CBSE Class 9 – Page 132

RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2H

January 5, 2022June 18, 2018 by Prasanna

RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2H

These Solutions are part of RS Aggarwal Solutions Class 9. Here we have given RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2H.

Other Exercises

Question 1.
Solution:
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2H Q1.1

Question 2.
Solution:
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2H Q2.1

Question 3.
Solution:
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2H Q3.1

Question 4.
Solution:
9x² + 16y² + 4z² – 24xy + 16yz – 12xz
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2H Q4.1

Question 5.
Solution:
25x² + 4y² + 9z² – 20xy – 12yz + 30xz
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2H Q5.1

Question 6.
Solution:
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2H Q6.1

Hope given RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2H are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

RD Sharma Class 9 Solutions Chapter 4 Algebraic Identities Ex 4.1

January 5, 2022June 18, 2018 by Prasanna

RD Sharma Class 9 Solutions Chapter 4 Algebraic Identities Ex 4.1

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 4 Algebraic Identities Ex 4.1

Question 1.
Evaluate each of the following using identities:
(i) (2x –\(\frac { 1 }{ x }\))²
(ii) (2x + y) (2x – y)
(iii) (a²b – b²a)²
(iv) (a – 0.1) (a + 0.1)
(v) (1.5.x² – 0.3y²) (1.5x² + 0.3y²)
Solution:
RD Sharma Class 9 Solutions Chapter 4 Algebraic Identities Ex 4.1 Q1.1

Question 2.
Evaluate each of the following using identities:
(i) (399)²
(ii) (0.98)²(iii) 991 x 1009
(iv) 117 x 83
Solution:
RD Sharma Class 9 Solutions Chapter 4 Algebraic Identities Ex 4.1 Q2.1

Question 3.
Simplify each of the following:
RD Sharma Class 9 Solutions Chapter 4 Algebraic Identities Ex 4.1 Q3.1
Solution:

Question 4.
RD Sharma Class 9 Solutions Chapter 4 Algebraic Identities Ex 4.1 Q4.1
Solution:

Question 5.
RD Sharma Class 9 Solutions Chapter 4 Algebraic Identities Ex 4.1 Q5.1
Solution:

Question 6.
RD Sharma Class 9 Solutions Chapter 4 Algebraic Identities Ex 4.1 Q6.1
Solution:

Question 7.
If 9x² + 25y² = 181 and xy = -6, find the value of 3x + 5y.
Solution:
9x² + 25y² = 181, and xy = -6
(3x + 5y)² = (3x)² + (5y)² + 2 x 3x + 5y
⇒ 9X² + 25y² + 30xy
= 181 + 30 x (-6)
= 181 – 180 = 1
= (±1 )²
∴ 3x + 5y = ±1

Question 8.
If 2x + 3y = 8 and xy = 2, find the value of 4X² + 9y².
Solution:
2x + 3y = 8 and xy = 2
Now, (2x + 3y)² = (2x)² + (3y)² + 2 x 2x x 3y
⇒ (8)² = 4x² + 9y² + 12xy
⇒ 64 = 4X² + 9y² + 12 x 2
⇒ 64 = 4x² + 9y² + 24
⇒ 4x² + 9y² = 64 – 24 = 40
∴ 4x² + 9y² = 40

Question 9.
If 3x -7y = 10 and xy = -1, find the value of 9x² + 49y²
Solution:
3x – 7y = 10, xy = -1
3x -7y= 10
Squaring both sides,
(3x – 7y)² = (10)²⇒ (3x)² + (7y)² – 2 x 3x x 7y = 100
⇒ 9X² + 49y² – 42xy = 100
⇒ 9x² + 49y² – 42(-l) = 100
⇒ 9x² + 49y² + 42 = 100
∴ 9x² + 49y² = 100 – 42 = 58

Question 10.
Simplify each of the following products:
RD Sharma Class 9 Solutions Chapter 4 Algebraic Identities Ex 4.1 Q10.1
Solution:

Question 11.
RD Sharma Class 9 Solutions Chapter 4 Algebraic Identities Ex 4.1 Q11.1
Solution:

Question 12.
RD Sharma Class 9 Solutions Chapter 4 Algebraic Identities Ex 4.1 Q12.1
Solution:

Question 13.
Simplify each of the following products:
RD Sharma Class 9 Solutions Chapter 4 Algebraic Identities Ex 4.1 Q13.1
Solution:

Question 14.
Prove that a² + b² + c² – ab – bc – ca is always non-negative for all values of a, b and c.
Solution:
RD Sharma Class 9 Solutions Chapter 4 Algebraic Identities Ex 4.1 Q14.1
∵ The given expression is sum of these squares
∴ Its value is always positive Hence the given expression is always non-negative for all values of a, b and c

Hope given RD Sharma Class 9 Solutions Chapter 4 Algebraic Identities Ex 4.1 are helpful to complete your math homework.

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RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G

January 5, 2022June 18, 2018 by Prasanna

RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G

These Solutions are part of RS Aggarwal Solutions Class 9. Here we have given RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2G.

Other Exercises

Factorize :

Question 1.
Solution:
x² + 11x + 30
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 1

Question 2.
Solution:
x² + 18x + 32
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 2.1

Question 3.
Solution:
x² + 7x – 18
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 3.1

Question 4.
Solution:
x² + 5x – 6
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 4.1

Question 5.
Solution:
y² – 4y + 3
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 5.1

Question 6.
Solution:
x² – 21x + 108
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 6.1

Question 7.
Solution:
x² – 11x – 80
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 7.1

Question 8.
Solution:
x² – x – 156
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 8.1

Question 9.
Solution:
z² – 32z – 105
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 9.1

Question 10.
Solution:
40 + 3x – x²
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 10.1

Question 11.
Solution:
6 – x – x²
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 11.1

Question 12.
Solution:
7x² + 49x + 84
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 12.1

Question 13.
Solution:
m² + 17mn – 84n²
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 13.1

Question 14.
Solution:
5x² + 16x + 3
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 14.1

Question 15.
Solution:
6x² + 17x + 12
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 15.1

Question 16.
Solution:
9x² + 18x + 8
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 16.1

Question 17.
Solution:
14x² + 9x + 1
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 17.1

Question 18.
Solution:
2x² + 3x – 90
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 18.1

Question 19.
Solution:
2x² + 11x – 21
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 19.1

Question 20.
Solution:
3x² – 14x + 8
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 20.1

Question 21.
Solution:
18x² + 3x- 10
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 21.1

Question 22.
Solution:
15x² + 2x – 8
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 22.1

Question 23.
Solution:
6x² + 11x – 10
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 23.1

Question 24.
Solution:
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 24.1

Question 25.
Solution:
24x² – 41x + 12
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 25.1

Question 26.
Solution:
2x² – 7x – 15
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 26.1

Question 27.
Solution:
6x² – 5x – 21
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 27.1

Question 28.
Solution:
10x² – 9x – 7
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 28.1

Question 29.
Solution:
5x² – 16x – 21
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 29.1

Question 30.
Solution:
2x² – x – 21
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 30.1

Question 31.
Solution:
15x² – x – 28
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 31.1

Question 32.
Solution:
8a² – 27ab + 9b²
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 32.1

Question 33.
Solution:
5x² + 33xy -14y²
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 33.1

Question 34.
Solution:
3x³ – x² – 10x
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 34.1

Question 35.
Solution:
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 35.1

Question 36.
Solution:
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 36.1

Question 37.
Solution:
√2x² + 3x + √2
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 37.1

Question 38.
Solution:
√5x² + 2x – 3√5
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 38.1

Question 39.
Solution:
2a² + 3√3x + 3
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 39.1

Question 40.
Solution:
2√3x² + x – 5√3
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 40.1

Question 41.
Solution:
5√5x² + 20x + 3√5
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 41.1

Question 42.
Solution:
7√x² – 10x – 4√2
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 42.1

Question 43.
Solution:
6√3 x² – 47x + 5√3
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 43.1

Question 44.
Solution:
7x² + 2√14x + 2
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 44.1

Question 45.
Solution:
2(x + y)² – 9(x + y) – 5
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 45.1

Question 46.
Solution:
9(2a-b)²-4(2a-b)-13
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 46.1

Question 47.
Solution:
7(x – 2y)² – 25 (x – 2y) + 12
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 47.1

Question 48.
Solution:
4x⁴ + 7x²-2
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2G 48.1

Hope given RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2G are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS

January 5, 2022June 18, 2018 by Prasanna

RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS

Mark the correct alternative in each of the following:
Question 1.
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q1.1
Solution:

Question 2.
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q2.1
Solution:

Question 3.
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q3.1
Solution:

Question 4.
The rationalisation factor of 2 + \(\sqrt { 3 } \) is
(a) 2 – \(\sqrt { 3 } \)
(b) \(\sqrt { 2 } \) + 3
(c) \(\sqrt { 2 } \) – 3
(d) \(\sqrt { 3 } \) – 2
Solution:
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q4.1

Question 5.
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q5.1
Solution:

Question 6.
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q6.1
Solution:

Question 7.
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q7.1
Solution:

Question 8.
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q8.1
Solution:

Question 9.
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q9.1
Solution:

Question 10.
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q10.1
Solution:

Question 11.
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q11.1
Solution:

Question 12.
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q12.1
Solution:

Question 13.
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q13.1
Solution:

Question 14.
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q14.1
Solution:

Question 15.
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q15.1
Solution:

Question 16.
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q16.1
Solution:

Question 17.
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q17.1
Solution:

Question 18.
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q18.1
Solution:

Question 19.
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q19.1
Solution:

Question 20.
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q20.1
Solution:

Question 21.
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q21.1
Solution:

Question 22.
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q22.1
Solution:

Question 23.
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q23.1
Solution:

Question 24.
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q24.1
Solution:

Question 25.
RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS Q25.1
Solution:

Hope given RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2F

January 5, 2022June 18, 2018 by Prasanna

RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2F

These Solutions are part of RS Aggarwal Solutions Class 9. Here we have given RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2F.

Other Exercises

Factorize :

Question 1.
Solution:
25x² – 64y²
= (5x)² – (8y)²
= (5x + 8y) (5x – 8y) Ans.

Question 2.
Solution:
100 – 9x²
(10)² – (3x)²
= (10 + 3x) (10 – 3x) Ans.

Question 3.
Solution:
5x² – 7y²
=(√5x)² +(√7y)²
=(√5x – √7y)(√5x – √7y) Ans

Question 4.
Solution:
(3x + 5y)² – 4z²
= (3x + 5y)² – (2z)²
= (3x + 5y + 2z) (3x + 5y – 2z) Ans.

Question 5.
Solution:
150 – 6x²
= 6(25 – x²)
= 6{(5)² – (x²)}
= 6 (5 + x) (5 – x) Ans.

Question 6.
Solution:
20x² – 45
= 5 (4x² – 9)
= 5{(2x)² – (3)²}
= 5 (2x + 3) (2x – 3) Ans.

Question 7.
Solution:
3x³ – 48x
= 3x (x² – 16)
= 3x {(x)² – (4)²}
= 3x (x + 4) (x – 4) Ans.

Question 8.
Solution:
2 – 50x²
= 2(1 – 25x²) = 2 {(1)² – (5x)²}
= 2 (1 + 5x) (1 – 5x) Ans.

Question 9.
Solution:
27a² – 48b²
= 3(9a² – 16b²)
= 3 {(3a)² – (4b)²}
= 3(3a + 4b) (3a – 4b) Ans.

Question 10.
Solution:
x – 64x³
= x (1 – 64x²)
= x{(1)² – (8x)²}
= x (1 + 8x) (1 – 8x) Ans.

Question 11.
Solution:
8ab² – 18a³
= 2a (4b² – 9a²)
= 2a {(2b)² – (3a)²}
= 2a (2b + 3a) (2b – 3a) Ans

Question 12.
Solution:
3a³b – 243ab³
= 2ab (a² -81 b²)
= 3ab {(a)² – (9b)²}
= 3ab (a + 9b) (a – 9b) Ans.

Question 13.
Solution:
(a + b)³ – a – b
= (a + b)³ – 1 (a + b)
= (a + b) {(a + b)² – 1}
= (a + b) {(a + b)² – (1)²}
= (a + b) (a + b + 1) (a + b – 1) Ans.

Question 14.
Solution:
108 a² – 3(b – c)²
= 3 {36a² – (b – c)²}
= 3 {(6a)² – (b – c)²}
= 3 {(6a + (b – c)} {6a – (b – c)}
= 3 (6a + b – c) (6a – b + c) Ans.

Question 15.
Solution:
x³ – 5x² – x + 5
= x²(x – 5) -1(x – 5)
= (x – 5) (x² – 1)
= (x – 5) {(x)² – (1)²}
= (x – 5) (x + 1) (x – 1) Ans.

Question 16.
Solution:
a² + 2ab + b² – 9c²
= (a + b)² – (3c)²
= {a² + b² + 2ab – (a + b)²}
= (a + b + 3c) (a + b – 3c) Ans.

Question 17.
Solution:
9 – a² + 2ab – b²
= 9 – (a² – 2ab + b²)
= (3)² -(a- b)²
{ ∴a² + b² – 2ab = (a – b)²}
= (3 + a – b) (3 – a + b) Ans.

Question 18.
Solution:
a²– b² – 4ac + 4c²
= a² – 4ac + 4c² – b²
= (a)² – 2 x a x 2c + (2c)² – (b)²
= (a – 2c)² – (b)²
= (a – 2c + b) (a – 2c – b)
= (a + b – 2c) (a – b – 2c) Ans.

Question 19.
Solution:
9a² + 3a – 8B – 64b²
= 9a² – 64b² + 3a – 8b
= (3a)² – (8b)² + 1(3a – 8b)
= (3a + 8b) (3a – 8b) + 1 (3a – 8b)
= (3a – 8b) (3a + 8b + 1) Ans.

Question 20.
Solution:
x² – y² + 6y _ 9
= (x)2 – (y² – 6y + 9)
= (x)2 – {(y)² – 2 x y x 3 + (3)²}
= (x)² – (y – 3)²
= (x + y – 3) (x – y + 3) Ans.

Question 21.
Solution:
4x² – 9y² – 2x – 3y
= (2x)² – (3y)² – 1(2x + 3y)
= (2x + 3y) (2x – 3y) – 1( 2x + 3y)
= (2x + 3y) (2x – 3y – 1) Ans.

Question 22.
Solution:
x⁴ – 1
= (x²)² – (1)²
= (x² + 1) (x² – 1)
= (x² + 1) {(x)² – (1)²}
= (x² + 1) (x + 1) (x – 1) Ans.

Question 23.
Solution:
a – b – a²+ b²
= 1 (a – b) – (a² – b²)
= 1 (a – b) – (a + b) (a – b)
= (a – b) (1 – a – b) Ans.

Question 24.
Solution:
x⁴ – 625
= (x²)² – (25)²
= (x² + 25) (x² – 25)
= (x² + 25) {(x)² – (5)²}
= (x² + 25) (x + 5) (x – 5) Ans.

Hope given RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2F are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.