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Q1
short answer
2 marks
Find the mode of the following frequency distribution :
Q2
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.
Q3
short answer
2 marks
Find the sum of first 30 terms of AP : 30, 24, 18, ..... .
Q4
short answer
2 marks
In an AP if $S_n = n (4n + 1)$, then find the AP.
Q4
short answer
2 marks
A cone of height 28 cm and radius of base 7 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere.
Q6
short answer
2 marks
Find the value of m for which the quadratic equation (m 1) $x^2$ + 2 (m 1) x + 1 = 0 has two real and equal roots.
Q6
short answer
2 marks
Rohan's age 5 years ago and 7 years from now, is one more than twice his present age. Find his present age.
Q7
short answer
2 marks
Solve the following quadratic equation for x : $3x^2$ + 10x + 73 = 0
Q8
short answer
3 marks
Following is the daily expenditure on lunch by 30 employees of a company : Daily Expenditure (in Rupees) 100-120 (8), 120-140 (3), 140-160 (8), 160-180 (6), 180-200 (5). Find the mean daily expenditure of the employees.
Q9
short answer
3 marks
The angle of elevation of the top of a building from the foot of the tower is $30^\circ$ and the angle of elevation of the top of the tower from the foot of the building is $60^\circ$. If the tower is 50 m high, then find the height of the building.
Q9
short answer
3 marks
If the median of the following data is 33, then find the value of $m$: Class 0-15 (17), 15-30 (35), 30-45 (40), 45-60 (18), 60-75 (m), 75-90 (2).
Q10
short answer
3 marks
From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are $30^\circ$ and $45^\circ$ 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
Construct a pair of tangents to a circle of radius 5 cm, which are inclined to each other at an angle of $60^\circ$.
Q11
short answer
4 marks
In Figure 1, a right triangle ABC in which $\angle B = 90^\circ$, $AB = 12$ cm and $BC = 5$ cm is shown. Find the radius of the circle inscribed in the triangle ABC.
Q15
short answer
4 marks
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.
Q16
short answer
4 marks
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?
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
Q17
short answer
2 marks
Write the AP for the number of triangles used in the figures. Also, write the $n^{th}$ term of this AP.
Q18
short answer
2 marks
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
(a) draw a well-labelled figure based on the above information;
Q20
short answer
2 marks
(b) find the height (h) of the point A above water level. (Use 3 = 1.73)
