Match the following. (One or more entries can match more than one option.) (A) The curve y = 2 e 2 x intersects the y-axis at an angle cot − 1 ( 3 8 n − 4 ) . Then the value of n is (p) 2 (B) Th

Question

Match the following. (One or more entries can match more than one option.)

(A) The curve $y = 2 e^{2 x}$ intersects the y-axis at an angle $cot^{- 1} (\frac{8 n - 4}{3})$ . Then the value of $n$ is	(p) 2
(B) The area of the triangle formed by the normal at the point $(1, 0)$ on the curve $x = e^{s i n y}$ with the axes is $\frac{2 t + 1}{6}$ sq. units. Then the value of $t$ is	(q) $- 1$
(C) The length of the sub-tangent to the curve $x^{2} y^{2} = 16$ at the point $(- 2, 2)$ is $∣ K ∣$ . Then the value of $K$ is	(r) $- 2$
(D) The slope of the tangent to the curve $y = 4 - x^{2}$ at the point where the ordinate and the abscissa are equal is	(s) 4

TestHub · Accepted Answer

(A) At ( 0 , 2 ) the slope is 4, so the angle with the y-axis is 2 π ​ − tan − 1 4 = cot − 1 4 . Then ​ 3 8 n − 4 ​ ​ = 4 , 8 n − 4 = ± 12 , n = 2 or -1 (p, q). (B) The normal at ( 1 , 0 ) is x + y = 1 , area 2 1 ​ . So ​ 6 2 t + 1 ​ ​ = 2 1 ​ , 2 t + 1 = ± 3 , t = 1 or -2; only -2 is (r). (C) x y = − 4 at (-2, 2), the sub-tangent is ​ d y / d x y ​ ​ = ∣ x ∣ = 2 , so K = ± 2 (p, r). (D) x = y = 2 ​ ; d x d y ​ = − y x ​ = − 1 (q).

Mathematics - Application of Derivative Question with Solution | TestHub

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