12th Mathematics Chapter Study Material English Medium 2021 By S Rajan M Sc M Phil M Ed May 2026

  • Typical solved example: Prove if f(x)=ax+b (a≠0) is bijective and find f⁻¹.
  • Practice: Determine domain/range and invertibility for given functions.
  • Pitfalls: Confusing one-to-one with monotonicity; forgetting domain restrictions.

    • The 2021 edition is divided into three logical sections, covering the entire Class 12 syllabus (reduced due to COVID-19, as per CBSE and many state boards). Each chapter follows a standardized template:

  • Example: Compute area between intersecting curves.
  • Pitfalls: Incorrect limits or axis of rotation.

    • Problem: Find the square root of $-8 - 6i$. Solution: Let $\sqrt-8-6i = a + ib$. Squaring both sides: $-8 - 6i = a^2 - b^2 + 2abi$. Equating real and imaginary parts: Typical solved example: Prove if f(x)=ax+b (a≠0) is

    Substitute $b$ in (1): $$a^2 - \left(\frac-3a\right)^2 = -8$$ $$a^2 - \frac9a^2 = -8$$ $$a^4 + 8a^2 - 9 = 0$$ Let $a^2 = t$. Then $t^2 + 8t - 9 = 0$. $(t+9)(t-1) = 0 \Rightarrow t = 1$ (since $t=a^2 \geq 0$). So, $a^2 = 1 \Rightarrow a = \pm 1$. If $a=1, b=-3$. If $a=-1, b=3$. Answer: $\pm(1 - 3i)$. The 2021 edition is divided into three logical

    | Parameter | S Rajan 2021 | RD Sharma | NCERT Exemplar | |-----------|--------------|-----------|----------------| | Language simplicity | High (targets average student) | Moderate | High (dry but accurate) | | Number of solved examples | 350+ | 1000+ (overwhelming) | 200+ | | Exam tricks & shortcuts | Yes (chapter-wise) | Few | No | | Pandemic-era syllabus alignment | Yes (2021 reduced syllabus) | No (full syllabus) | Yes (NCERT reduced) | | Best for | Board + state entrance exams | JEE Mains only | Conceptual clarity | Example: Compute area between intersecting curves

    Conclusion: S Rajan’s material is ideal for students aiming for 80% to 95% in board exams, especially those who find RD Sharma too dense.

  • Typical solved example: Prove if f(x)=ax+b (a≠0) is bijective and find f⁻¹.
  • Practice: Determine domain/range and invertibility for given functions.
  • Pitfalls: Confusing one-to-one with monotonicity; forgetting domain restrictions.

    • The 2021 edition is divided into three logical sections, covering the entire Class 12 syllabus (reduced due to COVID-19, as per CBSE and many state boards). Each chapter follows a standardized template:

  • Example: Compute area between intersecting curves.
  • Pitfalls: Incorrect limits or axis of rotation.

    • Problem: Find the square root of $-8 - 6i$. Solution: Let $\sqrt-8-6i = a + ib$. Squaring both sides: $-8 - 6i = a^2 - b^2 + 2abi$. Equating real and imaginary parts:

    Substitute $b$ in (1): $$a^2 - \left(\frac-3a\right)^2 = -8$$ $$a^2 - \frac9a^2 = -8$$ $$a^4 + 8a^2 - 9 = 0$$ Let $a^2 = t$. Then $t^2 + 8t - 9 = 0$. $(t+9)(t-1) = 0 \Rightarrow t = 1$ (since $t=a^2 \geq 0$). So, $a^2 = 1 \Rightarrow a = \pm 1$. If $a=1, b=-3$. If $a=-1, b=3$. Answer: $\pm(1 - 3i)$.

    | Parameter | S Rajan 2021 | RD Sharma | NCERT Exemplar | |-----------|--------------|-----------|----------------| | Language simplicity | High (targets average student) | Moderate | High (dry but accurate) | | Number of solved examples | 350+ | 1000+ (overwhelming) | 200+ | | Exam tricks & shortcuts | Yes (chapter-wise) | Few | No | | Pandemic-era syllabus alignment | Yes (2021 reduced syllabus) | No (full syllabus) | Yes (NCERT reduced) | | Best for | Board + state entrance exams | JEE Mains only | Conceptual clarity |

    Conclusion: S Rajan’s material is ideal for students aiming for 80% to 95% in board exams, especially those who find RD Sharma too dense.

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