For Rihan

 


Question 8

Given:
First term
Last term
Sum

(a) Formula to calculate sum of first terms


S_n = \frac{n}{2}(a + l)

(b) Find the total number of terms


220 = \frac{n}{2}(4 + 40)

220 = \frac{n}{2} \times 44 


220 = 22n

n = 10 

✅ Answer: Number of terms = 10

(c) What should be added to the third term so that first three terms form a GP?

AP terms:
1st = 4
2nd = 8
3rd = 12

Let required number =

New third term =

For GP:


(8)^2 = 4(12 + x)

64 = 48 + 4x 


4x = 16

x = 4 

✅ Answer: 4

Question 11

Given:
Length is 8 m more than breadth
Area = 384 sq.m

Let breadth = m
Length =

(a) Form the equation


x(x + 8) = 384

x^2 + 8x - 384 = 0 

(b) Find length and breadth


(x + 24)(x - 16) = 0


x = 16

Breadth = 16 m
Length = 24 m

✅ Answer: Length = 24 m, Breadth = 16 m

(c) How much should length be decreased to make it a square?


24 - 16 = 8 \text{ m}

✅ Answer: 8 m

Question 12

Given:
A circle with centre O
∠RMP and ∠RNP are angles standing on the same arc RP
∠ROP is the central angle

(a) Relation between ∠RMP and ∠RNP

Angles standing on the same arc are equal.


\angle RMP = \angle RNP

✅ Answer: Equal

(b) Find ∠MRN

Given:


\angle MRN = (7x - 2)^\circ

\angle MPN = (3x + 10)^\circ 

Since they stand on the same arc:


7x - 2 = 3x + 10

4x = 12 


x = 3


\angle MRN = 7(3) - 2 = 19^\circ

✅ Answer: 19°

(c) Relation between central and inscribed angle

Central angle is twice the inscribed angle.


\angle ROP = 2\angle RMP

✅ Verified


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