Class 10 Maths Exam Term 2 Question Paper & Answer Key 2022

Class 10 Term 2 Standard Maths Solution [Series- PPQQA/1 Set 1, Paper Code- 30/1/1]

SECTION A

Question 1- Find the sum of first 30 terms of AP: -30, 24, -18,/..

Solution- a= -30, d= 6

= 15 [-60 + 29 (6)]

= 15 [-60+174]

= 15 [114]

= 1710

Question 1- If an AP is Sn = n(4n+1), then find the AP

Solution- S1 = T1 = 5

S2= T1 + T2= 18

S2-S1 = T2= 13

AP= 5, 13, 21, 29, …

Question 2- 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.

Solution- r1 = 10.5 cm (sphere) and r2 (cone)= 3.5 cm, h2= 3cm

4/3πr³ = n x 1/3πr2² h

4r³ = nr2² h

4 x (105/10)³= n x 35/10 x 35/10 x 3

21 x 6= n

Number of cones formed= 126

Question 3 (a) Find the value of m for which the quadratic equation

(m-1) x² + 2(m-1)x + 1 = 0

Solution- D= 0

4 (m-1)² - 4(m-1) = 0

4 (m-1) [m-1-1]= 0

(m-1) (m-2)= 0

m= 2

(b) Solve the following quadratic equation for x: √3x² + 10x + 7√3= 0

Solution- √3x² + 3x + 7x + 7√3= 0

√3x (x+ √3) + 7 (x + √3)= 0

(x+ √3) [√3x + 7]= 0

x= √3 || x= -7/√3

Question 4- Find the mode of the following frequency distribution:

Solution- l= 40, f1= 17, f2= 4, fo= 12

Mode= l + f1-fo / 2f1 - fo- f2

= 40 + 17-12 / 34-12-4 x 10

= 40 + 5/18 x 10

= 40 + 25/9

= 40 + 2.78

= 42.78

Question 5- The product of Rehan's age (in years) 5 years ago and his age 7 years from now, is one more than twice his present age. Find his present age.

Solution

(x-5) (x+7) = 2x + 1

x² + 2x -35 = 2x+1

x² - 36 = 0

x² = 36

x= +_ 6

Present Age- 6 years

Question 6 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.

Solution-

SECTION B

Question 7- For what value of x, is the median of the following frequency distribution 34:5?

Solution-

Question 8- Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Construct tangents to the circle from these two points P and Q.

Solution-

Question 9-(a) The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, then find the height of the building.

Solution-

tan 60° = 50/b

b= 50/ tan 60°

b = 50/ √3

b= 50√3 / 3

tan 30° = h/(50√3/3)

h= 50√3/3 x 1/√3

= 50/3 m= 16.67 metres

(b) From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45° respectively. If the bridge is at a height of 3 m from the banks, then find the width of the river.

Solution-

Question 10- Following is the daily expenditure on lunch by 30 employees of a company, Find the mean daily expenditure of the employees.

Solution

Question 11- From a solid cylinder of the height of 30 cm and radius of 7 cm, a conical cavity of height of 24 cm and same radius is hollowed out. Find the total surface area of the remaining solid.

Solution- H= 30 cm

R= 7 cm

Total Surface Area of Cylinder = Curved Surface Area of Cylinder + Curved Surface Area of Cone + πr²

TSA = 2 πrh + πrl + πr²

= πr (2h+ l+ r)

= 22/7 x 7 (60+25 + 7)

= 22 x 92

TSA= 2024 cm

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?

Solution- Flow Rate= 12 kmph time= 1 hour b= 8 m h= 6m

lbh = LBH

lbh = Area x H

12x 8 x 6 x 1000 = Area x 5 /100

1152000 m² = Area

Question 12- In Figure 1, a triangle ABC with ㄥB = 90° 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.

CASE STUDY-1

Question 13- 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::

(a) Write the AP for the number of triangles used in the figures. Also, write the nth term of this AP. Which figure has 61 matchsticks?

Solution- AP = 4, 6, 8, 10

a= 4, d= 2

Tn = 4 + 2(n-1)

Tn= = 4 + 2n - 2

Tn= 2n +2

(b) Which figures has 61 matchstickes?

Solution- 12, 19, 26, …

Tn = 61

a + (n-1) d= 61

12 + 7(n-1) = 61

7(n-1) = 49

n-1 = 7

n= 8