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Q1
short answer
2 marks
For the A.P.; $a_1, a_2, a_3, ...$ if $\frac{a_3}{a_2} = \frac{7}{4}$, then find $\frac{a_8}{a_6}$.
Q2
short answer
2 marks
Solve for x : $2x^2 - 22x + 1 = 0$
Q3
short answer
2 marks
Find the value(s) of k for which the quadratic equation $x^2 + 5kx + 16 = 0$ has real and equal roots.
Q4
short answer
2 marks
Find the number of terms of the A.P. : 293, 285, 277, ..., 53
Q4
short answer
2 marks
In the following cumulative frequency table, find the values of a, b, c and d. Class: 0-10, 10-20, 20-30, 30-40, 40-50. Frequency: 5, 7, a, 5, b. Cumulative Frequency: 5, c, 18, d, 30.
Q5
short answer
2 marks
Find the sum of the first 40 positive integers divisible by 7.
Q5
short answer
2 marks
If the mode of the following data is 240, find the missing frequency: 0-100: 140, 100-200: 230, 200-300: 270, 300-400: x, 400-500: 150.
Q5
short answer
2 marks
If its mode is 240, find x for the given frequency distribution: Daily Household Expenditure (in ₹): 0-100 (140), 100-200 (230), 200-300 (270), 300-400 (x), 400-500 (150).
Q6
short answer
2 marks
In Figure 1, O is the centre of the circle. PQ and PR are tangent segments. Show that the quadrilateral PQOR is cyclic.
Q7
short answer
3 marks
Draw two concentric circles of radii 3 cm and 5 cm. By taking a point on the circle of radius 5 cm, construct the pair of tangents to the other circle of radius 3 cm.
Q8
short answer
3 marks
A man standing on the deck of a ship, which is 10 m above the water level, observes that the angle of elevation of the top of a hill is 60 and the angle of depression of the base of the hill is 30. Find the height of the hill.
Q10
long answer
3 marks
A canal is 300 cm wide and 120 cm deep. The water in the canal is flowing with a speed of 20 km/h. How much area will it irrigate in 20 minutes, if 8 cm of standing water is desired?
Q12
long answer
3 marks
The radius of the base and the height of a solid right circular cylinder are in the ratio 2 : 3 and its volume is 1617 cm$^3$. Find the total surface area of the cylinder. (Take $\pi = 22/7$)
Q12
long answer
4 marks
The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60. From a point Y, 40 m vertically above X, the angle of elevation of Q is 45. Find the height of the tower PQ and the distance XP. (Use $\sqrt{3} = 1.732$)
Q13
long answer
3 marks
A solid metallic sphere of radius 10.5 cm is melted and recast into a number of smaller solid cones, each of radius 3.5 cm and height 3 cm. Find the number of cones so formed.
Q15
long answer
4 marks
In Figure 2, two circles touch externally at P. A common tangent touches them at A and B and another common tangent is at P, which meets the common tangent AB at C. Prove that $\angle APB = 90^\circ$.
Q16
long answer
4 marks
In Figure 3, PQ and LM are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting PQ at A and LM at B. Prove that $\angle AOB = 90^\circ$.
Reading Passage
Social work aims at fulfilment of human needs. Social workers aim to open the doors of access and opportunity for those who are in greatest need. Free education is a great social work. By doing so, we can remove illiteracy from our society. Rohan, being a social worker, wants to donate his land to the Village Panchayat for opening of a school. Rohan's land is in the form of a rectangle 500 m by 400 m. The Village Panchayat decides to leave the area on all the four sides of the land for grass and flowers. If width of x m land is kept for grass and flowers on all the four sides (as shown in Figure 4).
Q18
long answer
2 marks
Find the lengths PQ and QR if area of grass and flowers region surrounding PQRS is 118400 square meters.
Q19
long answer
2 marks
Find the perimeter of rectangle PQRS.
Reading Passage
Health insurance is an agreement whereby the insurance company agrees to undertake a guarantee of compensation for medical expenses in case the insured falls ill or meets with an accident which leads to hospitalisation of the insured. The government also promotes health insurance by providing a deduction from income tax. An SBI health insurance agent found the following data for distribution of ages of 100 policy holders. The health insurance policies are given to persons having age 15 years and onwards but less than 60 years.
Q20
short answer
2 marks
Find the modal age of the policy holders. (Data provided: Age 15-20: 2, 20-25: 4, 25-30: 18, 30-35: 21, 35-40: 33, 40-45: 11, 45-50: 3, 50-55: 6, 55-60: 2)
Q21
short answer
2 marks
Find the median age of the policy holders.
