30-06-2012, 01:01 PM
Mathematics Sample Question Paper
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1. If the equation 5x2 + 3 x following is true?
A. < − B. = −
C. > − D. ≤ −
2. The sum of roots of a quadratic equation is and the product of its roots is . The quadratic equation is __________.
A. 6x2 -5x+7=0 B. 6x2 + 5x+7=0
C. 6x2-4x+7=0 D. 6x2 -5x +7=0
3. An AP 14, 18, 22, … contains 25 terms. The sum of its 25th and 15th terms is ______.
A. 132. B. 124. C. 128 D. 136.
4. If the nth term of an AP is 3n+1, then the value of Sn is _______.
A. [3 − 1] B. [3 + 5] C. [n+5] D [5 + 3]
5. The ratio in which the line segment joining the points (2, -4) and (-3, 6) is divided by Y-axis is _______.
A. 5 : 2 B. 3 : 2 C. 2 : 3 D. 1 : 4
6. Area of the triangle formed by P(2, 1), Q(6, 1) and R(2, 4) is ______ sq. unit.
A. 12 B. 6 C. 22 D. 18
7. From the top of a pole of height 80m, the angles of depression of the top and bottom of a tower are seen as 300 and 450 respectively. The distance between foot of the pole and foot of the tower is ____.
A. 70 m B. 80 m C. 71 m D. 73 m
8. In the given figure, O is the centre of the circle. If AB= 4 cm, OB = 5cm, then radius of the circle is ______ cm.
A. 4 cm B. 3 cm C. 2 cm D. 3.5 cm
9. The two sectors of a circle have the central angles as 1200 and 1500 respectively. Then the ratio between the areas of the two sectors is __________.
A. 3 : 5 B. 4 : 5 C. 5 : 6 D. 3.5 : 5.1
10. A solid sphere of radius r is melted and cast into the shape of a solid cone of height r. The radius of the base of the cone is _________.
A. 2r B. 3r C. 2r2 D. 3r2
Section-B
Question number 11 to 18 carry 2 marks each
11. Solve the equation
10x2 + 3bx + a2 -7ax – b2 = 0
12. Show that the points (a, b+c), (b, c +a) and (c, a+b) lie on the straight line.
13. A letter is chosen at radon from the English alphabets. Find the probability that it is
i. a vowel ii. a letter of the word ‘jAGANNATH’.
14. Show that = −2 is a solution of the equation 3 + 13 + 14 = 0.
15. If the 10th term of an A.P. is 47 and its first term is 2, find the sum of its first 15 terms.
16. Prove that the tangents drawn at the end points of diameter of a circle are parallel.
17. If a ladder is leaning against the building of height 25m makes angle 300 with horizontal line.
Then find the length of the ladder.
18. A metal sphere of radius 21cm is melted, and converted into a wire of uniform cross-section
area. If the radius of the wire is 7cm, then find the length of the wire.