Match the statements given in Column I with the values given in Column II: Column I Column II (A) If {a} = {j} + {{3k}} , {b} = -{j} + {3}{k} and {c} = 2{3}{k} form a triangle, then the internal angle of the triangle between {a} and {b} is (P) π/6 (B) If _{a}^{b} (f (x) - 3x) dx = a² - b², then the value of f≤ft(π/6) is (Q) 2π/3 (C) The value of π²/ 3 ₇/6}^{5/6} (π x) \, dx is (R) π/3 (D) The maximum value of ≤ft| ≤ft(1/1-z) | for z = 1, z ≠ 1 is given by (S) π (T) π/2 [JEE Adv 2011 P2]

Question

Examsnet · Accepted Answer

Correct Answer is : (A)→(Q), (B)→(P), (C)→(S), (D)→(T)

Column I	Column II
(A) If $\vec{a}$ = $\hat{j} + \sqrt{\hat{3k}}$ , $\vec{b}$ = $-\hat{j} + \sqrt{3}\hat{k}$ and $\vec{c}$ = $2\sqrt{3}\hat{k}$ form a triangle, then the internal angle of the triangle between $\vec{a}$ and $\vec{b}$ is	(P) $\frac{\pi}{6}$
(B) If $\int\limits_{a}^{b}$ (f (x) - 3x) dx = $a^2 - b^2$ , then the value of $f\left(\frac{\pi}{6}\right)$ is	(Q) $\frac{2\pi}{3}$
(C) The value of $\frac{\pi^2}{\ln 3} \int\limits_{\frac{7}{6}}^{\frac{5}{6}} \sec(\pi x) \, dx$ is	(R) $\frac{\pi}{3}$
(D) The maximum value of $\left\| \arg\left(\frac{1}{1-z}\right) \right\|$ for z = 1, z ≠ 1 is given by	(S) π
	(T) $\frac{\pi}{2}$

Vector Algebra