Tiêu đề Circle & Micro Organism- Daily-6 MCQ (Set-A)-Solve.pdf ✅

1 Varsity Daily-06 [Set-A (Solve Sheet)] wm‡jevm: e„Ë + AYyRxe c~Y©gvb: 60 †b‡MwUf gvK©: 0.25 mgq: 35 wgwbU MwYZ (Mathmatics) 1. GKK e ̈vmv‡a©i e„‡Ë AšÍwj©wLZ mgevû wÎfz‡Ri evûi ˆ`N© ̈ KZ GKK? 3 2 3 2 3 1 DËi: 3 e ̈vL ̈v: AOD = 60, OA = 1 AD = OA  sin60 = 3 2 AB = 2  AD = 3 2  2 = 3 GKK A B C D O 120 120 60 2. (x – 12) 2 + (y – 5) 2 = r2 e„ËwU g~jwe›`yMvgx n‡j, Gi e ̈vm KZ? 10 26 13 3 DËi: 26 e ̈vL ̈v: e„ËwU g~jwe›`yMvgx e‡j, 144 + 25 = r2  r = 13 GKK  e ̈vm = 2  13 = 26 GKK 3. 2x2 + 2y2 – 4x + 6y – 6 = 0 e„‡Ëi †K›`a- (– 4, 2) (– 3, 1) (2, – 1)     1  – 3 2 DËi:     1  – 3 2 e ̈vL ̈v: 2x2 + 2y2 – 4x + 6y – 6 = 0  x 2 + y2 – 2x + 3y – 3 = 0  †K›`a     1  – 3 2 4. x 2 + y2 – 4x – 6y – 7 = 0 e„‡Ëi (2, 2) we›`y‡Z Awfj‡¤^i mgxKiY †KvbwU? x + 2y + 4 = 0 x – 2 = 0 2x – y + 4 = 0 y – 2 = 0 DËi: x – 2 = 0 e ̈vL ̈v: †K›`a (2, 3) I (2, 2) we›`yMvgx Awfj‡¤^i mgxKiY, x – 2 2 – 2 = y – 3 3 – 2 x – 2 = 0 5. GKwU e„Ë (1, 3) I (2, 1) we›`y w`‡q AwZμg K‡i I Gi †K›`a x A‡ÿ Aew ̄’Z n‡j, e„ËwUi mgxKiY †KvbwU? x 2 + y2 – 5x + 15 = 0 x 2 + y2 + 5x – 15 = 0 x 2 + y2 + 3x – 15 = 0 x 2 + y2 + 3x + 15 = 0 DËi: x 2 + y2 + 5x – 15 = 0 e ̈vL ̈v: †K›`a x A‡ÿi Dci e‡j, f = 0  e„‡Ëi mgxKiY, x 2 + y2 + 2gx + c = 0 hv (1, 3) I (2, 1) we›`yMvgx,  1 + 9 + 2g + c = 0 ..........(i) 4 + 1 + 4g + c = 0 ............(ii) (ii) – (i) K‡i cvB, 4g + c + 5 – 10 – 2g – c = 0  2g = 5  g = 5 2 g = 5 2 (i) bs G ewm‡q, 10 + 2  5 2 + c = 0 c = – 15 wb‡Y©q e„‡Ëi mgxKiY, x 2 + y2 + 5x – 15 = 0 6. x 2 + y2 = 16 e„‡Ë †Kv‡bv R ̈v Gi ga ̈we›`y (2, 3) n‡j, R ̈vÕwUi Xvj KZ? 2 3 – 2 3 – 3 2 1 2 DËi: – 2 3 e ̈vL ̈v: (2, 3) we›`y‡Z R ̈vÕwUi Dci j‡¤^i Xvj = 3 – 0 2 – 0 = 3 2  R ̈vÕwUi Xvj = – 2 3 7. x 2 + y2 + 2x + c 2 = 0 Ges x 2 + y2 + 2y + c 2 = 0 e„ËØq ci ̄úi‡K ewnt ̄’fv‡e ̄úk© Ki‡j, c Gi gvb †KvbwU? 1 2 4 – 4 DËi: 1 e ̈vL ̈v: kZ©g‡Z, c1c2 = r1 + r2  2 = 1 – c 2 + 1 – c 2  2 = 2 1 – c 2  1 2 = 1 – c 2  1 2 = 1 – c 2  c 2 = 1 – 1 2  c 2 = 1 2  c = 1 c1 (– 1, 0) c2 = (0, – 1) r1 = 1 – c 2 r2 = 1 – c 2