Sri Chaitanya GTA | Part 4 Gets Serious 🚀#jeeadvanced

In this video, I solve a new set of selected questions from GTA 1 (Sri Chaitanya 2026) based on student doubts. Each problem is chosen to help you understand not just the solution, but the thinking process behind it. If you are preparing seriously, this session will help you improve your clarity and confidence in tackling tough problems. Watch till the end and test yourself before seeing the solution! 🔥 Questions: 0:00 Question 1 If \(f:\mathbb{R}\to\mathbb{R}\) and \(g:\mathbb{R}\to\mathbb{R}\) are two differentiable functions. \[g(x)=\left(\int f(x)\,dx + x\right)^{10}\] and satisfies \(T_4 + f(x)T_5 = {^{11}C_4}x^{10}, \forall x \in \mathbb{R}\), where \(T_4\) and \(T_5\) are the 4th and 5th terms in the binomial expansion of \(g(x)\), then the area bounded by \(f(x)\) and \(g(x)\) is equal to \_\_\_. \choice{\(\frac{9}{11}\)}{\(1\)}{\(\frac{10}{11}\)}{\(\frac{12}{11}\)} 11:36 Question 2 A cubic equation with real coefficients \(p(x)=0\) has one real root \((\alpha)\) and two imaginary roots \((\beta \pm i\gamma)\) represented by \(A, B\) and \(C\) on the argand plane respectively. Then \onech{roots of \(p'(x)=0\) are imaginary if \(A\) lies inside one of the two equilateral triangles with base \(BC\)}{roots of \(p'(x)=0\) are real if \(A\) lies inside one of the two equilateral triangles with base \(BC\)}{roots of \(p'(x)=0\) are imaginary if \(A, B, C\) are vertices of an isosceles (not equilateral) triangle}{roots of \(p'(x)=0\) are real and equal if \(\dfrac{\alpha-\beta}{\gamma}=\pm\sqrt{3}\)} 26:30 Question 3 Let \[ A=\left\{\hat{x}i+\hat{y}j+\hat{z}k:(x,y,z)\in \mathbb{R}^3,\ x^2+y^2+z^2=1\right\}, \] \[ B=\left\{xi+yj+zk:(x,y,z)\in \mathbb{R}^3,\ \magn{\sqrt{3}x+2y+3z-16}=14\right\}. \] Let \(\vec{a}, \vec{b}, \vec{c}\) be three distinct vectors in set \(A \cap B\) such that \[ \magn{\vec{a}-\vec{b}}=\magn{\vec{b}-\vec{c}}=\magn{\vec{c}-\vec{a}}. \] If \(V\) denotes the volume of parallelepiped determined by the vectors \(\vec{a}, \vec{b}, \vec{c}\), then \(16\sqrt{3}\,V\) equals \blank. 37:10 Question 4 Let \[ A=\left\{\hat{x}i+\hat{y}j+\hat{z}k:(x,y,z)\in \mathbb{R}^3,\ x^2+y^2+z^2=1\right\}, \] \[ B=\left\{xi+yj+zk:(x,y,z)\in \mathbb{R}^3,\ \magn{\sqrt{3}x+2y+3z-16}=14\right\}. \] Let \(\vec{a}, \vec{b}, \vec{c}\) be three distinct vectors in set \(A \cap B\) such that \[ \magn{\vec{a}-\vec{b}}=\magn{\vec{b}-\vec{c}}=\magn{\vec{c}-\vec{a}}. \] If \(V\) denotes the volume of parallelepiped determined by the vectors \(\vec{a}, \vec{b}, \vec{c}\), then \(16\sqrt{3}\,V\) equals \blank.