12th Mathematics - Book Back Answers - Chapter 3 - English Medium Guides

  

 

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Tamil Nadu Board 12th Standard Mathematics - Chapter 3: Book Back Answers and Solutions

    This post covers the book back answers and solutions for Chapter 3 from the Tamil Nadu State Board 12th Standard Chemistry 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 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 zero of x³+ 64 is
(1) 0 
(2) 4 
(3) 4i 
(4) – 4
Answer Key:
(4) – 4

 
2. If f and g are polynomials of degrees m and n respectively,
and if h(x) = (f  o g)(x) , then the degree of h is
(1) mn 
(2) m + n 
(3) mn
(4) nm
Answer Key:
(1) mn 

 
3. A polynomial equation in x of degree n always has
(1) n distinct roots 
(2) n real roots 
(3) n complex roots 
(4) at most one root.
Answer Key:
(3) n complex roots

 
4. If 𝞪, β and γ are the zeros of x³ + px² + qx + r  , then 1 ∑ $\frac{\mathbf{1}}{\mathit{a}}$ is
(1) $\mathbf{-}\frac{\mathit{q}}{\mathit{r}}$
(2) $\mathbf{-}\frac{\mathit{p}}{\mathit{r}}$
(3) $\frac{\mathit{q}}{\mathit{r}}$
(4) $\mathbf{-}\frac{\mathbf{q}}{\mathbf{p}}$
Answer Key:
(1) $\mathbf{-}\frac{\mathit{q}}{\mathit{r}}$

$\frac{\mathit{ }}{}$
5. According to the rational root theorem, which number is not possible rational zero of
4x⁷ + 2x⁴ −10x³ − 5 ?
(1) −1 
(2) $\frac{\mathbf{5}}{\mathbf{4}}$
(3) $\frac{\mathbf{4}}{\mathbf{5}}$
(4) 5
Answer Key:
(3) $\frac{\mathbf{4}}{\mathbf{5}}$

$\frac{\mathbf{ }}{}$
6. The polynomial x³ − kx² + 9x  has three real zeros if and only if, k satisfies
(1) |k| ≤ 6 
(2) |k| = 0 
(3) |k| > 6 
(4) |k| ≥ 6
Answer Key:
(4) |k| ≥ 6

 
7. The number of real numbers in [0, 2𝜋] satisfying sin⁴ x − 2sin²  x +1 is
(1) 2 
(2) 4 
(3)1 
(4) ∞
Answer Key:
(1) 2 

 
8. If x³ +12x² +10ax +1999  definitely has a positive zero, if and only if
(1) a ≥ 0 
(2) a > 0 
(3) a < 0 
(4) a  ≤ 0
Answer Key:
(3) a < 0 

 
9. The polynomial x³ + 2x + 3 has
(1) one negative and two imaginary zeros 
(2) one positive and two imaginary zeros
(3) three real zeros 
(4) no zeros
Answer Key:
(1) one negative and two imaginary zeros 

 
10. The number of positive zeros of the polynomial $\mathbf{\sum }_{\mathbf{j}\mathbf{=}\mathbf{0}}^{\mathbf{n}}$ ⁿC_r (-1)^rx^r is
(1) 0 
(2) n 
(3) < n 
(4) r
Answer Key:
(2) n 

 

II.Short Answer Questions.

12th Mathematics

III. Long Answer Questions.

12th Mathematics

IV. Exercise.

12th Mathematics