Title Straight Line Practice Sheet HSC FRB 24.pdf ✅

mij‡iLv  Final Revision Batch '24 1 03 mij‡iLv Straight Line Board Questions Analysis m„Rbkxj cÖkœ †evW© mvj XvKv gqgbwmsn ivRkvnx Kzwgjøv h‡kvi PÆMÖvg ewikvj wm‡jU w`bvRcyi 2023 1 1 1 1 1 1 1 1 2 2022 1 1 1 1 1 1 1 1 2 eûwbe©vPwb cÖkœ †evW© mvj XvKv gqgbwmsn ivRkvnx Kzwgjøv h‡kvi PÆMÖvg ewikvj wm‡jU w`bvRcyi 2023 5 4 4 5 4 4 4 8 4 2022 5 4 6 5 5 5 5 4 4 weMZ mv‡j †ev‡W© Avmv m„Rbkxj cÖkœ 1| Y X O B(– 1, 5) P(1, – 1) A(3, – 1) [XvKv †evW©- Õ23] (K) DÏxc‡Ki AB mij‡iLvwU Y Aÿ‡K †h we›`y‡Z †Q` K‡i Zvi wbY©q Ki| (L) P we›`yMvgx Ges AB mij‡iLvi mv‡_ 45 †KvY Drcbœ K‡i Giƒc mij‡iLv؇qi mgxKiY wbY©q Ki| (M) AB Gi Dci j¤^‡iLvi mgxKiY wbY©q Ki hv P we›`y †_‡K 2 GKK `~‡i Aew ̄’Z| DËi: (K)     0  7 2 ; (L) x + 5y + 4 = 0 ; 5x – y – 6 = 0 (M) 2x – 3y  2 13 – 5 = 0 2| `„k ̈Kí-1: B(1, – 1) C(6, 2) A(– 2, 4) Y D Y X X O AD || BC, ACD = 90 [ivRkvnx †evW©- Õ23] `„k ̈Kí-2: A(8, 3) Ges B = (p, q), AB Gi j¤^ mgwØLÛ‡Ki mgxKiY y = – 2x + 4 (K) x – 2y + 1 = 0 Ges 3x – y + 5 = 0 mij‡iLv؇qi AšÍfz©3 m~2‡KvY wbY©q Ki| (L) `„k ̈Kí-1 n‡Z D we›`yi ̄’vbvsK wbY©q Ki| (M) `„k ̈Kí-2 e ̈envi K‡i p Ges q Gi gvb wbY©q Ki| DËi: (K) 45 ; (L) (8, 10) ; (M) – 3 3| B(0, 7) C(– 4, 5) A(5, 0) Y D Y X X [h‡kvi †evW©- Õ23] (K) AB mij‡iLvi Aÿ؇qi ga ̈eZ©x LwÛZvs‡ki wÎLÛb we›`y wbY©q Ki| (L) (7, 9) we›`yMvgx Ges AB †iLvi mv‡_ 45 †KvY Drcbœ K‡i Giƒc mij‡iLvi mgxKiY wbY©q Ki| (M) D we›`yi ̄’vbvsK wbY©q Ki| DËi: (K)     10 3  7 3 ,     5 3  14 3 ; (L) x + 6y – 61 = 0 ; 6x – y – 33 = 0 (M)    –  15 37  280 37 4| Y Y X X C B O A 4x – 3y + 12 = 0 3x – 4y = 8 [Kzwgjøv †evW©- Õ23] (K) OAB Gi †ÿÎdj wbY©q Ki|
2  Higher Math 1st Paper Chapter-3 (L) Giƒc GKwU †iLvi mgxKiY wbY©q Ki hv C we›`yMvgx Ges x – y + 2 = 0 †iLvi mgvšÍivj| (M) †`LvI †h, DÏxc‡Ki †iLv؇qi AšÍf©y3 †Kv‡Yi mgwØLÛK؇qi ci ̄úi j¤^| DËi: (K) 8 3 eM© GKK ; (L) 7x – 7y + 4 = 0 5| `yBwU mij‡iLvi mgxKiY x – 2y + 3 = 0, 2x + 3y = 1 [PÆMÖvg †evW©- Õ23] (K) 2x – 3y + 5 = 0 Ges 7x + 4y – 3 = 0 mij‡iLv؇qi †Q`we›`y wbY©q Ki| (L) DÏxc‡K DwjøwLZ mgxKiY `yBwU †Kv‡bv mvgvšÍwi‡Ki `yBwU mwbœwnZ evû Ges D3 mvgvšÍwi‡Ki KY©Ø‡qi †Q`we›`y (2, – 3) n‡j Aci evû `yBwUi mgxKiY wbY©q Ki| (M) DÏxc‡K DwjøwLZ cÖ_g mij‡iLvi 5 GKK `~ieZ©x mgvšÍivj mij‡iLvi mgxKiY wbY©q Ki| DËi: (K)     – 11 29  41 29 ; (L) x – 2y – 19 = 0 ; 2x + 3y + 11 = 0 (M) x – 2y + 8 = 0 ; x – 2y – 2 = 0 6| Y Y X X A O 45 N B [wm‡jU †evW©- Õ23] (K) X Aÿ Ges (5, 4) we›`y n‡Z (1, t) we›`yi `~iZ¡ mgvb n‡j t Gi gvb wbY©q Ki| (L) ON †iLvi mgvšÍivj Ges Dnv n‡Z 6 2 GKK `~ieZ©x mij‡iLvi mgxKiY wbY©q Ki| (M) OAB Gi †ÿÎdj 18 eM© GKK n‡j AB Gi mgwÎLÛb we›`yi ̄’vbvsK wbY©q Ki| DËi: (K) 4 ; (L) x + y + 12 = 0, x + y – 12 = 0 (M) (– 4, 2) Ges (– 2, 4) 7| `yBwU mij‡iLv 12x – 5y + 26 = 0 ...(i) x + 5y = 13 ......(ii)[ewikvj †evW©- Õ23] (K) (– 1, – 1) we›`ywUi †cvjvi ̄’vbvsK wbY©q Ki| (L) (i) bs †iLv n‡Z 2 GKK `~ieZ©x Ges (ii) bs †iLvi Dci Aew ̄’Z we›`ymg~‡ni ̄’vbvsK wbY©q Ki| (M) ÔLÕ n‡Z cÖvß we›`yØq †Kv‡bv wÎfz‡Ri `yBwU kxl©we›`y n‡j Ges wÎfzRwUi j¤^we›`y     – 9 25  9 5 n‡j wÎfzRwUi Z...Zxq kx‡l©i ̄’vbvsK KZ? DËi: (K)     2  5 4 ; (L)     1  12 5 ,     – 3  16 5 (M)    –  108 109  – 738 545 8| `„k ̈Kí-1: 5GKK Y B C O(0, 0) A X OA = OB `„k ̈Kí-2: 4x – 3y + 1 = 0 Ges 3x + 4y + 8 = 0 [w`bvRcyi †evW©- Õ23] (K) (3, – 1) Ges (2, – 2) we›`y؇qi ms‡hvM‡iLv x A‡ÿi mv‡_ †h †KvY Drcbœ K‡i Zv wbY©q Ki| (L) `„k ̈Kí-1 Gi Av‡jv‡K AB mij‡iLvi Dci j¤^‡iLv OC Gi mgxKiY wbY©q Ki| (M) `„k ̈Kí-2 Gi Av‡jv‡K †iLv؇qi ga ̈eZ©x m~2‡Kv‡Yi mgwØLÛK Aÿ؇qi mv‡_ †h wÎfzR Drcbœ K‡i, Zvi †ÿÎdj wbY©q Ki| DËi: (K) 45 ; 135 ; (L) x – y = 0 (M) 3 1 2 eM© GKK ; 5 11 14 eM© GKK 9| `„k ̈Kí-1: Y X Y X ax + 3y + 6 = 0 2x + by + 4 = 0 B A O `„k ̈Kí-2: 3x + 4y – 24 = 0 GKwU mij‡iLvi mgxKiY| [w`bvRcyi †evW©- Õ23] (K) x 2 + y2 – 4y = 0 mgxKiY‡K †cvjvi mgxKi‡Y cÖKvk Ki| (L) `„k ̈Kí-1 Gi Av‡jv‡K AB †iLvi mgxKiY wbY©q Ki| (M) `„k ̈Kí-2 Gi mij‡iLvwU Aÿ؇qi ga ̈eZ©x LwÛZ Ask‡K mgvb wZbfv‡M wef3 K‡i Ggb we›`y؇qi mv‡_ g~jwe›`yi ms‡hvRK †iLvi mgxKiY wbY©q Ki| DËi: (K) 4sin ; (L) x + y + 2 = 0 (M) 3x – 8y = 0 ; 3x – 2y = 0
mij‡iLv  Final Revision Batch '24 3 10| L  (4, 3), M  (3, 5), N  (6, 4) [gqgbwmsn †evW©- Õ23] (K) L we›`yi †cvjvi ̄’vbvsK wbY©q Ki| (L) LM †iLvs‡ki j¤^wØLÛ‡Ki mgxKiY wbY©q Ki| (M) MN I NL †iLv؇qi AšÍf©y3 †Kv‡Yi mgwØLÛ‡Ki mgxKiY wbY©q Ki| DËi: (K) (5, 36.87 ; (L) 2x – 4y + 9 = 0 (M) (1 – 2)x + (3 + 2 2)y– 18 – 2 2 = 0 ; (1 + 2) x + (3 – 2 2)y – 18 + 2 2 = 0 11| A C B O Y Y X X D [XvKv †evW©- Õ22] AB = 4x + 3y – 12 = 0 Ges AB || CD. (K) AB †K Xvj AvKv‡i cÖKvk K‡i Bnvi Xvj wbY©q Ki| (L) g~j we›`y n‡Z AB I CD †iLvi `~iZ¡ mgvb n‡j CD †iLvi mgxKiY wbY©q Ki| (M) †`LvI †h, ABCD GKwU i¤^m| DËi: (K) – 4 3 ; (L) 4x + 3y + 12 = 0 12| [ivRkvnx †evW©- Õ22] A(1, 5) C(h, k) B(2, 2) D(k, h) (K) 2x – 3y + k = 0 Ges 2x – 3y = 0 †iLv؇qi ga ̈eZ©x `~iZ¡ 2 13 GKK n‡j k Gi gvb wbY©q Ki| (L) AC Ges BD †iLv؇qi Xvj h_vμ‡g – 2 Ges – 1 n‡j x Aÿ‡K CD †iLv †h we›`y‡Z †Q` K‡i Zvi ̄’vbv1⁄4 wbY©q Ki| (M) AB †iLvs‡ki j¤^-wØLЇKi mgxKiY wbY©q Ki| DËi: (K)  26 ; (L) (4, 0) ; (M) x – 3y + 9 = 0 13| B(6,6) O Y X N(3,4) M(4,3) C(– 6,– 2) A(– 2,– 6) [Kzwgjøv †evW©- Õ22] (K) AM †iLvwU x Aÿ Øviv †h Abycv‡Z AšÍwe©f3 nq, Zv wbY©q Ki| (L) B(6, 6) we›`y n‡Z AC mij‡iLvi j¤^`~iZ¡ wbY©q Ki| (M) †`LvI †h, B Gi mgwØLÐKØq ci ̄úi j¤^| DËi: (K) 2 : 1 ; (L) 10 2 GKK 14| L(2, – 1), M(– 3, 3) Ges 2x – y + 1 = 0 [h‡kvi †evW©- Õ22] (K) (1, 1) we›`y †_‡K †h mKj we›`yi `~iZ¡ me©`vB 5 GKK, H mKj we›`yi mÂvic‡_i mgxKiY wbY©q Ki| (L) L I M we›`y؇qi ms‡hvM mij‡iLvi Dci Aw1⁄4Z j¤^ wØLЇKi mgxKiY wbY©q Ki| (M) L we›`yMvgx Ges DÏxc‡Ki mij‡iLvwUi mv‡_ tan–1     1 3 †KvY Drcbœ K‡i Giƒc mij‡iLvi mgxKiY wbY©q Ki| DËi: (K) x 2 – y 2 – 2x – 2y – 23 = 0 (L) 10x – 8y + 13 = 0 (M) 7x – y – 15 = 0 ; x – y – 3 = 0 15| [PÆMÖvg †evW©- Õ22] Q(2,4) O Y X P(–10,–5) B C A Ges OC †iLvi Xvj = – 4 3 (K) (3, 6) we›`yMvgx 1 3 x + 5y + 8 = 0 †iLvi mgvšÍivj †iLvi mgxKiY wbY©q Ki| (L) OAB Gi †ÿÎdj wbY©q Ki| (M) †`LvI †h, OC †iLv I x-Aÿ‡iLvi ga ̈eZ©x †Kv‡Yi mgwØLÐKØq ci ̄úi j¤^| DËi: (K) x + 15y – 93 = 0 ; (L) 25 6 eM© GKK 16| `„k ̈Kí-1: [ewikvj †evW©- Õ22] O Y X A(4,0) D X Y B(0,6) C 90 GLv‡b C, AB Gi ga ̈we›`y `„k ̈Kí-2: 4x – 3y = – 4, 3x – 4y = – 5 (K) GKwU e„‡Ëi †K‡›`ai ̄’vbvsK (2, – 4), Dnv X Aÿ‡K ̄úk© Kwi‡j e„ËwUi mgxKiY wbY©q Ki| (L) `„k ̈Kí-1 n‡Z CD mij‡iLvi mgxKiY I Zvi Xvj wbY©q Ki| (M) `„k ̈Kí-2 Gi †iLv؇qi ga ̈eZ©x m~2‡Kv‡Yi mgwØLÐK Aÿ؇qi mv‡_ †h wÎfzR MVb K‡i †ÿÎdj wbY©q Ki|
4  Higher Math 1st Paper Chapter-3 DËi: (K) x 2 + y2 – 4x + 8y + 4 = 0 (L) 2 3 ; 2x – 3y + 5 = 0 ; (M) 81 98 eM© GKK 17| O Y X A(3,0) X Y B(0,4) D C(2,1) [wm‡jU †evW©- Õ22] (K) x 2 + y2 – 3y = 0 †K †cvjvi mgxKi‡Y cÖKvk Ki| (L) D we›`yi ̄’vbv1⁄4 wbY©q Ki| (M) ACB Gi mgwØLЇKi mgxKiY wbY©q Ki| DËi: (K) r 2 – 3rsin = 0 ; (L)     54 25  28 25 (M) ( 13 – 3 2)x + ( 13 – 2 2)y + 8 2 – 3 13 = 0 18| [w`bvRcyi †evW©- Õ22] O Y X X Y C B A P Q wP‡Î OA = 4, OB = 2 Ges OC = 3 (K) (2, – 3) we›`yMvgx Ges x A‡ÿi abvZ¥K w`‡Ki mv‡_ 45 †KvY Ggb mij‡iLvi mgxKiY wbY©q Ki| (L) AP = PQ = QB n‡j OPQ Gi †ÿÎdj wbY©q Ki| (M) A we›`yMvgx Ges AC †iLvi mv‡_ 45 †KvY Drcbœ K‡i Giƒc mij‡iLvi mgxKiY wbY©q Ki| DËi: (K) x – y – 5 = 0 ; (L) 4 3 eM©GKK (M) x – 7y – 4 = 0 ; 7x + y – 28 = 0 19| A(3, –2), B(5, 6) `ywU we›`y| 3x + 4y – 1 = 0 I 5x – 12y + 3 = 0 `ywU mij‡iLvi mgxKiY| [w`bvRcyi †evW©- Õ22] (K) (5, –5) we›`yi †cvjvi ̄’vbvsK wbY©q Ki| (L) AB Gi j¤^ mgwØLÐK †iLvwU y Aÿ‡K †h we›`y‡Z †Q` K‡i Zv wbY©q Ki| (M) DÏxc‡K ewY©Z †iLv؇qi ga ̈eZ©x ̄’~j‡Kv‡Yi mgwØLÐK †iLvi mgxKiY wbY©q Ki| DËi: (K)     5 2 7 4 A_ev,     5 2 –  4 ; (L) (0, 3) (M) 32x – 4y + 1 = 0 20| [gqgbwmsn †evW©- Õ22] O Y X X Y C 45 A B (K) Ggb GKwU mij‡iLvi mgxKiY wbY©q Ki hv x a – y b = 1 †iLvi Dci j¤^ Ges cÖ`Ë †iLv x-Aÿ‡K †h we›`y‡Z †Q` K‡i H we›`yMvgx| (L) hw` AOB = 8 eM© GKK nq, Z‡e AB †iLvi mgxKiY wbY©q Ki| (M) BAX Gi mgwØLÐK †iLvi mgxKiY wbY©q Ki| DËi: (K) x + by – a 2 = 0 ; (L) x + y – 4 = 0 (M) x + (1 – 2)y – 4 = 0 21| DÏxcK: [XvKv †evW©- Õ21] O Y X A(1,2) P(3,2) B(4,5) (K) (– 3, –1) we›`yi †cvjvi ̄’vbv1⁄4 wbY©q Ki| (L) DÏxcK n‡Z, AB = 3BC n‡j, AC Gi j¤^wØLЇKi mgxKiY wbY©q Ki| (M) DÏxcK n‡Z, P we›`y †_‡K AB †iLvi Dci Aw1⁄4Z j‡¤^i cv`we›`yi ̄’vbv1⁄4 wbY©q Ki| DËi: (K)     2 7 6 ; (L) x + y = 7 ; (M) (2, 3) 22| [XvKv †evW©- Õ21] A D B O Y Y X X C M 45 45 (K) Y-Aÿ I (2, 2) we›`y †_‡K (a, 5) we›`ywUi `~iZ¡ mgvb n‡j, a Gi gvb wbY©q Ki| (L) DÏxcK n‡Z, CD mij‡iLvi mgxKiY wbY©q Ki| (M) DÏxcK ewY©Z OAB Gi †ÿÎdj 18 eM© GKK n‡j, AB mij‡iLvi mgxKiY wbY©q Ki| DËi: (K) 13 4 ; (L) x + y = 0 ; (M) x + y – 6 = 0