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Q1
short answer
2 marks
Find the sum of first 30 terms of AP : 30, 24, 18, ..... .
Q2
short answer
2 marks
In an AP if Sn = n (4n + 1), then find the AP.
Q2
short answer
2 marks
A solid metallic sphere of radius 10·5 cm is melted and recast into a number of smaller cones, each of radius 3·5 cm and height 3 cm. Find the number of cones so formed.
Q4
short answer
2 marks
Find the value of m for which the quadratic equation (m 1) x2 + 2 (m 1) x + 1 = 0 has two real and equal roots.
Q4
short answer
2 marks
Find the mode of the following frequency distribution: Class 10-20 20-30 30-40 40-50 50-60; Frequency 15 10 12 17 4
Q5
short answer
2 marks
Solve the following quadratic equation for x : 2 3 x2 + 10x + 7 3 = 0
Q5
short answer
2 marks
A man's age 5 years ago and 7 years from now, is one more than twice his present age. Find his present age.
Q6
short answer
2 marks
Two concentric circles are of radii 4 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
Q7
short answer
3 marks
For what value of x, is the median of the following frequency distribution 34·5? Class: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60, 60-70; Frequency: 3, 5, 11, 10, x, 3, 2
Q8
short answer
3 marks
Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Construct tangents to the circle from these two points P and Q.
Q9
short answer
3 marks
(b) From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30 and 45 respectively. If the bridge is at a height of 3 m from the banks, then find the width of the river.
Q10
short answer
3 marks
Following is the daily expenditure on lunch by 30 employees of a company: 100-120 (8), 120-140 (3), 140-160 (8), 160-180 (6), 180-200 (5). Find the mean daily expenditure of the employees.
Q11
short answer
3 marks
The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, then find the height of the building.
Q11
short answer
4 marks
(a) From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and same radius is hollowed out. Find the total surface area of the remaining solid.
Q11
short answer
4 marks
(b) Water in a canal, 8 m wide and 6 m deep, is flowing with a speed of 12 km/hour. How much area will it irrigate in one hour, if 0·05 m of standing water is required ?
Q12
short answer
4 marks
In Figure 1, a triangle ABC with B = 90 is shown. Taking AB as diameter, a circle has been drawn intersecting AC at point P. Prove that the tangent drawn at point P bisects BC.
Reading Passage
In Mathematics, relations can be expressed in various ways. The matchstick patterns are based on linear relations. Different strategies can be used to calculate the number of matchsticks used in different figures. One such pattern is shown below. Observe the pattern and answer the following questions using Arithmetic Progression : Figure 1 Figure 2 Figure 3
Q13
short answer
2 marks
(a) Write the AP for the number of triangles used in the figures. Also, write the nth term of this AP.
Q13
short answer
2 marks
(b) Which figure has 61 matchsticks ?
Reading Passage
Gadisar Lake is located in the Jaisalmer district of Rajasthan. It was built by the King of Jaisalmer and rebuilt by Gadsi Singh in 14th century. The lake has many Chhatris. One of them is shown below : Observe the picture. From a point A h m above from water level, the angle of elevation of top of Chhatri (point B) is 45 and angle of depression of its reflection in water (point C) is 60 . If the height of Chhatri above water level is (approximately) 10 m, then
Q19
short answer
2 marks
draw a well-labelled figure based on the above information;
Q20
short answer
2 marks
find the height (h) of the point A above water level. (Use 3 = 1·73)
