SECTION A
Question number 1 to 10 carry 1 mark each.
1. Find the discriminant of the quadratic
equation x+2x+30=20
2. If a, 2 are three consecutive terms of an A.P., then fine the value of a.
3. If the areas of two similar triangles are in the ratio 25 : 64, write the ratio of their corresponding sides.5. Two coins are tossed simultaneously. Find the probability of getting exactly one head.
6. Find the [HCF X LCM] for the numbers 100 and 190.
7. If 1 is a zero of the polynomial p(x) = ax2 – 3(a – 1)x – 1, then find the value of a.
8. If sec2? (1 + sin ?)(1 – sin ?) = k, then find the value of k.
9. If the diameter of a semicircular protractor is 14 cm, then find its perimeter.
10. Find the number of solutions of the following pair of linear equations:
x + 2y – 8 = 0
2x + 4y = 16
SECTION B
11. If the points A (4, 3) and B (x, 5) are on the circle with the centre O (2, 3), find the value of x.
12. Which term of the A.P. 4, 12, 20, 28, … will be 120 more than its 21st term?
14. Find all the zeroes of the polynomial x3 + 3x2 – 2x – 6,
15. ?ABD is a right triangle, right-angled at A and AC ^ BD. Prove that AB2 = BC . BD
SECTION C
Question number 16 to 25 carry 3 marks each.
16. Prove that 1/2 is an rational number.
17. Draw a right triangle in which sides (other than hypotenuse) are of lengths 8 cm and 6 cm.
18. Two dice are thrown simultaneously. What is the probability that
(i) 5 will not come up on either of them?
(ii) 5 will come up on at least one?
(iii) 5 will come up at both dice?
20. The sum of first six terms of an arithmetic progression is 42. The ratio of its 10th term to its 30th term is 1 : 3. Calculate the first and the thirteenth term of the A.P.2. Find the ratio in which the point (x, -1) divides the line segment joining the points (-3, 5) and (2, - 5). Also find the value of x.
23. Find the area of the quadrilateral ABCD whose vertices are A (1, 0), B (5, 3), C (2, 7) and D(-2, 4).
25. Solve for x and y:
ax – by = 2ab
SECTION D
Question 26
26. A juice seller serves his customers using a glass as shown in figure 6. The inner diameter of the cylindrical glass is 5 cm, but the bottom of the glass has a hemispherical portion raised which reduces the capacity of the glass. If the height of the glass is 10 cm, find the apparent capacity of the glass and its actual capacity. (Use p = 3.14)
28. A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at that instant is 60°. After some time, the angle of elevation reduces to 30°. Find the distance travelled by the balloon during the interval.
9. Solve the following equation for x.
9x2 – 9(a + b)x + (2a2 + 5ab + 2b2) = 0Labels: India Question Papers