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Q1
short answer
2 marks
Find the number of terms in the following AP: 5, 11, 17, ....., 203
Q2
short answer
2 marks
Find the sum of the first 20 terms of an AP whose nth term is given as $a_n = 5 - 3n$.
Q2
short answer
2 marks
Find the roots of the quadratic equation $9x^2 - 6\sqrt{2}x + 2 = 0$.
Q3
short answer
2 marks
How many spherical shots each having diameter 3 cm can be made by melting a cuboidal solid of dimensions 18 cm x 22 cm x 6 cm?
Q4
short answer
2 marks
The mode of the following distribution is 24 and the sum of all frequencies is 50. Find the missing frequencies x and y: Class: 0-10, 10-20, 20-30, 30-40, 40-50; Frequency: 4, x, 20, y, 6.
Q4
short answer
2 marks
The mode of the following distribution is 24 and the sum of all frequencies is 50. Find the missing frequencies x and y.
Class Frequency
0-10 4
10-20 x
20-30 20
30-40 y
40-50 6
Q5
short answer
2 marks
In two concentric circles, a chord of length 48 cm of the larger circle is a tangent to the smaller circle, whose radius is 7 cm. Find the radius of the larger circle.
Q7
short answer
2 marks
The product of two consecutive odd positive integers is 255. Find the integers, by formulating a quadratic equation.
Q7
short answer
3 marks
Write the steps of construction for constructing a pair of tangents to a circle of radius 4 cm from a point P, at a distance of 7 cm from its centre O.
Q8
short answer
2 marks
Find the value(s) of k for the quadratic equation, $(k + 3)x^2 + kx + 1 = 0$, to have two real and equal roots.
Q9
short answer
3 marks
The following frequency distribution shows the ages of 50 policyholders. Calculate the median age, if policies are given only to persons having age 18 years onwards, but less than 60 years.
Age (in years): Below 20, 30, 40, 50, 60
Number of Policyholders: 1, 12, 39, 46, 50
Q10
short answer
3 marks
The table below shows the daily expenditure on food of 50 households of a locality. Find the mean daily expenditure.
Daily Expenditure (in ₹): 200-250, 250-300, 300-350, 350-400, 400-450
Number of Households: 8, 10, 12, 10, 10
Q11
short answer
3 marks
As observed from the top of a lighthouse 60 m high from the sea level, the angles of depression of two ships are 45° and 60°. If one ship is exactly behind the other on the same side of the lighthouse, then find the distance between the two ships. [Use $\sqrt{3} = 1.732$]
Q12
short answer
3 marks
A 1.6 m tall boy stands at a distance of 3 m from a lamp-post and casts a shadow of length 4 m on the ground. Find the height of the lamp-post.
Q12
short answer
4 marks
At a point on the level ground, the angle of elevation of the top of a vertical tower is found to be $\alpha$, such that $\tan \alpha = 12/5$. On walking 192 m towards the tower, the angle of elevation is $\beta$ such that $\tan \beta = 4/3$. Find the height of the tower.
Q15
short answer
4 marks
If two circles touch each other externally, then prove that the point of contact lies on the line joining their centres.
Q16
short answer
4 marks
Prove that the lengths of two tangents drawn from an external point to a circle are equal.
Reading Passage
While buying an expensive item like a house or a car, it becomes easier for a middle-class person to take a loan from a bank and then repay the loan along with interest in easy instalments. Aman buys a car by taking a loan of ₹ 2,36,000 from the bank and starts repaying the loan in monthly instalments. He pays ₹ 2,000 as the first instalment and then increases the monthly instalment by ₹ 500.
Q18
short answer
2 marks
Find out the amount he pays in the 25th instalment.
Reading Passage
While buying an expensive item like a house or a car, it becomes easier for a middle-class person to take a loan from a bank and then repay the loan along with interest in easy instalments. Aman buys a car by taking a loan of ₹ 2,36,000 from the bank and starts repaying the loan in monthly instalments. He pays ₹ 2,000 as the first instalment and then increases the instalment by ₹ 500 every month.
Q19
short answer
2 marks
Find the total amount paid by him in first 25 instalments.
Reading Passage
Conical bottom tanks in which an inverted cone at the bottom is surmounted by a cylinder of same diameter, are very advantageous in industry, specially where getting every last drop from the tank is important. Vikas designed a conical bottom tank where the height of the conical part is equal to its radius and the height of the cylindrical part is two times of its radius. The tank is closed from the top.
Q20
short answer
2 marks
If the radius of the cylindrical part is 3 m, then find the volume of the tank.
Q21
short answer
2 marks
Find the ratio of the volume of the cylindrical part to the volume of the conical part.
