Introduction to Linear Polynomials Class 9 Mathematics Ganita Manjari [LATEST] Solutions Exercise Set 2.2 in English - CBSE Study
NCERT Solutions for Class 9 Mathematics Ganita Manjari are carefully prepared according to the latest CBSE syllabus and NCERT textbooks to help students understand every concept clearly. These solutions cover all important Introduction to Linear Polynomials with detailed explanations and step-by-step answers for better exam preparation. Each Exercise Set 2.2 is explained in simple language so that students can easily grasp the fundamentals and improve their academic performance. The study material is designed to support daily homework, revision practice, and final exam preparation for Class 9 students. With accurate answers, concept clarity, and structured content, these NCERT solutions help learners build confidence and score higher marks in their examinations. Whether you are revising a specific topic or preparing an entire chapter, this resource provides reliable and syllabus-based guidance for complete success in Mathematics Ganita Manjari.
Class 9 English Medium Mathematics Ganita Manjari All Chapters:
Introduction to Linear Polynomials
2. Exercise Set 2.2
Q1. Find the value of the linear polynomial 5x – 3 if:
(i) x = 0 (ii) x = –1 (iii) x = 2
Solutions:
P(x) = 5x - 3
(i) x = 0
P(0) = 5(0) - 3
= 0 - 3
= - 3 Ans
(ii) x = -1
P(-1) = 5(-1) - 3
= -5 - 3
= - 8 Ans
(iii) x = 2
P(2) = 5(2) - 3
= 10 - 3
= 7 Ans
Q2. Find the value of the quadratic polynomial 7s2 – 4s + 6 if:
(i) s = 0 (ii) s = –3 (iii) s = 4
Solution:
P(s) = 7s2 - 4s + 6
(i) s = 0
P(0) = 7(0)2 - 4(0) + 6
= 0 - 0 + 6
= 6 Ans
(ii) s = –3
P(–3) = 7(–3)2 - 4(–3) + 6
= 63 + 12 + 6
= 81 Ans
(iii) s = 4
P(4) = 7(4)2 - 4(4) + 6
= 112 - 16 + 6
= 118 - 16
= 102 Ans
Q3. The present age of Salil’s mother is three times Salil’s present age. After 5 years, their ages will add up to 70 years. Find their present ages.
Solution:
Let the Salil's present Age be x
Salil's Mother present age = 3x
After 5 years
Salil's age = x + 5
Salil's mother age = 3x + 5
So,
Therefore, Salil's Present Age = 15 years
Salil's Mother Present Age = 3 x 15 = 45 years
Q4. The difference between two positive integers is 63. The ratio of the two integers is 2:5. Find the two integers.
Solution:
Ratio of the two integers = 2 : 5
Let the first integer be 2x
And the second integer be 5x
So, 5x - 2x = 63
3x = 63
x = 63/3
x = 21
The first integer = 2 x 21 = 42
The second integer = 5 x 21 = 105
Q5. Ruby has 3 times as many two-rupee coins as she has five rupee-coins. If she has a total 88, how many coins does she have of each type?
Solution:
Let the number of five-rupee coins be x.
Then, the number of two-rupee coins will be 3x.
Value of five-rupee coins = 5x
Value of two-rupee coins = 2(3x)
According to the question:
5x + 2(3x) = 88
Now solve:
5x + 6x = 88
11x = 88
x = 88/11
x = 8
So, number of five-rupee coins = 8
Number of two-rupee coins = 3 × 8 = 24
Therefore:
Five-rupee coins = 8
Two-rupee coins = 24
Q6. A farmer cuts a 300 feet fence into two pieces of different sizes. The longer piece is four times as long as the shorter piece. How long are the two pieces?
Solution:
Let the length of the shorter piece be x feet.
Then, the length of the longer piece will be 4x feet.
According to the question:
x + 4x = 300
Now solve:
5x = 300
x = 300/5
x = 60
So, length of the shorter piece = 60 feet
Length of the longer piece = 4 × 60
= 240 feet
Therefore:
Shorter piece = 60 feet
Longer piece = 240 feet
Q7. If the length of a rectangle is three more than twice its width and its perimeter is 24 cm, what are the dimensions of the rectangle?
Solution:
Let the width of the rectangle be x cm.
Then, the length of the rectangle will be 2x + 3 cm.
Perimeter of rectangle = 2(length + width)
According to the question:
2[(2x + 3) + x] = 24
Now solve:
2(3x + 3) = 24
6x + 6 = 24
6x = 24 − 6
6x = 18
x = 18/6
x = 3
So, width of the rectangle = 3 cm
Length of the rectangle = 2(3) + 3
= 6 + 3
= 9 cm
Therefore:
Width = 3 cm
Length = 9 cm
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