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Q1
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.
Q2
short answer
2 marks
Solve the following quadratic equation for x : $\sqrt{3}x^2 + 10x + 7\sqrt{3} = 0$
Q2
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.
Q4
short answer
2 marks
Find the sum of the first twelve 2-digit numbers which are multiples of 6.
Q4
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.
Q5
short answer
2 marks
In an AP, if $a_2 = 26$ and $a_{15} = 26$, then write the AP.
Q5
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.
Q6
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)
Q6
short answer
2 marks
Find the mode of the following frequency distribution : \begin{tabular}{|l|c|c|c|c|c|} \hline Class & 10-20 & 20-30 & 30-40 & 40-50 & 50-60 \\ \hline Frequency & 15 & 10 & 12 & 17 & 4 \\ \hline \end{tabular}
Q8
short answer
3 marks
Draw a line segment AB = 7 cm. Divide it in the ratio 3 : 2.
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
For what value of x, is the median of the following frequency distribution 34·5 ? \begin{tabular}{|l|c|} \hline Class & Frequency \\ \hline 0-10 & 3 \\ 10-20 & 5 \\ 20-30 & 11 \\ 30-40 & 10 \\ 40-50 & x \\ 50-60 & 3 \\ 60-70 & 2 \\ \hline \end{tabular}
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
The following table gives the production yield of wheat of farms of a village : \begin{tabular}{|l|c|c|c|c|c|} \hline Production Yield (in kg/ha) & 50-60 & 60-70 & 70-80 & 80-90 & 90-100 \\ \hline Number of Farms & 7 & 12 & 11 & 8 & 2 \\ \hline \end{tabular} Find the mean production yield, using assumed mean method.
Q11
long answer
4 marks
In Figure 1, a triangle ABC with $\angle B = 90^\circ$ 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.
Q16
long answer
4 marks
In Figure 2, from a solid cube of side 7 cm, a cylinder of radius 2·1 cm and height 7 cm is scooped out. Find the total surface area of the remaining solid.
Q17
long answer
4 marks
A well of diameter 5 m is dug 24 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 3 m to form an embankment. Find the height of the embankment.
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
Q18
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.
Q19
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
Q20
short answer
2 marks
draw a well-labelled figure based on the above information;
Q21
short answer
2 marks
find the height (h) of the point A above water level. (Use $\sqrt{3} = 1.73$)
