1. If one of the roots of the quadratic equation2x^2+px-4=0is 4, then the value of p is:
A. 7
B. -7
C. 5
D. 8
2. If the 17thterm of an AP exceeds the 10thterm by 7, then the common difference is:
A. 3
B. 2
C. 1
D. 4
3. From a point Q, the length of the tangent to a circle is 15 cm, and the distance of Q from the centre is 17 cm. The radius of the circle is:
A. 7 cm
B. 12 cm
C. 14 cm
D. 8 cm
4.
A. 5 cm
B. 10 cm
C. 12 cm
D. 8 cm
5. A line segment that intersects a circle at two distinct points is called a:
A. Radius
B. Diameter
C. Tangent
D. Secant
6. The angle between any tangent and the radius at the point of contact of a circle is:
A. 450
B. 900
C. 600
D. 300
7. The area of a sector of a circle with radius 7 cm and angle at centre 600is:
A.
B.
C.
D.
8. The radius and height of a cylinder are in the ratio 2 : 3, and its volume is 12936 cm3. The height of the cylinder is:
A. 21 cm
B. 14 cm
C. 15 cm
D. 24 cm
9.
A.
B.
C.
D.
10. A bag contains five red balls and three black balls. A ball is drawn at random from the bag. The probability that the ball drawn is red is:
A.
B.
C.
D.
SECTION B
11. If one root of the quadratic equation 2x2+ kx 6 = 0 is 2, find the value of k. Also find the other root.
12. If the second term of an AP is 4 and the seventh term is 11, find its 18thterm.
13. If AB, AC and PQ are tangents in the given figure, and AB = 6 cm, find the perimeter of ΔAPQ.
14. Find the radius of the circle whose perimeter and area are numerically equal.
15. The radius and slant height of a cone are in the ratio 7 : 13, and its curved surface area is 286 cm2. Find its radius.
16. Find the point on the X-axis that is equidistant from the points (2, 5) and (2, 3).
17. Find the relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear.
18. A letter is chosen at random from a given word. Find the probability that the letter is a vowel if the word is MATHEMATICS.
SECTION C
19. Find the sum of all natural numbers between 200 and 1502 that are exactly divisible by 3.
20. A two-digit number is four times the sum of its digits and twice the product of its digits. Find the number.
21. From a point P at a distance of 7.5 cm from the centre O of a circle of radius 3 cm, draw tangents to the circle using its centre.
22. Two concentric circles are of radii 10 cm and 8 cm. A chord of the larger circle touches the smaller circle. Find the length of the chord.
23. A cylindrical bucket, 28 cm high and with the radius of base 7 cm, is field with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 21 cm, find its radius and slant height.
24. Two concentric circles have their areas in the ratio 4 : 9. The radius of the inner circle is 7 cm. Calculate the diameter of the outer circle.
25. A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30. The car is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60. Find the time taken by the car to reach the foot of the tower from this point.
26. Find the area of quadrilateral ABCD formed by the points A (2, 2), B (5, 1), C (2, 4) and D (1, 5).
27. The mid-points of sides AB, BC, CA of triangle ABC are D (2, 1), E (1, 0) and F (-1, 3), respectively. Find the coordinates of the vertices of triangle ABC.
28. A bag contains five white balls and some red balls. If the probability of drawing a red ball is double that of drawing a white ball, find the number of red balls in the bag.
SECTION D
29. The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is
30. The sums of n terms of three arithmetical progressions are S1, S2and S3. The first term of each is unity, and the common differences are 1, 2 and 3, respectively. Prove that S1+ S3= 2S2.
31. Prove that the line segment joining the points of contact of two parallel tangents to a circle is a diameter of the circle.
32. Find the area of the shaded region in the figure given here, if BC = BD = 8 cm, AC = AD = 15 cm, and O is the centre of the circle.
33. Water is flowing at the rate of 15 km per hour through a pipe of diameter 14 cm into a rectangular tank that is 50m long and 44 m wide. Find the time in which the level of water in the tank will rise by 21 cm.
34. From a window p metres high above the ground in a street, the angles of elevation and depression of the top and the foot of another house on the opposite side of the street are θand ø, respectively. Show that the height of the opposite house, in metres, is p (1 + tan θ cot ø).
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