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Time Allowed : 3(1/2) Hours Maximum Marks: 90
General Instructions:
(i) All questions are compulsory.
(ii) The question paper consists of 34 questions divided into four sections A, B, C and D, Section A comprises of 8 questions of 1 mark each. Section B comprises of 6 questions of 2 marks each. Section C comprises of 10 questions of 3 marks each and Section D comprises of 10 questions of 4 marks each.
(iii) Questions 1 to 8 in section A are multiple choice questions where you are to select one correct option out of the given four.
(iv) Use of calculators is not permitted.
SECTION - A
Question number 1 to 4 carry one ,mark each.
1.Write the equation x=5 in the standard form of linear equation in two variables.
2.Chord AB subtends ∠AOB = 60° at the centre of a circle. If OA = 5 cm, find the length of AB
in cm.
3.Force is directly proportional to the acceleration produced in the body. Write an equation
in two variables to express this.
4.What is the probability of getting 7 when we throw a die? How many total possibility
outcomes we have ? Name the event.
SECTION -B
Questions 5 to 10 carry two marks each.
5. Construct an angle of 45° using compass.
6. Find the canvas required to make a covered cubicle of edge 8m.
7. Write down the frequency of the class 30-40 in the following date:
27,15,18,25,35,37,25,40,30,37,32,28,29,16,39,45,30,41,36 and 29
8. The volume of a right circular cylinder of base radius 10 m is 880 m³. Find the total surface area of the cylinder.
9. Find the mean of all the prime numbers lying between 20 and 30.
10.Find the mode of first seven even natural numbers.
SECTION - C
Questions number 11 to 20 carry three marks each.
11. Represent 5x + y = 6 by a graph. Write the coordinates of the point where it meets
(a) x-axis (b) y-axis
12. ABC is a triangle with AD | BC show that ar(ΔABC) = (1/2) x AD x BC.
13. ABCD is parallelogram and O is the point of intersection of its diagonals. If ar(ΔAOD) =
4cm²., find area(ABCD).
14.Weight of a table is two and half times the weight of a chair. Represent this situation in the form of a linear equation in two variables and draw its graph.
15. Prove that the quadrilateral formed by joining the mid points of the sides of a square is
also a square.
16. Construct a right angle triangle ΔABC in which ∠C = 90°, BC = 2.56 cm and AC + AB = 4.5 cm.
17. Small spherical balls of 0.6 cm each are formed by melting a solid sphere of radius 3 cm.
Find the number of small balls such formed.
18. Find the number of cubes, each having ede 3 m, that can be cut from a cuboid having
dimensions 18 m x 12 m x 9 m.
19. The sum of the base radius and the height of a solid right circular cylinder is 37 cm.If the
total surface area of the cylinder is 1628 cm, then find the volume of the cylinder.
20. Following are the actual weights of 10 boxes of dry fruits distributed on the occasion of
Diwali: 4 kg 798 g, 7.975 kg, 4.805 kg, 4.810 kg, 4825 kg, 4.801 kg, 4.798 kg, 4.800,
4.800 kg and 4.817 kg,
A box is chosen at random. Find the probability that:
(a) Its weight is more than 4 kg 800 g.
(b) Its weight is 4.800 kg or less that it.
SECTION -D
Question numbers 21 to 31 carry four marks each.
21.A conical tent is made of 4.5 m wide tarpaulin. Vertical height of the conical tent is 4 m
and base radius is 3 m. Find the length of the tarpaulin used, assuming that 10% extra
material is required for stitching margins and wastage in cutting. (Take π = 3.14)
22.Find three integral solutions of 3x + 4y + 24 = 0. Represent this equation by a graph. Does it pass through origin.
23.In the figure, O is the centre of the circle, ∠AOB = ∠BOC = ∠COA and AO = 2√3 cm. Find the perimeter of ΔABC.
area.
25.Show that the quadrilateral formed by joining the mid points of the sides of rectangle is
order in a rhombus.
26.ABCD is a square. M is the point on AB such that AM= MB. P and Q are points on sides and extended CB such that CM | PQ. Show that ar(CPM) = ar(CQM).
| Age group(in years) | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
| No. of people (in hundreds)) | 27 | 33 | 39 | 45 | 27 | 15 |
Construct a frequency polygon for the above data.
28.If the mean of the following distribution is 6, find the value of p
| x | 2 | 4 | 6 | 10 | p + 5 |
| y | 3 | 2 | 3 | 1 | 2 |
29.A lending library has fixed charge for the first three days and an additional charge for each day thereafter. Amita paid Rs. 27 for a book kept for seven days. Write a linear equation which satisfies this data. Draw the graph for the same.
30.ABCD is a kite with AB=AD and CD=CB. Prove that the figure formed by joining the mid-points of the consecutive sides is a rectangle.
31.Sunita has a plot of land which she decides to use for building an old age home and dispensary for the needy. Her plot is shown in the figure. Plot ABCD is a rhombus.
(a) If R is point on diagonal BD, show that equal areas are allotted for the building old age home and dispensary.
(b) What value is depicted by the above situation.?
(Open Text)
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