Match each statement to its numerical value(s). Column I: (A) A circle cuts an intercept of length 8 on the x -axis and k on the y -axis. Its tangent at ( 9 , 3 ) is vertical. Find k . (B) If y = 2 ⌊

Question

Match each statement to its numerical value(s). Column I: (A) A circle cuts an intercept of length 8 on the $x$ -axis and $k$ on the $y$ -axis. Its tangent at $(9, 3)$ is vertical. Find $k$ . (B) If $y = 2 ⌊ 2 x - 1 ⌋ - 1 = 3 ⌊ 2 x - 2 ⌋ + 1$ , which values can $⌊ y + 5 x ⌋$ take? (C) Number of roots of $cos x 16 sin^{2} x = 1$ in $(- π, π)$ . (D) If one root of $(a - 6) x^{2} - (a + 6) x + 10 = 0$ is below 1 and the other above 2, which listed values can $a$ take? Column II: (p) 12 (q) 8 (r) 7 (s) 6 (t) 4

Column I	Column II
(A) Circle intercepts 8 on x-axis, k on y-axis; tangent at (9,3) vertical. Find k	(p) 12
(B) If y=2⌊2x−1⌋−1=3⌊2x−2⌋+1, possible values of ⌊y+5x⌋	(q) 8
(C) Number of roots of cos x √(16 sin²x)=1 in (−π,π)	(r) 7
(D) One root of (a−6)x²−(a+6)x+10=0 is <1, other >2. Possible a	(s) 6; (t) 4

TestHub · Accepted Answer

A: with centre ( h , 3 ) and rightmost point ( 9 , 3 ) , the source diagram gives an x -intercept 8 and a 6 -unit y -intercept. B: let m = ⌊ 2 x ⌋ ; then 2 m − 3 = 3 m − 5 gives m = 2 , y = 1 , x ∈ [ 1 , 3/2 ) , and ⌊ y + 5 x ⌋ ∈ { 6 , 7 , 8 } . C: 4∣ sin x ∣ cos x = 1 forces cos x > 0 , ∣ sin 2 x ∣ = 1/2 , with four roots. D: sign tests at 1 and 2 give 6 < a < 13 , so 7, 8, 12 are listed.

Mathematics - Circle Question with Solution | TestHub

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