10th Maths - Book Back Answers - Chapter 3 Excercise 3.20 - English Medium Guides

  

 

SSLC / 10th - Maths - Book Back Answers - Chapter 3 Excercise 3.20 - English Medium

Tamil Nadu Board 10th Standard Maths - Chapter 3 Excercise 3.20: Book Back Answers and Solutions

    This post covers the book back answers and solutions for Chapter 3 Excercise 3.20 – Maths from the Tamil Nadu State Board 10th Standard Maths textbook. These detailed answers have been carefully prepared by our expert teachers at KalviTips.com.

    We have explained each answer in a simple, easy-to-understand format, highlighting important points step by step under the relevant subtopics. Students are advised to read and memorize these subtopics thoroughly. Once you understand the main concepts, you’ll be able to connect other related points with real-life examples and confidently present them in your tests and exams.

    By going through this material, you’ll gain a strong understanding of Chapter 3 Excercise 3.20 along with the corresponding book back questions and answers (PDF format).

Question Types Covered:

• 1 Mark Questions: Choose the correct answer, Fill in the blanks, Identify the correct statement, Match the following 
• 2 Mark Questions: Answer briefly 
• 3, 4, and 5 Mark Questions: Answer in detail

All answers are presented in a clear and student-friendly manner, focusing on key points to help you score full marks.

All the best, Class 10 students! Prepare well and aim for top scores. Thank you!

Chapter 3 Algebra Ex 3.20

1. A system of three linear equations in three variables is inconsistent if their planes
(1) intersect only at a point
(2) intersect in a line
(3) coincides with each other
(4) do not intersect
Answer Key:

(4) do not intersect

 

2. The solution of the system x + y -3z = -6, -7y + 7z = 7,3z = 9 is
(1) x = 1, y = 2, z = 3
(2) x = -1, y = 2, z = 3
(3) x = -1, y = -2, z = 3
(4) x = 1, y = 2, z = 3
Answer Key:
(4) x = 1, y = 2, z = 3
Hint:
x + y – 3z = -6
-7y + 7z = 7
3z = 9
z = 3
-7y + 21 = 7
-7y = -14
y = 2
x + 2 -3 × 3 = -6
x + 2 – 9 = -6 .
x = -6 + 7 = 1

 

3. If (x – 6) is the HCF of x² – 2x – 24 and x² – kx – 6 then the value of k is ……………..
(1) 3
(2) 5
(3) 6
(4) 8
Answer Key:
(2) 5
Hint.
HCF = x – 6
p(x) = x² – 2x – 24
= (x – 6) (x + 4)
g(x) = x² – kx – 6
∴ x – 6 is the common factor.
g (6) = 6² – k(6) – 6
= 36 – 6k – 6
= 30 – 6k
g(6) = 0
30 – 6k = 0
30 = 6k ⇒ k = $\frac{30}{6}$= 5
The value of k = 5

 

4. $\frac{\mathbf{3}\mathbf{y}\mathbf{-}\mathbf{3}}{\mathbf{y}}\mathbf{+}\frac{\mathbf{7}\mathbf{y}\mathbf{-}\mathbf{7}}{\mathbf{3}{\mathbf{y}}^{\mathbf{2}}}$is …………

(1) $\frac{\mathbf{9}\mathbf{y}}{\mathbf{7}}$

(2)$\frac{\mathbf{9}{\mathbf{y}}^{\mathbf{3}}}{\mathbf{(}\mathbf{21}\mathbf{y}\mathbf{-}\mathbf{21}\mathbf{)}}$

(3) $\frac{\mathbf{21}{\mathbf{y}}^{\mathbf{2}}\mathbf{-}\mathbf{42}\mathbf{y}\mathbf{+}\mathbf{21}}{\mathbf{3}{\mathbf{y}}^{\mathbf{3}}}$

(4) $\frac{\mathbf{7}\mathbf{(}{\mathbf{y}}^{\mathbf{2}}\mathbf{-}\mathbf{2}\mathbf{y}\mathbf{+}\mathbf{1}\mathbf{)}}{{\mathbf{y}}^{\mathbf{2}}}$ 

Answer Key:

(1) $\frac{\mathbf{9}\mathbf{y}}{\mathbf{7}}$

Hint:

$\frac{\mathbf{ }}{}$

  

 

5. ${\mathrm{y}}^2+\frac{1}{y^2}$ is not equal to ………….

(1) $\frac{{\mathrm{y}}^2+1}{{\mathrm{y}}^2}$

(2) (y +$\frac{\mathbf{1}}{\mathbf{y}}$)²
(3) (y -$\frac{\mathbf{1}}{\mathbf{y}}$)²
(4) (y +$\frac{\mathbf{1}}{\mathbf{y}}$)² – 2
Answer Key:
(2) (y +$\frac{\mathbf{1}}{\mathbf{y}}$)²
Hint.

${\mathrm{y}}^2+\frac{1}{y^{\mathrm{2=}}}$ (y +$\frac{\mathbf{1}}{\mathbf{y}}$)² – 2$\frac{\mathbf{<math\; xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi\; mathvariant="normal"></mi></mfrac><mo>\times y</mo></math>}}{}$$\frac{\mathbf{<math\; xmlns="http://www.w3.org/1998/Math/MathML"><mo>\times </mo></math>}}{}$$\frac{\mathbf{1}}{\mathbf{y}}$                        [a²+b²=(a+b)²-2ab]

$\frac{\mathbf{ \; \; \; \; \; \; = }}{}$(y +$\frac{\mathbf{1}}{\mathbf{y}}$)² – 2≠ (y +$\frac{\mathbf{1}}{\mathbf{y}}$)²

 

6. $\frac{\mathbf{x}}{{\mathbf{x}}^{\mathbf{2}}\mathbf{-}\mathbf{25}}\mathbf{-}\frac{\mathbf{8}}{{\mathbf{x}}^{\mathbf{2}}\mathbf{+}\mathbf{6}\mathbf{x}\mathbf{+}\mathbf{5}}$ gives …………..

Answer Key:

Hint.

 

7. The square root of $\frac{256x^8{y}^4{z}^{10}}{25x^6{y}^6{z}^6}$ is equal to ………….

Answer Key: 

Hint.

8. Which of the following should be added to make x⁴ + 64 a perfect square
(1) 4x²
(2) 16x²
(3) 8x²
(4) -8x²
Answer Key:
(2) 16x²
Hint:
x⁴ + 64 = (x²)² + 8² + 2 × 8x²
= (x² + 8)²

 

9. The solution of (2x – 1)² = 9 is equal to ………..
(1) -1
(2) 2
(3) -1, 2
(4) None of these
Answer Key:
(3) -1, 2
Hint.
(2x – 1)² = 9 ⇒ (2x – 1) = 9–√
2x – 1 = ± 3 ⇒ 2x – 1 = 3 or 2x – 1 = 3
2x – 1 = 3
2x = 4 ⇒ x = 42 = 2
2x – 1 = -3 ⇒ 2x = -3 + 1
x = -1

 

10. The values of a and b if 4x⁴ – 24x³ + 76x² + ax + b is a perfect square are ………..
(1) 100,120
(2) 10,12
(3) -120,100
(4) 12,10
Answer Key:
(3) -120,100
Hint.
Since it is a perfect square
a + 120 = 0
a = -120
b – 100 = 0

b = 100

11. If the roots of the equation q²x² + p²x + r² = 0 are the squares of the roots of the equation qx² + px + r = 0 , then q,p,r are in ……………..
(1) A.P.
(2) G.P.
(3) Both A.P and G.P
(4) none of these
Answer Key:
(2) G.P.
Hint.
q²x² + p²x + r² = 0
Let the roots be α² + β²
α² + β² = $\frac{-p^2}{q^2}$
α²β² =$\frac{r^2}{q^2}$
qx² + px + r = 0
Let the root be α and β

12. Graph of a linear polynomial is a
(1) straight line
(2) circle
(3) parabola
(4) hyperbola
Answer Key:

(1) straight line

 

13. The number of points of intersection of the quadratic polynomial x2 + 4x + 4 with the X axis is …………….
(1) 0
(2) 1
(3) 0 or 1
(4) 2
Answer Key:
(2) 1
Hint:
(x + 2)² = 0 ⇒ (x + 2) (x + 2) = 0
x + 2 = 0 or x + 2 = 0 ⇒ x = -2 or x = -2
Number of points of intersection is 1 (both the values are same)

 

14. For the given matrix

the order of the matrix A^T is ……………
(1) 2 × 3
(2) 3 × 2
(3) 3 × 4
(4) 4 × 3
Answer Key:
(3) 3 × 4

 

15. If A is a 2 × 3 matrix and B is a 3 × 4 matrix, how many columns does AB have ………..
(1) 3
(2) 4
(3) 2
(4) 5
Answer Key:

(2) 4

Hint.

The order of AB is 2 × 4
∴ Number of columns is 4.

 

16. If the number of columns and rows are not equal in a matrix then it is said to be a
(1) diagonal matrix
(2) rectangular matrix
(3) square matrix
(4) identity matrix
Answer Key:

(2) rectangular matrix

 

17. Transpose of a column matrix is …………..
(1) unit matrix
(2) diagonal matrix
(3) column matrix
(4) row matrix
Answer Key:

(4) row matrix

 

18.Find the matrix X if

Answer Key:

Hint.

 

19. Which of the following can be calculated from the given matrices?

(i) A²
(ii) B²
(iii) AB
(iv) BA
(1) (i) and (ii) only
(2) (ii) and (iii) only
(3) (ii) and (iv) only
(4) all of these
Answer Key:
(3) (ii) and (iv) only
Hint: 

(i) A² is possible to find
(ii) B² is also possible to find
(iii) not possible: order of A= (3 × 2) order of B is (3 × 3). AB is not possible number of column of matrix A ≠ number of rows of the matrix B.
(iv) Possible number column of the matrix is equal to the number of the matrix A.

  

20. Which of the following statements are correct?

(1) (i) and (ii) only
(2) (ii) and (iii) only
(3) (iii) and (iv)
(4) all of these
Answer Key:
(1) (i) and (ii) only
Hint.
(i) AB + C : order of A = 2 × 3
order of B = 3 × 2
order of AB = 2 × 2
order of C = 2 × 2
It is possible to add AB + C

 

(ii) BC :
order of B = 3 × 2
order of C = 2 × 2
It is possible to find BC

 

(iii) BA is not possible
order of B = 3 × 2
order of A = 3 × 2
BA does not exist.
BA + C is not a correct statement

 

(iv) ABC is not possible
order of A = 2 × 3 order of
B = 3 × 2
order of AB = 2 × 2
order of C = 3 × 2
It is not possible to multiply AB and C.
∴ The statement ABC is not correct.