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General Instructions:
1. | E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that ∆ABE ~ ∆CFB. | [1] |
2. |
Find the roots of the quadratic equation | [1] |
3. |
For what value of k will k+9, 2k-1 and 2k+7 are the consecutive terms of an A.P? | [1] |
4. |
Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear | [1] |
5. |
Write a rational number between . | [1] |
6. | Write the value of sin2 69° + sin2 21°. | [1] |
7. |
A card is drawn at random from a well -shuffled fled pack of 52 playing cards. Find the probability of getting neither a red card nor a queen. | [2] |
8. | The present age of a father is equal to the sum of the ages of his 5 children. 12 years hence, the sum of the ages of his children will be twice the ages of their father. Find the present age of the father. | [2] |
9. | Find the largest number which divides 245 and 1029 leaving remainder 5 in each case. | [2] |
10. |
Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right-angled isosceles triangle. | [2] |
11. |
Three different coins are tossed together. Find the probability of getting | [2] |
12. | Three numbers are in A .P. if the sum of these numbers is 27 and the product 585, find the numbers. | [2] |
13. |
Consider the following distribution of daily wages of 50 workers of a factory.
Find the mean daily wages of the workers. | [3] |
14. |
A conical vessel, with base radius 5 cm and height 24 cm, is full of water. This water is emptied into a cylindrical vessel of base radius 10 cm. Find the height to which the water will rise in the cylindrical vessel. (π = 22/7) | [3] |
15. |
In Fig. , PQ is tangent at point C to a circle with centre O. If AB is a diameter and ∠CAB = 30°, find ∠PCA. | [3] |
16. |
In Fig. find the area of the shaded region, enclosed between two concentric circles of radii 7 cm and 14 cm where ∠AOC = 40°. (use π =22/7) | [3] |
17. |
Show that ΔABC, where A(–2, 0), B(2, 0), C(0, 2) and ΔPQR where P(–4, 0), Q(4, 0), R(0, 2) are similar triangles. | [3] |
In the given Fig. PB and QA are perpendiculars to segment AB. If PO = 5 cm, QO = 7 cm and area ∆POB = 150 cm2 find the area of ∆QOA.
18. |
Write the simplest value of | [3] |
19. |
Prove that is irrational. | [3] |
20. |
The points A (4, 7), B (p, 3) and C (7, 3) are the vertices a right triangle, right-angled at B find the value of p. | [3] |
If the coordinates of points A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P such that AP = 3/7 AB, where P lies on the line segment AB.
21. | Tanvika went to a hotel in a town with her big family. They consumed 23 idlies, ISpoories, 7 dosas and 19 vadas. the bill was Rs. 108. Next day they consumed 34 idlies, 8 vadas, 22 poories and 7 dosas. The bill came to Rs. 114 if one idilie cost same as vada. What is the cost of one poori ? | [3] |
22. |
Find all the zeroes of the polynomial given that are two of its zeroes. | [3] |
23. |
In the given figure, the side of square is 28 cm and radius of each circle is half of the length of the side of the square where O and O' are centres of the circles. Find the area of shaded region. | [4] |
24. |
What is the value of the median of the data using the graph in figure, of 'less than' ogive and 'more than ogive'? | [4] |
25. |
Construct a ΔABC in which AB = 6 cm, ∠A = 30o and ∠B = 60o. Construct another ΔAB'C' similar to ΔABC with base AB' = 8 cm | [4] |
26. |
The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60o. From a point Y, 40 m vertically above X, the angle of elevation of the top Q of the tower is 45o. Find the height of the tower PQ and the distance PX. | [4] |
27. |
In the given Fig, two triangles ABC and DBC lie on the same side of base BC. P is a point on BC such that PQ || BA and PR || BD. Prove that: QR || AD. | [4] |
28. | In right-triangle ABC, right angled at B, if Show that | [4] |
29. |
Find the sum of n terms of the series | [4] |
30. |
Speed of a boat in still water is 15 km/h. It goes 30 km upstream and returns back at the same point in 4 hours 30 minutes. Find the speed of the stream. | [4] |
Solve for x: