Match the following: - List - I List - II (A) If a , b 0 a + b = 1 , then minimum value of ( a 2 + a 2 1 ) 2 + ( b 2 + b 2 1 ) 2 is (p) 2 3 (B) The perpendicular distance of the image of the p

Question

Match the following: - List - I List - II (A) If a , b > 0 a + b = 1 , then minimum value of ( a 2 + a 2 1 ​ ) 2 + ( b 2 + b 2 1 ​ ) 2 is (p) 2 3 ​ (B) The perpendicular distance of the image of the point (3, 4-12) in the xy-plane from the z-axis is (q) 5 (C) The area of the quadrilateral whose vertices are 1, i, ω , i ω is ( ω is the cube root of unity) (r) 8 (D) The minimum value of ( sin 2 x + cos 2 x + cosec 2 2 x ) 3 is (s) 8 289 ​

TestHub · Accepted Answer

(A) a=b=1/2 gives (1/4+4)^2 x 2 = 289/8 = min (S). (B) reflection of (3,4,-12) in xy-plane is (3,4,12); distance from z-axis = sqrt(9+16) = 5 (Q). (C) shoelace on 1, i, w, iw gives area 3/2 (P). (D) (1+cosec^2 2x)^3 >= 8, min 8 at sin 2x = +-1 (R). So A-S, B-Q, C-P, D-R.

List - I	List - II
(A) If $a, b > 0 a + b = 1$ , then minimum value of $(a^{2} + \frac{1}{a ^{2}})^{2} + (b^{2} + \frac{1}{b ^{2}})^{2}$ is	(p) $\frac{3}{2}$
(B) The perpendicular distance of the image of the point (3, 4-12) in the xy-plane from the z-axis is	(q) 5
(C) The area of the quadrilateral whose vertices are 1, i, $ω, i ω$ is ( $ω$ is the cube root of unity)	(r) 8
(D) The minimum value of $(sin^{2} x + cos^{2} x + cosec^{2} 2 x)^{3}$ is	(s) $\frac{289}{8}$

Mathematics - Application of Derivative Question with Solution | TestHub

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