same graph paper. Find the area of the triangle formed by two lines and x-axis.
20. The taxi fare in a city is as follows. For the first kilometre, the fare is Rs. 8 and for the
subsequent distance it is Rs. 5 per km. Taking the distance covered as x km and total
fare as Rs. y. Write a linear equation for this information and calculate from the equation
total fare of 15 km distance.
21. Construct a DABC in which AB55.8 cm, BC1CA58.4 cm and B 60∠ 5 8 .
22. In figure, ABCD is a parallelogram. The circle through A, B and C intersects CD
produced at E. Prove that AE 5 AD.
23. XY is a line parallel to side BC of DABC. BE ?? AC and CF ?? AB meets XY is E and F
respectively. Show that ar(ABE)5ar(ACF).
In figure, ABCD is a trapezium in which AB ?? DC. E is the mid point of AD and F is a
point on BC such that EF ?? DC. Prove that F is the mid point of BC.
24. From a right circular cylinder with height 8 cm and radius 6 cm, a right circular cone
of the same height and base is removed. Find the total surface area of the remaining
25. How many spherical lead shots each 4.2 cm diameter can be obtained from a solid
cuboid of lead with dimensions 66 cm, 42 cm and 21 cm.
An iron pipe 20 cm long has external diameter equal to 25 cm. If the thickness of the
pipe is 1 cm, find the total surface area of the pipe.
26. Three unbiased coins are tossed together. Find the probability of getting
(i) two heads (ii) at least two heads (iii) no head
A bag contains 12 balls out of which x are white. If one ball is taken out from the bag,
find the probability of getting a white ball. If 6 more white balls are added to the bag
and the probability now for getting a white ball is double the previous one, find the
value of x.
27. The marks obtained by 40 students of class IX in Mathematics are given below :
81, 55, 68, 79, 85, 43, 29, 68, 54, 73, 47, 35, 72, 64, 95, 44, 50, 77, 64, 35, 79, 52, 45, 54,
70, 83, 62, 64, 72, 92, 84, 76, 63, 43, 54, 38, 73, 68, 52, 54
Prepare a frequency distribution table with class - size of 10 marks.
28. Find the median of the following data
19, 25, 59, 48, 35, 37, 30, 32, 51.
If 25 is replaced by 52 what will be the new median.
SECTION - D
Question numbers 29 to 34 carry 4 marks each
29. Solve for x,
( )4 23 5 25 7
3 5 15
A and B are friends. A is elder to B by 5 years. Bs sister C is half the age of B while As
father D is 8 years older than twice the age of B. If the present age of D is 48 years, find
the present ages of A, B and C.
30. Prove that the parallelograms on the same base and beween the same parallels are
equal in area.
Diagonals AC and BD of a trapezium ABCD with AB ?? DC intersect each other at O.
Prove that ar(DAOD) 5 ar(DBOC)
31. Draw a histogram of frequency polygon for the following data
Marks 10 - 15 15 - 20 20 - 25 25 - 30 30 - 40 40 - 60 60 - 80
No. of students 7 9 8 5 12 12 8
32. In figure, diagonals AC and BD of quadrilateral ABCD intersect at O, such that
OB5OD. If AB5CD show that
(i) ar (DOC) 5 ar (AOB)
(ii) ar (DCB) 5 ar (ACB)
(iii) ABCD is a parallelogram.
33. In figure, two circles intersect at B and C. Through B two line segments ABD and PBQ
are drawn to intersect the circles at A, D, and P, Q respectively. Prove that
ACP QCD∠ ∠5 .
34. A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in
the interior. The diameter of the pencil is 7 mm and the diameter of graphite is 1 mm.
If the length of the pencil is 14 cm. Find the volume of wood and that of graphite.
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