1) The work done by (x-3) men in (2x+1) days and the work done by (2x+1) men in (x+4) days are in ratio 3:10. Find the value of x. 42
2) Find the mean of the following:
Class-interval Frequency
00-50 4
50-100 8
100-150 16
150-200 13
200-250 6
250-309 3. 143
3) Prove: cos x/(1- tan x)+ sin x/(1- cot x) = cos x + sin x.
4) An Auditorium, seats were arranged in rows and columns. The number of rows was equal to the number of seats in each row. When the number of rows was doubled and the number of seats in each row was reduced by 10, The total number of seats increased by 300. Find
A) the number of rows in the original arrangement. 30
B) the number of seats in the Auditorium after rearrangement. 1200
5) Draw a histogram and hence estimate the mode for the following frequency distribution :
Class Frequency
00-10 2
10-20 8
20-30 10
30-40 5
40-50 4
50-60 3. 23
6) A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite Bank in 60°. When he moves 50m away from the bank, he finds the angle of the elevation to be 30°. Calculate:
A) the width of the river. 25
B) the height of the tree. 25√3
7) A vessel is in the form of an inverted cone. Its height is 11 cm and the radius of its top which is open, is 2.5 cm. It is filled with water up to the Rim. When lead shots, each of which is a sphere of radius 0.25cm dropped Into The vessel, 2/5 of the water flows out. Find the number of lead shots dropped into the vessel. 440
8) In a triangle PQR, L and M are two points on the base QR , such that angle LPQ = angle QRP and angle RPM = angle RQP. Prove that:
A) ∆ PQL similar to ∆ RPM
B) QL. RM = PL. PM
C) PQ² = QR. QL.
1) Class: 50 60 70 80 90 100 110
Workers: 2 4 8 12 10 6 8
A) calculate the mean wage, correct to the nearest rupee. 85
B) If the number of workers in each category is doubled, what would be the new wage. 85
2) In ∆ ABC, AD is the perpendicular on BC. Tan B= 3/4 and tanC= 5/12, BC= 56cm. Calculate the length of AD. 15
3) AB and CD chord extended to meet at X of the circle whose centre is O. Given AB= 4, BX=6, XD= 5cm, calculate the length of CD. 7
4) Given 5 Cos A - 12 sin A = 0 without using table find (Sin A + Cos A)/(2 cos A - sin A). 12/13
5) Two circles of radii 4cm and 2.5cm with their centres 9cm apart. Calculate the length of the transverse common tangent. 6.2225 cm
6) Age number of casualties
05-15 6
15-25 10
25-35 15
35-45 13
45-55 24
55-65 8
65-75 7
A) Construct the 'less than' cumulative frequency curve for the above data, using 2cm= 10 years, on x-axis and 2cm= 10 casualties on the other.
B) From your graph determine
i) the median. 43 years
7) The cross section of an ice-cream cone consisting of a cone surmounted by a hemisphere. The radius of the hemisphere is 3.5cm and height of the cone is 10.5cm. The outer shell is shaded and is not filled with ice-cream. AE= DC= 0.5 cm, AB||EF and BC||FD. Calculate the volume of icecream. 174.69
8) The distance by the road between two towns A and B 216km, and by rail it is 208km. A car travels at a speed of x km/hr, and the train travels at a speed of which is 16 km/ hour faster than the car. Calculate:
A) time taken by the car to reach Town B from A, in terms of x.
B) time taken by the train to reach on B from A in terms of x.
C) if the train takes 2 hours less than the car to reach Town B, obtain an equation in x and solve it.
D) Hence find the speed of the train. 52
9) A total buys x articles for a total cost of ₹600.
A) write down the cost of one article in terms of x.
if the cost per article were ₹5 more, the number of articles that can be bought for ₹600 would be 4 less.
B) write down the equation in x for the above situation and solve it for x. 24
10) A metal container in the form of a cylinder is a surmounted by a hemisphere of the same radius. The internal height of the cylinder is 7m and the internal radius 3.5m. Calculate
A) the total area of the internal surface, excluding the base. 231m²
B) the internal volume of the container in m³. 1078/3 m³
11) the surface area of a solid metallic sphere is 1256cm³. It is the melted and recast into solid right circular cone of radius 2.5cm and height 8 cm. Calculate
A) radius of the solid sphere. 10, 80
B) the number of cones recast (π=3.14).
12) Two numbers are in the ratio 3:5. If 8 is added to each number, the ratio becomes 2:3, Find the numbers. 24,40
13) Prove: 1 - cos²x/((1+ sin x) = sin x.
14) A, B and C are three points on a circle. The triangle at C meets BA produced at T. Given that angle ATC= 36° and that the angle ACT= 48°, Calculate the angle subtended by AB at the centre of the circle. 96
15) An exhibition tent is in the form of a cylinder surmounted by a cone. The height of the tent above the ground is 85m and the height of the cylindrical part is 50m. if the diameter of the base is 168m. find the quantity of Canvas required to make the tent. Allow 20% extra for folds and for stitching. give your answer to nearest m². 60509
16) In triangle ABC, angle B= 90° and D is the midpoint of BC. Prove that: AC²= AD²+ 3CD².
17) Using the data given below construct the community frequency table and draw the Ogive. From the Ogive determine the median.
Marks No. of students
00-10 3
10-20 8
20-30 12
30-40 14
40-50 10
50-60 6
60-70 5
70-80 2 35
18) Prove: 1/(sinx + cos x) + 1/(sinx - cosx) =2 sin x/(1- 2 + cos²x).
19) The following table gives the weekly wages of workers in a factory:
Weekly wages in ₹ No. of workers
50-55 5
55-60 20
60-65 10
65-70 10
70-75 9
75-80 6
80-85 12
85-90 8
Calculate
A) the mean. 69
B) the modal class. 55-60
C) the number of workers getting weekly wages, below ₹80. 60
D) the number of workers getting ₹65 or more, but less than ₹85 as weekly wages. 27
20) A hollow sphere of internal and external diameter 4cm and 8 cm respectively, is melted into a cone of base diameter 8cm. Find the height of the cone. 14cm
21) An aeroplane Travelled a distance of 400k.m at an average speed of X km/ hr. On the return journey, the speed was increased by 40 km/hr. Write down an expression for the time taken for:
A) onward journey
B) the return journey.
if the return journey took 30 minutes less than the onward journey, write down an equation in x and find its value. 160
22) The shadow of a vertical Tower AB on level ground is increased by 10m, when the altitude of the sun changes from 45° to 30°, find the height of the tower and give your answer, correct to 1/10 of a metre. 13.7
23) In the right angled ∆PQR. PM is an altitude. Given that QR= 8cm and MQ = 3.5 cm, Calculate the value of PR. 6
24) the marks obtained by 120 students test in a mathematics test is given below :
Marks No of students
00-10 5
10-20 9
20-30 16
30-40 22
40-50 26
50-60 18
60-70 11
70-80 6
80-90 4
90-100 3 Draw an Ogive for the given distribution on a graph sheet. Use a suitable scale for your Ogive. Use your Ogive to estimate:
A) the median. 43
B) the lower quartile. 30
C) the number a students who obtained more than 75% in the test. 10
D) the number of students who did not pass in the test if the pass percentage was 40. 52
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