12th Mathematics - Book Back Answers - Chapter 9 - English Medium Guides

  

 

Plus Two / 12th Mathematics - Book Back Answers - Chapter 9 - English Medium

Tamil Nadu Board 12th Standard Mathematics - Chapter 9: Book Back Answers and Solutions

    This post covers the book back answers and solutions for Chapter 9 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 9 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. The value of $\underset{\mathbf{0}}{\overset{\frac{\mathbf{2}}{\mathbf{3}}}{\mathbf{\int }}}\frac{\mathbf{d}\mathbf{x}}{\sqrt{\mathbf{4}\mathbf{-}\mathbf{9}{\mathbf{x}}^{\mathbf{2}}}}$  is
(1) $\frac{\mathbf{\pi }}{\mathbf{6}}$
(2) $\frac{\mathbf{\pi }}{\mathbf{2}}$
(3) $\frac{\mathbf{\pi }}{\mathbf{4}}$
(4) $\frac{\mathbf{\pi }}{}$
Answer Key:
(1) $\frac{\mathbf{\pi }}{\mathbf{6}}$

$\frac{\mathbf{ }}{}$
2. The value of ${\mathbf{\int }}_{\mathbf{-}\mathbf{1}}^{\mathbf{2}}\mathbf{\left|}\mathbf{x}\mathbf{\right|}\mathbf{d}\mathbf{x}$ is
(1) $\frac{\mathbf{1}}{\mathbf{2}}$
(2) $\frac{3}{\mathbf{2}}$
(3) $\frac{5}{2}$
(4) $\frac{7}{2}$
Answer Key:
(3) $\frac{5}{2}$

$\frac{\mathrm{ }}{}$
3. For any value of n∈Z, ${\mathbf{\int }}_{\mathbf{0}}^{\mathbf{\pi }} {\mathbf{e}}^{{\mathbf{cos}}^{\mathbf{2}\mathbf{ }\mathbf{x}}}\mathbf{ }\mathbf{c}\mathbf{o}{\mathbf{s}}^{\mathbf{3}}$ [( 2n + )x] dx  is
(1) $\frac{\mathbf{\pi }}{\mathbf{2}}$
(2) $\frac{\mathbf{\pi }}{}$
(3) 0 
(4) 2
Answer Key:
(3) 0

 
4. The value of $\underset{\mathbf{-}\frac{\mathbf{\pi }}{\mathbf{2}}}{\overset{\frac{\mathbf{\pi }}{\mathbf{2}}}{\mathbf{\int }}}$ sin²cosx dx is
(1) $\frac{\mathbf{3}}{\mathbf{2}}$
(2) $\frac{1}{2}$
(3) 0
(4) $\frac{\mathbf{2}}{\mathbf{3}}$
Answer Key:
(4) $\frac{\mathbf{2}}{\mathbf{3}}$

$\frac{\mathbf{ }}{}$
5. The value of $\underset{\mathbf{-}\mathbf{4}}{\overset{\mathbf{4}}{\mathbf{\int }}}$  [tan^-1  +tan^-1

(1) $\frac{\mathbf{\pi }}{}$

(2) 2$\frac{\mathbf{\pi }}{}$ 
(3) 3$\frac{\mathbf{\pi }}{}$ 
(4) 4$\frac{\mathbf{\pi }}{}$
Answer Key:
(4) 4$\frac{\mathbf{\pi }}{}$

$\frac{\mathbf{ }}{}$
6. The value of $\underset{\mathbf{-}\frac{\mathbf{\pi }}{\mathbf{4}}}{\overset{\frac{\mathbf{\pi }}{\mathbf{4}}}{\mathbf{\int }}}$dx is
(1) 4 
(2) 3 
(3) 2 
(4) 0
Answer Key:
(3) 2

 
7. If f(x)=$\underset{\mathbf{0}}{\overset{\mathbf{x}}{\mathbf{\int }}}$ t cost dt, then $\frac{\mathbf{d}\mathbf{f}}{\mathbf{d}\mathbf{x}}$=
(1) cos x − x sin x 
(2) sin x + x cos x 
(3) x cos x 
(4) x sin x
Answer Key:
(3) x cos x 

 
8. The area between y² = 4x and its latus rectum is
(1) $\frac{\mathbf{2}}{\mathbf{3}}$
(2) $\frac{\mathbf{4}}{\mathbf{3}}$
(3) $\frac{\mathbf{8}}{\mathbf{3}}$
(4) $\frac{\mathbf{5}}{\mathbf{3}}$
Answer Key:
(3) $\frac{\mathbf{8}}{\mathbf{3}}$

$\frac{\mathbf{ }}{}$
9. The value of  $\underset{\mathbf{0}}{\overset{\mathbf{1 }}{\mathbf{\int }}}$x$\mathbf{(}\mathbf{1}\mathbf{-}\mathbf{x}{\mathbf{)}}^{\mathbf{99}}$ dx  is
(1) $\frac{\mathbf{1}}{\mathbf{11000}}$
(2) $\frac{\mathbf{1}}{\mathbf{10100}}$
(3) $\frac{\mathbf{1}}{\mathbf{10010}}$
(4) $\frac{\mathbf{1}}{\mathbf{10001}}$
Answer Key:
(2) $\frac{\mathbf{1}}{\mathbf{10100}}$

$\frac{\mathbf{ }}{}$
10. The value of  $\frac{\mathbf{d}\mathbf{x}}{\mathbf{1}\mathbf{+}{\mathbf{5}}^{\mathbf{cos}\mathbf{x}}}$ is
(1) $\frac{\mathbf{\pi }}{\mathbf{2}}$
(2) $\frac{\mathbf{\pi }}{}$
(3) $\frac{\mathbf{3}\mathbf{\pi }}{\mathbf{2}}$
(4) 2$\frac{\mathbf{\pi }}{}$
Answer Key:
(1) $\frac{\mathbf{\pi }}{\mathbf{2}}$

$\frac{\mathbf{ }}{}$
11. If $\frac{\mathbf{\Gamma }\mathbf{(}\mathbf{n}\mathbf{+}\mathbf{2}\mathbf{)}}{\mathbf{\Gamma }\mathbf{\left(}\mathbf{n}\mathbf{\right)}}$ = 90 then n is
(1) 10 
(2) 5 
(3) 8 
(4) 9
Answer Key:
(4) 9

 
12. The value of $\underset{\mathbf{0}}{\overset{\frac{\mathbf{\pi }}{\mathbf{6}}}{\mathbf{\int }}}$ cos³3x dx is
(1) $\frac{\mathbf{2}}{\mathbf{3}}$
(2) $\frac{\mathbf{2}}{\mathbf{9}}$
(3) $\frac{\mathbf{1}}{\mathbf{9}}$
(4) $\frac{\mathbf{1}}{\mathbf{3}}$
Answer Key:
(2) $\frac{\mathbf{2}}{\mathbf{9}}$

$\frac{\mathbf{ }}{}$
13. The value of sin⁴ x dx is
(1) $\frac{\mathbf{3}\mathbf{\pi }}{\mathbf{10}}$
(2) $\frac{\mathbf{3}\mathbf{\pi }}{\mathbf{8}}$
(3) $\frac{\mathbf{3}\mathbf{\pi }}{\mathbf{4}}$
(4) $\frac{\mathbf{3}\mathbf{\pi }}{\mathbf{2}}$
Answer Key:
(2) $\frac{\mathbf{3}\mathbf{\pi }}{\mathbf{8}}$

$\frac{\mathbf{ }}{}$
14. The value of $\underset{\mathbf{0}}{\overset{\mathbf{\infty }}{\mathbf{\int }}}$ ${\mathbf{e}}^{\mathbf{-}\mathbf{3}\mathbf{x}}$ x² dx is
(1) $\frac{\mathbf{7}}{\mathbf{27}}$
(2) $\frac{\mathbf{5}}{\mathbf{27}}$
(3) $\frac{\mathbf{4}}{\mathbf{27}}$
(4) $\frac{\mathbf{2}}{\mathbf{27}}$
Answer Key:
(4) $\frac{\mathbf{2}}{\mathbf{27}}$

$\frac{\mathbf{ }}{}$
15. If  dx = $\frac{\mathbf{\pi }}{\mathbf{8}}$ then a is
(1) 4 
(2) 1 
(3) 3 
(4) 2
Answer Key:
(4) 2

 
16. The volume of solid of revolution of the region bounded by y² = x(a − x) about x-axis is
(1) $\mathbf{\pi }{\mathbf{a}}^{\mathbf{3}}$
(2) $\frac{\mathbf{\pi }{\mathbf{a}}^{\mathbf{3}}}{\mathbf{4}}$
(3) $\frac{\mathbf{\pi }{\mathbf{a}}^{\mathbf{3}}}{\mathbf{5}}$
(4) $\frac{\mathbf{\pi }{\mathbf{a}}^{\mathbf{3}}}{\mathbf{6}}$
Answer Key:
(4) $\frac{\mathbf{\pi }{\mathbf{a}}^{\mathbf{3}}}{\mathbf{6}}$

$\frac{\mathbf{ }}{}$
17. If f(x) = $\underset{\mathbf{1}}{\overset{\mathbf{x}}{\mathbf{\int }}}$ $\frac{{\mathbf{e}}^{\mathbf{sin} \mathrm{u}}}{\mathbf{u}}$  du, x>1 and $\underset{\mathbf{1}}{\overset{\mathbf{3}}{\mathbf{\int }}}$ $\frac{{\mathbf{e}}^{\mathbf{sin} {\mathrm{x}}^2}}{\mathbf{x}}$ dx=$\frac{\mathbf{1}}{\mathbf{2}}$ [f(a)-f(1)], then one of the possible value of a is
(1) 3 
(2) 6 
(3) 9 
(4) 5
Answer Key:
(3) 9

 
18. The value of $\underset{\mathbf{0}}{\overset{\mathbf{1}}{\mathbf{\int }}}$(sin^-1 x) dx is
(1) $\frac{{\mathbf{\pi }}^{\mathbf{2}}}{\mathbf{4}}\mathbf{-}\mathbf{1}$
(2) $\frac{{\mathbf{\pi }}^{\mathbf{2}}}{\mathbf{4+2 }}$
(3) $\frac{{\mathbf{\pi }}^{\mathbf{2}}}{\mathbf{4+1}}$
(4) $\frac{{\mathbf{\pi }}^{\mathbf{2}}}{\mathbf{4-2}}$
Answer Key:
(4) $\frac{{\mathbf{\pi }}^{\mathbf{2}}}{\mathbf{4-2}}$

$\frac{\mathbf{ }}{}$
19. The value of  dx is
(1) $\frac{\mathbf{\pi }{\mathbf{a}}^{\mathbf{3}}}{\mathbf{16}}$
(2) $\frac{\mathbf{3}\mathbf{\pi }{\mathbf{a}}^{\mathbf{4}}}{\mathbf{16}}$
(3) $\frac{\mathbf{3}\mathbf{\pi }{\mathbf{a}}^{\mathbf{2}}}{\mathbf{8}}$
(4) $\frac{\mathbf{3}\mathbf{\pi }{\mathbf{a}}^{\mathbf{4}}}{\mathbf{8}}$
Answer Key:
(2) $\frac{\mathbf{3}\mathbf{\pi }{\mathbf{a}}^{\mathbf{4}}}{\mathbf{16}}$

$\frac{\mathbf{ }}{}$
20. If $\underset{0}{\overset{\mathrm{x}}{\int }}$ f(t) dt = x+$\underset{\mathbf{x}}{\overset{\mathbf{1}}{\mathbf{\int }}}$ tf(t)dt, then the value of f (1) is
(1) $\frac{1}{\mathbf{2}}$
(2) 2 
(3) 1 
(4) $\frac{3}{4}$
Answer Key:
(1) $\frac{1}{\mathbf{2}}$

 

II.Short Answer Questions.

12th Mathematics

III. Long Answer Questions.

12th Mathematics

IV. Exercise.

12th Mathematics