The edition is a highly effective, comprehensive resource for competitive exam aspirants. It effectively demystifies the complexities of Advanced Mathematics by balancing foundational concepts with exam-day shortcut techniques.
Detailed explanation of remainders, factors, and Cartesian planes. 2. The "Smart Approach" to Problem Solving gagan pratap advance maths complete class notes exclusive
: All content, including theory and solutions, is provided in both Hindi and English to cater to a diverse range of aspirants. Comprehensive Coverage The edition is a highly effective, comprehensive resource
Explanation: $x^3 - \frac1x^3 = (x - \frac1x)^3 + 3(x - \frac1x)$. We know $(x - \frac1x)^2 = (x + \frac1x)^2 - 4 = 13 - 4 = 9$. So $(x - \frac1x) = 3$ or $-3$. Value $= (3)^3 + 3(3) = 27 + 9 = 36$... Wait, let's check options. Actually, formula is $x^3 - \frac1x^3 = (x - \frac1x) [(x - \frac1x)^2 + 3]$. Wait, standard formula: $x^3 - y^3 = (x-y)(x^2+xy+y^2)$. Here $y=1/x$. $x^3 - 1/x^3 = (x-1/x)( (x-1/x)^2 + 3 )$. If $x-1/x = 3$, Value $= 3(9+3) = 36$. Correction: There seems to be a calculation trick often used. Let's re-evaluate: $x + 1/x = \sqrt13$. Square it: $x^2 + 1/x^2 + 2 = 13 \implies x^2 + 1/x^2 = 11$. $x^3 - 1/x^3 = (x - 1/x)((x+1/x)^2 - 1)$. Wait, $x^3 - y^3 = (x-y)(x^2+y^2+xy)$. $x^3 - 1/x^3 = (x-1/x)(x^2+1/x^2+1)$. Need $x - 1/x$. $(x - 1/x)^2 = x^2 + 1/x^2 - 2 = 11 - 2 = 9$. So $x - 1/x = \pm 3$. Value $= 3(11+1) = 36$. Self-Correction in Options: The options in typical Gagan Pratad papers might involve $\sqrt13$. Let's check option (B) $4\sqrt13$. If $x^3 + 1/x^3$ was asked: $(x+1/x)^3 - 3(x+1/x) = 13\sqrt13 - 3\sqrt13 = 10\sqrt13$. If the question is $x^3 - 1/x^3$, answer is 36. Assuming standard question types, let's select the correct logic. Answer is 36. We know $(x - \frac1x)^2 = (x + \frac1x)^2 - 4 = 13 - 4 = 9$
For students preparing for competitive exams like , CPO , CHSL , and CDS , mastering Advance Maths is often the deciding factor between selection and rejection. Among the various study resources available, the "Gagan Pratap Advance Maths Complete Class Notes Exclusive" have gained legendary status. Authored by Gagan Pratap, a renowned mathematics educator, these notes are meticulously designed to simplify complex concepts and boost problem-solving speed.
The hallmark of these notes is Gagan Pratap’s philosophical signature: “Sikho concept, phir shortcut” (Learn the concept, then the shortcut). The notes meticulously bifurcate every topic into two distinct layers:
(A) 11 (B) $\frac1+\sqrt452$ (C) $\frac1+\sqrt532$ (D) $\frac-1+\sqrt452$