Given,

2.2 dm³ of brass is to be drawn into a cylindrical wire of Diameter = 0.25 cm

So, radius of the wire (r) = d/2

= 0.25/2 = 0.125*10^-2 cm

Now, 1 cm = 0.01 m

So, 0.1cm = 0.001 m

Let the length of the wire be (h)

We know that,

Volume of the cylinder = pr²h

It’s understood that,

Volume of cylindrical wire = Volume of brass of 2.2 dm³

h = 448 m

Therefore, the length of the cylindrical wire drawn is 448 m

Given cost of 40 meters of cloth = Rs 200

Cost of 1 meter of cloth = (200/40)

Therefore, the cost of 50 chocolates = (200/40) × 50

= Rs 250

Given that number of kilometres a car can cover by using 36 litres of petrol = 522 km

Number of kilometres a car can cover by using 1 litre of petrol = 522/36

Hence, the number of kilometres a car can cover by using 14 litres = (522/36) × 14

= 203 km

Given cost of 20 chocolates = Rs 320

Cost of 1 chocolate = (320/20)

Therefore, the cost of 35 chocolates = (320/20) × 35

= Rs 560

Given,

A metallic block of dimension 11dm x 1m x 5dm

The diameter of each bullet = 5 cm

We know that,

Volume of the sphere = 4/3 pr³

Since, 1 dm = 10^-1m = 0.1 m

The volume of the rectangular block = 1.1 x 1 x 0.5 = 0.55 m³

Radius of the bullet = 5/2 = 2.5 cm

Let the number of bullets made from the rectangular block be n.

Then from the question,

The volume of the rectangular block = sum of the volumes of the n spherical bullets

0.55 = n x 4/3 p(2.5)³

Solving for n, we have

n = 8400

Therefore, 8400 can be cast from the rectangular block of metal.

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it is a process by which any individual reproduce and give birth to their offsprings.

Given: AP is 41, 38, 35,…, 8

Here, first term = a = 41

Last term = 8

Common difference = d = 38 – 41 = -3

To find: the number of terms (n)

Last term = a + (n – 1)d

8 = 41 + (n – 1)(-3)

8 – 41 = (n – 1)(-3)

n – 1 = 11

n = 11 + 1 = 12

There are 12 terms.

Given: AP is 6, 10, 14, 18,…, 174

Here, first term = a = 6

Common difference = d= 10 – 6 = 4

To find: the number of terms (n)

Last term = a + (n – 1)d

174 = 6 + (n – 1) 4

174 – 6 = (n – 1) 4

n – 1 = 168 /4 = 42

n = 42 + 1 = 43

There are 43 terms.

n^th term of AP is 4n – 10 (Given)

Putting n = 1, 2, 3, 4, …, we get

At n = 1: 4n – 10 = 4 x 1 – 10 = 4 – 10 = -6

At n = 2: 4n – 10 = 4 x 2 – 10 = 8 – 10 = -2

At n = 3: 4n – 10 = 4 x 3 – 10 = 12 – 10 = 2

At n = 1: 4n – 10 = 4 x 4 – 10 = 16 – 10 = 6

We see that -6, -2, 2, 6,… are in AP

(i) first term = -6

(ii) Common difference = -2 – (-6) = 4

(iii) 16th term:

Using formula: a_n = a + (n – 1)d

Here n = 16

a₁₆ = -6 + (16 – 1)4 = 54