Q1
short answer
2 marks
Find the mode of the given frequency distribution : Class 15-25 (6), 25-35 (11), 35-45 (22), 45-55 (23), 55-65 (14), 65-75 (5).
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Q2
short answer
2 marks
For what values of $n$ are the $n^{th}$ terms of the APs: 9, 7, 5, ..... and 15, 12, 9, ..... the same?
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Q3
short answer
2 marks
150 spherical marbles, each of diameter $1.4$ cm, are dropped in a cylindrical vessel of diameter $7$ cm containing some water, and are completely immersed in water. Find the rise in the level of water in the cylindrical vessel.
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Q4
short answer
2 marks
Three cubes of side $6$ cm each, are joined as shown in Figure 1. Find the total surface area of the resulting cuboid.
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Q5
short answer
2 marks
For what value of $m$, the quadratic equation $mx^2 - 2(m-1)x + (m+2) = 0$ has two real and equal roots?
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Q5
short answer
2 marks
In Figure 2, PQ and PR are tangents to the circle centred at O. If $\angle OPR = 45^{\circ}$, then prove that ORPQ is a square.
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Q6
short answer
2 marks
The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.
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Q6
short answer
2 marks
Find the sum of first 20 terms of an AP in which $d = 5$ and $a_{20} = 135$.
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Q7
short answer
3 marks
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle of $30^{\circ}$ with it. The height of the breaking point from the ground is 2 m. Find the total height of the tree.
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Q8
short answer
3 marks
The percentage of marks obtained by 100 students in an examination are given below: Percentage of Marks 30-35 (16), 35-40 (14), 40-45 (18), 45-50 (20), 50-55 (18), 55-60 (12), 60-65 (2). Determine the median percentage of marks.
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Q8
short answer
3 marks
The percentage of marks obtained by 100 students in an examination are given below:
Percentage of Marks: 30-35, 35-40, 40-45, 45-50, 50-55, 55-60, 60-65
Number of Students: 16, 14, 18, 20, 18, 12, 2
Determine the median percentage of marks.
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Q10
short answer
3 marks
The weights (in kg) of 50 wild animals of a National Park were recorded and the following data was obtained:
Weight (in kg): 100-110, 110-120, 120-130, 130-140, 140-150
Number of animals: 4, 12, 23, 8, 3
Find the mean weight (in kg) of animals, using assumed mean method.
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Q11
short answer
4 marks
The angle of elevation of an aeroplane from a point on the ground is $60^\circ$. After a flight of 30 seconds, the angle of elevation from the same point becomes $30^\circ$. If the aeroplane is flying at a constant height of $3000\sqrt{3}$ m, find the speed of the aeroplane.
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Q12
short answer
3 marks
Draw a line segment AB of length 8 cm and locate a point P on AB such that AP : PB = 1 : 5.
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Q13
short answer
3 marks
Draw a circle of radius 3 cm. From a point P lying outside the circle at a distance of 6 cm from its centre, construct two tangents PA and PB to the circle.
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Q16
short answer
4 marks
In Figure 3, two circles with centres at O and O' of radii 2r and r respectively, touch each other internally at A. A chord AB of the bigger circle meets the smaller circle at C. Show that C bisects AB.
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Q17
short answer
4 marks
In Figure 4, O is centre of a circle of radius 5 cm. PA and BC are tangents to the circle at A and B respectively. If OP = 13 cm, then find the length of tangents PA and BC.
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In the picture given below, one can see a rectangular in-ground swimming pool installed by a family in their backyard. There is a concrete sidewalk around the pool of width x m. The outside edges of the sidewalk measure 7 m and 12 m. The area of the pool is 36 sq. m.
Q18
short answer
2 marks
Based on the information given above, form a quadratic equation in terms of x.
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Q19
short answer
2 marks
Find the width of the sidewalk around the pool.
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Q20
short answer
2 marks
In the picture given below, one can see a rectangular in-ground swimming pool installed by a family in their backyard. There is a concrete sidewalk around the pool of width $x$ m. The outside edges of the sidewalk measure 7 m and 12 m. The area of the pool is 36 sq. m. Based on the information given above, form a quadratic equation in terms of $x$.
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John planned a birthday party for his younger sister with his friends. They decided to make some birthday caps by themselves and to buy a cake from a bakery shop. For these two items, they decided the following dimensions : Cake : Cylindrical shape with diameter 24 cm and height 14 cm. Cap : Conical shape with base circumference 44 cm and height 24 cm.
Q21
short answer
2 marks
How many square cm paper would be used to make 4 such caps ?
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Q22
short answer
2 marks
The bakery shop sells cakes by weight (0·5 kg, 1 kg, 1·5 kg, etc.). To have the required dimensions, how much cake should they order, if 650 cm$^3$ equals 100 g of cake ?
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