Q. 1. Find the zeros of the polynomial ( x + 2 ) ( 2x – 1 ) ( 3x – 2 ).
Q. 2. If αand β are the zeros of the quadratic polynomial f ( x ) = x2 – px + q, find the value ofα2 + β 2.
Q. 3. Find the coordinates of the point where the line 3x – y = 5 meets the x-axis and y-axis.
Q. 4. If a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, then what will be the condition of consistency of infinitely many solution?
Q. 5. Find the values of k for which the equation 2x2 – kx + x + 8 = 0 will have real and equal roots.
Q. 6. In a flower bed, there are 23 rose plants in the first row, 19 in the second, 15 in the third, and so on. There are 7 rose plants in the last row. How many rows are in the flower bed?
Q. 7. Shobha started work in 1995 at an annual salary of Rs 5000 and received an increment of Rs 200 each year, in which year did her income reach Rs 7000.
Q. 8. Find the area of the triangle enclosed between the coordinate axes with vertices ( 8, 0 ) and ( 0, 13 ).
Q. 9. What will be the area of the triangle whose vertices are A( x1, y1 ), B( x2, y2 ) and C( x3, y3 )?
Q. 10. If cos α = 1/√2 and tan β = 1, find the value of sin ( α + β ).
Q. 11. The& length of the shadow of a tower is 1/√3 times that of; its length. Find the angle of elevation of the sun.
Q. 12. A sheet of paper is in the form of a rectangle ABCD in which AB = 40cm and AD = 28cm. A semicircular portion& with BC as diameter is cut off. Find the area of the remaining part of the rectangle.
Q. 13. A play ground has the shape of a rectangle, with two semi-circles on its smaller sides as diameter, added to its outside. If the sides of the rectangle& are 36m and 24m, find the area of the playground.
Q. 14. A protractor is in the shape of a semicircle of radius 7cm, find its perimeter.
Q. 15. A die is rolled once. Find the probability of getting an even prime number.
Q. 16. State the Fundamental Theorem of Arithmetic.
Q. 17. A man saves Rs 5 on day 1, Rs 10 on day 2, Rs 15 on day 3 and so on. How much money will he save in the month of February 2008?
Q. 18. Which measure of central tendency is given by the x-coordinate of the point of intersection of the ‘more than’ ogive and ‘ less than’ ogive.
Q. 19. Express sin 630; + cos 670 in terms of trigonometric ratios of angles between 00 and 450.
Q. 20. If tan A = ¾ A + B = 900, then what is the value of cotB?
Q. 21. What is the maximum value of 1/cosecθ?
Q. 22. Find the median when mean = 20 and mode = 18.
Q. 23. State Euclid’s division lemma.
Q. 24. Find the probability of getting 53 Sundays in a leap year.
Q. 25. In family two children, find probability of at least one boy.
Q. 26. One card is chosen from a well shuffled deck of 52 cards. Calculate the probability that the card drawn will be an ace.
Q. 27. Without doing actual division, determine whether 621/1500 has a terminating or non-terminating decimal expansion.
Q. 28. How many prime numbers are of the form 10n + 1, where n is whole number such that 1 ≤ n ≤ 10.
Q. 29. Find the prime factorization of 2310.
Verify that 2 is zero of x3 4x2 + 5x2.
Answers
1.– 2,1/2, 2/3 |
11. 600 |
21. 1 |
2. 2q |
12. 812 |
22. 19.33 |
3. ( 5/3, 0 ), ( 0, - 5 ) |
13. 1316.16 |
23. ……………… |
4. a1/a2 – b1/b2 = c1/c2 |
14. 36 |
24. 2/7 |
5. 9, - 7 |
15. 1/6 |
25. 3/4 |
6. 5 |
16. …………… |
26. 1/13 |
7.11th year, 2005 |
17. Rs 2175 |
27. terminating |
8. 52 sq units |
18. median |
28. 6 |
9. ………….. |
19. cos270 + sin230 |
29. 2 x 3 x 5 x 7 x 11 |
10.1 |
20. 3/4 |
30. yes |
