12th Mathematics - Book Back Answers - Chapter 8 - English Medium Guides

  

 

Plus Two / 12th Mathematics - Book Back Answers - Chapter 8 - English Medium

Tamil Nadu Board 12th Standard Mathematics - Chapter 8: Book Back Answers and Solutions

    This post covers the book back answers and solutions for Chapter 8 from the Tamil Nadu State Board 12th Standard Mathematics 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 8 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 12 students! Prepare well and aim for top scores. Thank you!

 

I. Multiple Choice Questions

1. A circular template has a radius of 10 cm. The measurement of radius has an approximate
error of 0.02 cm. Then the percentage error in calculating area of this template is
(1) 0.2% 
(2) 0.4% 
(3) 0.04% 
(4) 0.08%
Answer Key:
(2) 0.4%

 
2. The percentage error of fifth root of 31 is approximately how many times the percentage
error in 31?
(1) $\frac{\mathbf{1}}{\mathbf{31}}$
(2) $\frac{\mathbf{1}}{\mathbf{5}}$
(3) 5
(4) 31
Answer Key:
(2) $\frac{\mathbf{1}}{\mathbf{5}}$

$\frac{\mathbf{ }}{}$
3. If u (x, y)  = ${\mathit{e}}^{{\mathit{x}}^{\mathbf{2}\mathbf{+}{\mathit{y}}^{\mathbf{2}}}}$, then $\frac{\mathbf{\partial }\mathit{u}}{\mathbf{\partial }\mathit{x}}$ is equal to
(1) ${\mathit{e}}^{{\mathit{x}}^{\mathbf{2}\mathbf{+}{\mathit{y}}^{\mathbf{2}}}}$ 
(2) 2xu 
(3) ${{\mathit{x}}^{\mathbf{2}\mathbf{}}}^{}$u 
(4) ${{{\mathit{y}}^{\mathbf{2}}}^{}}^{}$u
Answer Key:
(2) 2xu

 
4. If v(x, y)  = log( ${\mathit{e}}^{{\mathit{x}}^{}}$+ e^y) , then $\frac{\mathbf{\partial }\mathbf{v}}{\mathbf{\partial }\mathbf{x}}\mathbf{+}\frac{\mathbf{\partial }\mathbf{v}}{\mathbf{\partial }\mathbf{y}}$ is equal to
(1) ${\mathit{e}}^{{\mathit{x}}^{}}$+ e^y 
(2) $\frac{\mathbf{1}}{{\mathbf{e}}^{\mathbf{x}}\mathbf{+}{\mathbf{e}}^{\mathbf{y}}}$
(3) 2 
(4) 1
Answer Key:
(4) 1

 
5. If w (x, y) = x^y ,  x> 0 , then $\frac{\mathbf{\partial }\mathbf{w}}{\mathbf{\partial }\mathbf{x}}$ is equal to
(1) x^y x log 
(2) y log x 
(3) $\mathbf{y}{\mathbf{x}}^{\mathbf{y}\mathbf{-}\mathbf{1}}$ 
(4) x log y
Answer Key:
(3) $\mathbf{y}{\mathbf{x}}^{\mathbf{y}\mathbf{-}\mathbf{1}}$

${\mathbf{ }}^{}$
6. If f(x, y) = ${\mathbf{e}}^{\mathbf{x}\mathbf{y}}$, then $\frac{{\mathbf{\partial }}^{\mathbf{2}}\mathit{f}}{\mathbf{\partial }\mathit{x}\mathbf{\partial }\mathit{y}}$ is equal to
(1) xy${\mathbf{e}}^{\mathbf{x}\mathbf{y}}$
(2) (1+ xy)${\mathbf{e}}^{\mathbf{x}\mathbf{y}}$
(3) (1+ y)${\mathbf{e}}^{\mathbf{x}\mathbf{y}}$
(4) (1+ x)${\mathbf{e}}^{\mathbf{x}\mathbf{y}}$
Answer Key:
(2) (1+ xy)${\mathbf{e}}^{\mathbf{x}\mathbf{y}}$

${\mathbf{ }}^{}$
7. If we measure the side of a cube to be 4 cm with an error of 0.1 cm, then the error in our
calculation of the volume is
(1) 0.4 cu.cm 
(2) 0.45 cu.cm 
(3) 2 cu.cm 
(4) 4.8 cu.cm
Answer Key:
(4) 4.8 cu.cm

 
8. The change in the surface area S = 6${{\mathit{x}}^{\mathbf{2}}}^{}$ of a cube when the edge length varies from x₀ to
x₀ + dx  is
(1) 12x₀ + dx 
(2) 12x₀dx 
(3) 6x₀dx 
(4) 6x₀ + dx
Answer Key:
(2) 12x₀dx

 
9. The approximate change in the volume V of a cube of side x metres caused by increasing
the side by 1% is
(1) 0.3xdxm³ 
(2) 0.03xm³
(3) 0.03${{\mathit{x}}^{\mathbf{2}}}^{}$m³ 
(4) 0.03${{\mathbf{}}^{}}^{}$X³m³
Answer Key:
(4) 0.03${{\mathbf{}}^{}}^{}$X³m³

 
10. If g(x, y) = 3${{\mathit{x}}^{\mathbf{2}}}^{}$ − 5y + 2${{\mathbf{}{\mathit{y}}^{\mathbf{2}}}^{}}^{}$ , x(t) = e^t and y(t) = cos t , then $\frac{\mathbf{d}\mathbf{g}}{\mathbf{d}\mathbf{t}}$  is equal to
(1) 6e^2t + 5sint − 4cost sint 
(2) 6e^2t − 5sint + 4cost sint
(3) 3e^2t+ 5sint - 4cost sint 
(4) 3e^2t − 5sint + 4cost sint
Answer Key:
(1) 6e^2t + 5sint − 4cost sint 

 
11. If f(X)= , then its differential is given by
(1) $\frac{\mathbf{-}\mathbf{1}}{\mathbf{(}\mathbf{x}\mathbf{+}\mathbf{1}{\mathbf{)}}^{\mathbf{2}}}\mathbf{d}\mathbf{x}$

(2) $\frac{\mathbf{1}}{\mathbf{(}\mathbf{x}\mathbf{+}\mathbf{1}{\mathbf{)}}^{\mathbf{2}}}\mathbf{d}\mathbf{x}$
(3) $\frac{\mathbf{1}}{\mathbf{x}\mathbf{+}\mathbf{1dx}}$
(4) $\frac{\mathbf{-}\mathbf{1}}{\mathbf{x}\mathbf{+}\mathbf{1}}$
Answer Key:
(2) $\frac{\mathbf{1}}{\mathbf{(}\mathbf{x}\mathbf{+}\mathbf{1}{\mathbf{)}}^{\mathbf{2}}}\mathbf{d}\mathbf{x}$

$\mathbf{ }$
12. If u(x, y) = ${{\mathit{x}}^{\mathbf{2}}}^{}$ + 3xy + y − 2019 , then $\frac{\mathbf{\partial }\mathbf{u}}{\mathbf{\partial }\mathbf{x}}$${\mathbf{|}}_{}$_{(4, -5)} is equal to
(1) −4 
(2) −3 
(3) −7 
(4) 13
Answer Key:
(3) −7

 
13. Linear approximation for g(x) = cos x at x =$\frac{\mathbf{\pi }}{\mathbf{2}}$ is
(1) x+$\frac{\mathbf{\pi }}{\mathbf{2}}$
(2) -x+$\frac{\mathbf{\pi }}{\mathbf{2}}$
(3) x-$\frac{\mathbf{\pi }}{\mathbf{2}}$
(4) -x-$\frac{\mathbf{\pi }}{\mathbf{2}}$
Answer Key: 

(2) -x+$\frac{\mathbf{\pi }}{\mathbf{2}}$

$\frac{\mathbf{ }}{}$
14. If w(x, y, z) = ${{\mathit{x}}^{\mathbf{2}}}^{}$ ( y − z) + ${{{\mathit{y}}^{\mathbf{2}}}^{}}^{}$ (z − x) + z² (x − y) , then $\frac{\mathbf{\partial }\mathbf{w}}{\mathbf{\partial }\mathbf{x}}\mathbf{+}\frac{\mathbf{\partial }\mathbf{w}}{\mathbf{\partial }\mathbf{y}}\mathbf{+}\frac{\mathbf{\partial }\mathbf{w}}{\mathbf{\partial }\mathbf{z}}$ is
(1) xy + yz + zx 
(2) x( y + z) 
(3) y(z + x) 
(4) 0
Answer Key:
(4) 0

 
15. If f (x, y, z) = xy + yz + zx , then f_x-f_y is equal to
(1) z − x 
(2) y − z 
(3) x − z 
(4) y – x
Answer Key:
(1) z − x

 

II.Short Answer Questions.

12th Mathematics

III. Long Answer Questions.

12th Mathematics

IV. Exercise.

12th Mathematics