1. Write the condition to be satisfied by q so that a rational number
has a terminating decimal expansion.
2. The sum and product of the zeroes of a quadratic polynomial are – ½ and -3 respectively. What is the quadratic polynomial?
3. For what values of k the quadratic equation x² – kx + 4 = 0 has equal roots?
, what is the value of
5. Which term of the sequence 114, 109, 104, …. is the first negative term?
6. A cylinder, a cone, and a hemisphere are of equal base and have the same height. What is the ratio in their volumes?
7. In the figure given below, DE is parallel to BC and AD = 1cm, BD = 2cm. What is the ratio of the area of ABC to the area of ADE?
8. In the figure given below, PA and PB are tangents to the circle; drawn from an external point P. CD is the third tangent touching the circle at Q. If PB = 10 cm, and CQ = 2 cm, what is the length of PC?
9. Cards each marked with one of the numbers 4, 5, 6….20 are placed in a box and mixed thoroughly. One card is drawn at random from the box. What is the probability of getting an even prime number?
10. A student draws a cumulative frequency curve, for the marks obtained by 40 students of a class, as shown below. Find the median marks obtained by the students of the class.
11 Without drawing the graphs, state whether the following pair of linear equations will represent intersecting lines, coincident lines or parallel lines: 6x – 3y + 10 = 0 2x – y + 9 = 0 Justify your answer.
12. Without using trigonometric tables, find the value of
13 Find a point on the y-axis, which is equidistant from the points A (6, 5) and B (- 4, 3).
14 In the figure given below, AC is parallel to BD, Is
? Justify your answer.
15 A bag contains 5 red, 8 green and 7 white balls. One ball is drawn at random from the bag, find the probability of getting (i) a white ball or a green ball. (ii) neither a green ball not a red ball. OR One card is drawn from a well shuffled deck of 52 playing cards. Find the probability of getting (i) a non-face card (ii) a black king or a red queen.
16 Using Euclid’s division algorithm, find the HCF of 56, 96 and 404. OR Prove that
is an irrational number.
17 If two zeroes of the polynomial x4+ 3×3 – 20×2 – 6x + 36 are
, find the remaining zeroes of the polynomial.
18. Draw the graph of the following pair of linear equations x + 3y = 6 2x – 3y = 12 Hence, find the area of the region bounded by the x = 0, y = 0 and 2x – 3y = 12.
19 A contract on a construction job specifies a penalty for delay of completion beyond a certain date as follows: Rs 200 for first day, Rs. 250 for second day, Rs. 300 for third day and so on. If the contractor pays Rs 27750 as penalty, find the number of days for which the construction work is delayed.
20. Prove that:
21. Observe the graph given below, and state whether triangle ABC is scalene, isosceles or equilateral. Justify your answer. Also find its area.
22. Find the area of the quadrilateral whose vertices taken in order are A (-5, -3), B (-4, -6), C (2, -1) and D (1, 2).
23. Construct a ABC in which CA = 6 cm, AB = 5cm and BAC = 45°, then construct a triangle similar to the given triangle whose sides are
of the corresponding sides of the
24 Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre of the circle.
25. A square field and an equilateral triangular park have equal perimeters. If the cost of ploughing the field at rate of Rs 5/m2 is Rs 720, find the cost of maintaining the park at the rate of Rs 10/m2. OR An iron solid sphere of radius 3 cm is melted and recast into small spherical balls of radius 1 cm each. Assuming that there is no wastage in the process, find the number of small spherical balls made from the given sphere.
26. Some students arranged a picnic. The budget for food was Rs 240. Because four students of the group failed to go, the cost of food to each student got increased by Rs 5. How many students went for the picnic? OR A plane left 30 minutes late than its scheduled time and in order to reach the destination 1500 km away in time, it had to increase the speed by 250 km/h from the usual speed. Find its usual speed.
27 From the top of a building 100 m high, the angles of depression of the top and bottom of a tower are observed to be 45° and 60° respectively. Find the height of the tower. Also find the distance between the foot of the building and bottom of the tower. OR The angle of elevation of the top a tower at a point on the level ground is 30°. After walking a distance of 100 m towards the foot of the tower along the horizontal line through the foot of the tower on the same level ground, the angle of elevation of the top of the tower is 60°. Find the height of the tower.
28. Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Using the above, solve the following: A ladder reaches a window which is 12 m above the ground on one side of the street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 9 m high. Find the width of the street if the length of the ladder is 15 m.
29. The interior of a building is in the form of a right circular cylinder of radius 7 m and height 6 m, surmounted by a right circular cone of same radius and of vertical angle 60°. Find the cost of painting the building from inside at the rate of Rs 30/m2.
30 The following table shows the marks obtained by 100 students of class X in a school during a particular academic session. Find the mode of this distribution.
Marks No. of students
Less than 10 7
Less than 20 21
Less than 30 34
Less than 40 46
Less than 50 66
Less than 60 77
Less than 70 92
Less than 80 100