1. Write linear equations representing a line which is parallel to y-axis and is at a distance of 2 units on the left side of y-axis.
2. Find whether (0, −3) is a solution of linear equation, x – y + 3 =0?
3. Construct an acute angle and draw its bisector.
4. The edge of a solid cube is 6 cm. How many cubes of 6cm edge can be formed from this cube?
5. The curved surface area of a right circular cylinder of height 21 cm is 957cm2. Find the diameter of the base of the cylinder.
6. Find the radius of largest sphere that is carved out of the cube of side 8 cm.
Section-B
7. In the given figure, P is any point on the diagonal AC of the parallelogram ABCD. Show that ar(ΔADP) = ar (ΔABP).
8. In the given figure, O is the centre of the circle and BA = AC. If ∠ABC = 50o, find ∠BOC and ∠BDC.
9. Using ruler and compass, construct ∠XYZ = 105o.
10. A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. Find the radius of sphere.
11. A die is rolled 150 times and its outcomes are recorded as below:
Find the probability of getting:
(i) An odd number
(ii) A multiple of 4
12. Check whether 7/6 can be an emperical probability or not. Give reasons.
Section-C
13. Find two integral solutions of 13x + 17y = 221. Represent this equation by a graph. Does it pass through origin.
14. Plot A(3, 0), B(0, 2), C(-3, 0) and D(0, -2) on a graph paper. Join A to B, B to C, C to D and D to A to form a quadrilateral ABCD. Is ABCD is rhombus? Also write the equations of AC and BD.
15. PQRS is a quadrilateral. A line through S parallel to PR meets QR produced in X. Show that ar(PQRS) = ar(ΔPXQ).
16. Small spherical balls, each of diameter 0.6 cm, are formed by melting a solid sphere of radius 3 cm. Find the number of balls thus obtained.
17. Draw a line segment SR of length 10 cm. Divide it into 4 equal parts, using compass and rular.
18. There are 100 students in a class. The mean height of the class is 150 cm. If the mean height of 60 boys is 70 cm, find the mean height of the girls in the class.
19. If adjacent angles A and B of parallelogram ABCD are in the ratio 7:5, then find all the angles of parallelogram.
20. 26. A Room is 30m long, 24 m broad and 18 m high. Find:
(a) Iength of the longest rod that can be placedd in the room.
(b) its total surface area.
(c) its volume.
(a) Iength of the longest rod that can be placedd in the room.
(b) its total surface area.
(c) its volume.
21. Two coins were tossed 20 times simultaneously. Each time the number of heads occurring was noted as follows:
0, 1, 1, 2, 0, 1, 2, 0, 0, 1, 2, 2, 0, 2, 1, 0, 1, 1, 0, 2
Prepare a frequency distribution table for the data.
22. Weekly wages (in rupees) of workers in a factory are as follow:
Find the probability that a worker chosen at random earns:
(a) Rs. 1800 or more but less than Rs. 1850.
(b) Below Rs. 1825.
(c) at least Rs. 1775.
Section-D
23. Draw the graphs of the following equations on the same graph sheet:
x – y = 0, x + y = 0, y + 5 = 0. Also, find the area enclosed between these lines.
24. Let the cost of a pen and a pencil be Rs. x and Rs. y respectively. Anuj pays Rs. 34 for 3 pens and 2 pencils. Write the given data in the form of a linear equation in two variables. Also, represent it graphically.
25. Construct a ΔABC in which BC = 7.2 cm, ∠B = 45 and AB – AC = 3cm.
26. In the given figure, ABCD is a parallelogram in which CB is produced to E such that BC = BE. The line segment DE intersects side AB at F. If ar( ΔADF) = 4cm2, find the area of parallelogram ABCD.
27. Prove that the angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.
28. A group of 21 school students shared the ice-cream brick in lunch break to celebrate the Independence Day. If each one takes a hemispherical scoop of ice-cream of 3 cm radius, find the volume of ice-cream eaten by them.
(a) If the dimensions of the ice-cream brick are 10cm × 10cm × 12cm, how much volume of cream is left?
(b) Which value is depicted by the students?
(Use π = 22/7)
29. A cone, hemisphere and a cylinder stand on the same base and have equal height. Find the ratio of their:
(a) Volumes,
(b) Curved surface areas.
30. Without drawing a histogram, construct a frequency polygon for the given frequency distribiution:
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