PRACTICE PAPER (CLASS -X)
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1) (i) If 7 is the mean of
5,3,0.5,4.5,b,8.5,9.5 find b.
(ii) if each observation is decreased in value by 1 unit,what would the new mean be ?
2) solve by formula
(x+3)/(2x+3) =(x+1)/(3x+2).
3) From the following table, find:
(i) The average wage of a worker, give your answer, correct to the nearest paise.
(ii) The modal class.
Wages in Rs. No of workers
Below 10. 15
Below 20. 35
Below 30. 60
Below 40. 80
Below 50. 96
Below 60. 127
Below 70. 190
Below 80. 200.
4) prove.√{(1+cos x)/(1-cos x)} =
Cosec x + Cot x.
5) Find mean and mode :
C-I: 58-61 62-64 64-67 67-70 70-73
F:. 5 18 42 27 8
6) In a cricket match Ram took 3 wickets less than twice the number of wickets taken by Anshu. If the product of the number of wickets taken by them is 20, find the number of wickets taken by each.
7) Evaluate :
{(1+sin30)/cos 30 +
Cos30/(1+sin30)}² .
sin²60/(1-cos²60tan²60)
8)
Marks. Frequency
1-10 10
11-20 40
21-30 80
31-40 140
41-50 170
51-60 130
61-70 100
71-80 70
81-90 40
91-100 20
From the ogive find:
i) What% of the candidates pass the examination, if the pass marks is 40.
ii) What should the pass marks be, if it is decided to allow 80% of the candidates to pass ?
iii)If scholarship are awarded to the top 15% of the students, what should be the lowest mark to gain a scholarship
9) When 7x² -3x+8 is divided by
x -4, find the remainder.
10) Calculate the length of the tangent drawn to a circle of diameter 8cm from a point 5cm away from the centre of the circle.
11) Find p and q if g(x)=x+2 is a factor of f(x)=x³-px+x+q and f(2)=4
12) The volume of a cylinder 14cm long is equal to that of a cube having an edge 11cm. Calculate the radius of the cylinder.
13) The mean of Numbers 6,y,7,x and 14 is 8 Express y in terms of x.
14) Solve: x²-5x-2=0. Give your answer correct to 3 significant figures.
15) find mean median and mode of 12,11,10,12,13,14,13,15,13.
16) The work done by (2x-3) men in (3x+1) days and the work done by (3x+1) men in (x+8) days are in the ratio of 11:15. Find x.
17) prove: Sinx + cosx =
Sinx/(1-Cotx) + Cosx/(1-tanx).
18) In 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 15, the total number of seats increased by 400
Find a) The Number of rows in the original arrangement.
b) The Number of seats in the auditorium after rearrangement.
19) find mode
X: 0-20 20-40 40-60 60-80 80-100
F: 3 8 10 6 4.
20) A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60°. When he moves 40 m away from the bank, he finds the angle of elevation to be 30°. Find
a) the width of the river.
b) the height of the tree.
21) Find the length of the tangent drawn to a circle of radius 4cm from a point 5cm away from the centre of the circle.
22) If 7 is the mean of 5, 3, 0.5, 4.5,
b,8.5, 9.5 find b.
23) Solve:
(x+3)/(2x+3) =(x+1)/(3x+2)
24) A boy standing on a vertical cliff in a jungle observes two rest-houses in line with him on opposite sides deep in the jungle below. If their angles of depression are30° and 60° and the distance between them is 222m, find the height of the cliff.
25) Find mean and mode
X: Bel10 -20 -30 -40 -50 -60 -70
Age: 15 35 60 80 96 127 190
26) 5,6,8,9,10,11,11,12,13, 13, 14,
14,15,15,15, 16,1618,19,20. Find
Mean, Median, Mode.
27) Prove
1/(SinA +CosA) +1/(SinA-CosA)=
2SinA/(2Sin²A -1)
28) An aeroplane travelled a distance of 800 km at an average speed of x km/hr. On return journey, the speed was increased by 40 km/hr. Write down an expression for the time taken for:
a) the onward journey
b) the return journey
If the return journey took 40 minutes less than the onward journey, write down an equation in x and find its value.
29) Solve: 3x²-5x=1. Up to 2 dec.
30) If 2 tan²A -1=0 prove
Cos3A= 4cos³A - 3cosA
31) SinA(1+tanA) +cosA(1+ cotA)
=Cosec A + SecA
32) A vertical tower 40m high. A man standing at some distance from the tower knows that the cosine of the angle of elevation is 60° . How far is he standing from the foot of the tower ?
33) A bag contains 4 white and 3 green balls. One ball is drawn at random. Find the probability that it is white.
34) What is the probability that the sum of the faces is not less than 10 when two unbiased dice are thrown
35) The midpoint of AB is P(-2,4). The coordinates of the point A and B are (a,0),(0,b) . Find A, B
36) Calculate median and mode of
9,0, 2,8,5,3,5,4,1,5,2,7.
37) Solve y - √(3y -6) =2.
38) If -5 is a root of the x²+ kx - 130=0
Find k, Hence find the other root.
39) An open cylindrical vessel of internal diameter 49cm and height 64cm stands on a horizontal platform. Inside this is placed a solid metallic right circular cone whose base has a diameter of 10.5cm and whose height is 12cm. Calculate the volume of water required to fill the tank. (π=22/7)
40) The perimeter of a rectangular plot is 180m and its area is 1800m². If the length is x m, Express the breadth in terms of x. Hence, form an Equation in x. Solve the Equation and find the length and the breadth of the rectangle.
41) Prove (1+tan²x)/(1+cot²x)=
sin²x/cos²x.
42) X:2-4 4-6 6-8 8-10 10-12 12-14
F: 6 9 16 13 4 2
Find mode
43) The angle of elevation of a cloud from a point 50m above a lake is 30° and the measure of the angle of depression of its reflection in the lake is 60°, find the height of the cloud.
44) A solid cylinder of radius 14cm and height 21cm is melted down and recast into spheres of radius 3.5cm each. Calculate the number of spheres that can be made.
45) The Mean of 12,18,x,13,19,22 is 16, find x.
46) Solve 3x²+8x+1=0. Give your answer correct to two decimal places.
47) From the top of a building AB, 60 metres high, the angles of depression of the top and bottom of a vertical lamp post CD are observed to be 30° and 60°. Find
a) the horizontal distance between AB and CD.
b) the height of the lamp post CD.
48) SOLVE: 24x² - 334x + 135=0
49) An open cylindrical vessel is made of steel. The internal diameter is 14cm, the internal depth is 20.6cm and the metal is everywhere 4mm thick. Calculate
a) the internal volume
b) the volume of the metal correct to the nearest cm³.
50) The line joining A(-3,4) and
B(a,9) is divided in the ratio 2:3 at P, the point where the line segment AB intersects y-axis. Find
a) the value of a
b) the coordinates of P.
51) John sends his servant to the market to buy oranges worth Rs15. The servant having eaten three oranges on the way. John pays 25 paise per orange more than the market price. Taking x to be the number of oranges which John receives, form a quadratic equation in x. Hence, find the value of x.
52)X:0-5 5-10 10-15 15-20 20-25
F: 3 7 15 24 16
Find Mean correct to 2 decimal.
53) A man is standing on a level ground, observes that a pole 30m away subtends an angle of 50° at his eye, which is 2.0m above the ground level. Calculate the height of the pole. (Give your answer correct to a length of a metre).
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