Algebra Sheet - 01 PDF

1. What is the product of (x+a) and (x+b) ? (CHSL 2021) (x+a) vkSj (x+b) dk xq.kuQy D;k gS\ (a) x² + (a+b)x+ab (b) x² + (a–b)x+ab (c) x² + (a+b)x–ab (d) x² + (a–b)x–ab 2. What i...

1. What is the product of (x+a) and (x+b) ? (CHSL 2021) (x+a) vkSj (x+b) dk xq.kuQy D;k gS\ (a) x² + (a+b)x+ab (b) x² + (a–b)x+ab (c) x² + (a+b)x–ab (d) x² + (a–b)x–ab 2. What is the expansion of (x+11) (x–11)? (x+11) (x–11) dk çlkj D;k gS\ (a) x² + 11 (b) x² – 121 (c) x² + 121 (d) x² – 11 SSC CHSL TIER – I 2022 𝟑 𝟑 3. If 16y² – k = (𝟒𝒚 + ) (𝟒𝒚 − ), then the value of k is: (CPO 2022) 𝟐 𝟐 𝟑 𝟑 ;fn 16y² – k = (𝟒𝒚 + ) (𝟒𝒚 − ) gS] rks k dk eku D;k gS\ 𝟐 𝟐 (a) 9/4 (b)11/4 (c) 6/4 (d) 7/4 4. If m² – n² = 21 and m – n = 3, find the value of m + n. ;fn m² – n² = 21 and m – n = 3, gS] rks m + n dk eku Kkr dhft,A (a) 7 (b) 4 (c) 24 (d) 18 SSC CHSL TIER – I 2022 36a 2 - 49b2 5. Simiplify. 6a + 7b 𝟑𝟔𝒂𝟐 −𝟒𝟗𝒃𝟐 dks ljy dhft,A 𝟔𝒂+𝟕𝒃 (a) 6a – 7b (b) (c) 6a + 7b (d) 7b – 6a 1 6𝑎−7𝑏 𝟏 6. If = 𝒙𝟐 − 𝒂𝟐, then the value of x is? 𝒙𝟐 +𝒂𝟐 यदि = 𝒙𝟐 − 𝒂𝟐 है , तो x का मान क्या होगा? 𝟏 𝒙𝟐 +𝒂𝟐 𝟏 A) (𝟏 − 𝒂𝟒 )𝟒 B) 𝒂 𝟏 C) (𝒂𝟒 − 𝟏)𝟒 𝟏 D) (𝒂𝟒 + 𝟏)𝟒 7. Simplify the expression (CHSL 2021) (36p² + 49q²) (6p + 7q) (6p – 7q) Oa;td (36p² + 49q²) (6p + 7q) (6p – 7q) dk eku Kkr dhft,A (a) 1296 p4 + 2401 q4 (b) 36p4 – 49 q4 Telegram Channel : https://t.me/mathsbygaganpratap  (c) 1296p4 – 2401 q4 (d) 36p4 + 49q4 𝟐𝟓𝟔𝒙𝟒 −𝟏𝟔𝒚𝟒 8. Simplify : (𝟖𝟎𝒙𝟐 −𝟐𝟎𝒚𝟐 )(𝟏𝟔𝒙𝟐 +𝟒𝒚𝟐 ) 𝟐𝟓𝟔𝒙𝟒 −𝟏𝟔𝒚𝟒 को सरलीकृत कीजिए । (𝟖𝟎𝒙𝟐 −𝟐𝟎𝒚𝟐 )(𝟏𝟔𝒙𝟐 +𝟒𝒚𝟐 ) 1. 5 2. 1/20 3. 1/5 4. 2/5 SSC CGL 2023 PRE 9. (𝒂 + 𝒃 − 𝒄 + 𝒅)𝟐 − (𝒂 − 𝒃 + 𝒄 − 𝒅)𝟐 =? A) 4a(b+d-c) B) 2a(a+b-c) C) 2a(b+c-d) D) 4a(b-d+c) 10. Simplify the following expression: (𝒂 + 𝒃 + 𝒄)𝟐 − (𝒂 − 𝒃 + 𝒄)𝟐 + 𝟒𝒂𝒄? ननम्नलिखित ब्यंजक को सरि बनाएं: (𝒂 + 𝒃 + 𝒄)𝟐 − (𝒂 − 𝒃 + 𝒄)𝟐 + 𝟒𝒂𝒄 A) 4(bc+ac) B) 2(ab+bc+ca) C) 4(ab+bc+ca) D) 4(bc+ab) (𝑎2 +𝑏 2 −𝑐 2 )−(𝑎2 −𝑏 2 +𝑐 2 )2 11. Simplify the following expression. ? 𝑏 2 −𝑐 2 𝟐 𝟐 (𝒂𝟐 +𝒃𝟐 −𝒄𝟐 ) −(𝒂𝟐 −𝒃𝟐 +𝒄𝟐 ) fuEufyf[kr O;atd dks ljy dhft,A 𝒃𝟐 −𝒄𝟐 2 2 (a) 5a (b) 2a (c) 3a2 (d) 4a2 12. Simplify the following expression: (𝒙 + 𝒚)(𝒙 − 𝒚)(𝒙𝟐 + 𝒚𝟐 )(𝒙𝟒 + 𝒚𝟒 )(𝒙𝟖 + 𝒚𝟖 )(𝒙𝟏𝟔 + 𝒚𝟏𝟔 )? ननम्नलिखित अलिव्यक्क्त (𝒙 + 𝒚)(𝒙 − 𝒚)(𝒙𝟐 + 𝒚𝟐 )(𝒙𝟒 + 𝒚𝟒 )(𝒙𝟖 + 𝒚𝟖 )(𝒙𝟏𝟔 + 𝒚𝟏𝟔 ) को सरि बनाएं: (SSC SELECTION POST XII GRADUATE LEVEL) A) 𝒙𝟏𝟐𝟖 − 𝒚𝟏𝟐𝟖 B) 𝒙𝟔𝟒 − 𝒚𝟔𝟒 C) 𝒙𝟐𝟓𝟔 − 𝒚𝟐𝟖 D) 𝒙𝟑𝟐 − 𝒚𝟑𝟐 13. Simplify the following expression. जिम्नजलखित व्यंिक को सरल कीजिए। [ (1+p)(1+p2)(1+p4)(1+p8)(1+p16)(1 − p) − 1] (a) −p32 (b) p32 (c) (1 + p32) (d) (1 − p32) SSC CGL 2023 PRE 14. What is the value of 𝟏 𝟏 𝟏 𝟏 𝟏 𝟏 (𝒌 − ) (𝒌𝟐 + ) (𝒌𝟒 + ) (𝒌𝟖 + ) (𝒌𝟏𝟔 + ) (𝒌𝟑𝟐 + )? 𝒌 𝒌² 𝒌𝟒 𝒌𝟖 𝒌𝟏𝟔 𝒌𝟑𝟐 SSC CHSL TIER – I 2022 dk eku D;k gS\ 𝟏 𝒌𝟔𝟒 − 𝟔𝟒 (a) 𝒌 𝟏 𝒌+ 𝒌 𝟏 𝒌𝟑𝟐 − 𝟑𝟐 (b) 𝒌 𝟏 𝒌− 𝒌 𝟏 𝒌𝟑𝟐 − 𝟑𝟐 (c) 𝒌 𝟏 𝒌+ 𝒌 𝟏 𝒌𝟑𝟐 + 𝟔𝟒 (d) 𝒌 𝟏 𝒌+ 𝒌 Telegram Channel : https://t.me/mathsbygaganpratap 15. Simplify the following expression 𝟒𝟗𝒂𝟐 + 𝟕𝟎𝒂𝒃 + 𝟐𝟓𝒃𝟐 ? ननम्नलिखित अलिव्यक्क्त को सरि बनाएं 𝟒𝟗𝒂𝟐 + 𝟕𝟎𝒂𝒃 + 𝟐𝟓𝒃𝟐 ? (SSC SELECTION POST XII HIGHER SECONDARY LEVEL) A) (𝟕𝒂 − 𝟓𝒃)𝟐 B) (𝟕𝒂 + 𝟓𝒃)𝟐 C) (𝟓𝒂 + 𝟕𝒃)𝟐 D) (𝟓𝒂 − 𝟕𝒃)𝟐 𝟗𝒙𝟐 +𝟏𝟐𝒙𝒚+𝟒𝒚² 16. What is the value of ? 𝟑𝟔 𝟗𝒙𝟐 +𝟏𝟐𝒙𝒚+𝟒𝒚² dk eku D;k gS\ 𝟑𝟔 𝒙 𝒚 𝟐 (a) ( + ) 𝟑 𝟐 𝒙 𝒚 𝟐 (b) ( − ) 𝟐 𝟑 𝒙 𝒚 𝟐 (c) ( + ) 𝟐 𝟑 𝒙 𝒚 𝟐 (d) ( + ) SSC CHSL TIER – I 2022 𝟒 𝟑 17. Simplify √𝟑𝟔𝒙𝟐 − 𝟏𝟎𝟖𝒙 + 𝟖𝟏 √𝟑𝟔𝒙𝟐 − 𝟏𝟎𝟖𝒙 + 𝟖𝟏 dks ljy dhft,A (a) 2x – 9 (b) 6x – 9 (c) 5x – 9 (d) 3x – 3 (SSC CGL 2022) 18. Which among the below option can be a square root of? (CHSL 2021) fuEufyf[kr dk oxZewy D;k gS\ (x²–14x+49) (x²+6x+9) (a) (x-4)(x+9) (b) (x-1)(x+17) (c) (x-7)(x+3) (d) (x-3)(x+8) 19. Simplify (𝟓𝒙 + 𝟒𝒚)𝟐 + (𝟓𝒙 − 𝟒𝒚)𝟐 ? (𝟓𝒙 + 𝟒𝒚)𝟐 + (𝟓𝒙 − 𝟒𝒚)𝟐 सरल कीजिये A) 𝟑𝟐𝒙𝟐 + 𝟓𝟎𝒚𝟐 B) 𝟓𝟎𝒙𝟐 + 𝟑𝟐𝒚𝟐 C) – 𝟖𝟎𝒙𝒚 D) 𝟖𝟎𝒙𝒚 20. Find the value of (𝟐𝒂 + 𝟑𝒃)𝟐 − (𝟐𝒂 − 𝟑𝒃)𝟐 ? (𝟐𝒂 + 𝟑𝒃)𝟐 − (𝟐𝒂 − 𝟑𝒃)𝟐 का मान ज्ञात कीजिए ? a)12ab b)16ab c)24ab d)18ab 𝟏 𝟏 𝟐 𝟏 𝟐 21. What is the simplied value of: {(𝒙 + ) − (𝒙 − ) }? 𝟖 𝒚 𝒚 𝟏 𝟏 𝟐 𝟏 𝟐 {(𝒙 + ) − (𝒙 − ) } dks ljy dhft,A (CPO 2019) 𝟖 𝒚 𝒚 𝒙 𝟐𝒙 𝒙 𝟒𝒙 (a) (b) (c) (d) 𝒚 𝒚 𝟐𝒚 𝒚 𝒔𝟐 +𝒕𝟐 +𝟐𝒔𝒕−𝒖𝟐 22. Simplify the expression 𝟐 , 𝒑𝒓𝒐𝒗𝒊𝒅𝒆𝒅 (𝒔 + 𝒕 + 𝒖) ≠ 𝟎? 𝒔𝟐 −𝒕𝟐 −𝟐𝒕𝒖−𝒖 Telegram Channel : https://t.me/mathsbygaganpratap  𝒔𝟐 +𝒕𝟐 +𝟐𝒔𝒕−𝒖𝟐 ब्यंजक को सरि बनाएं, यदि (𝒔 + 𝒕 + 𝒖) ≠ 𝟎? 𝒔𝟐 −𝒕𝟐 −𝟐𝒕𝒖−𝒖𝟐 𝒔+𝒕−𝒖 A) 𝒔−𝒕−𝒖 𝒔+𝒕+𝒖 B) 𝒔−𝒕+𝒖 𝒔−𝒕−𝒖 C) 𝒔+𝒕−𝒖 𝒔−𝒕+𝒖 D) 𝒔+𝒕+𝒖 𝒙+𝒚 23. If 𝒙𝟐 + 𝒚𝟐 = 𝟒𝟐𝟕 & 𝒙𝒚 = 𝟐𝟎𝟐, then find ? 𝒙−𝒚 यदि 𝒙𝟐 + 𝒚𝟐 = 𝟒𝟐𝟕 & 𝒙𝒚 = 𝟐𝟎𝟐, तो िोजें? SSC CGL Pre 2023 𝒙+𝒚 𝒙−𝒚 𝟖𝟑𝟓 A) √ 𝟐𝟑 𝟖𝟑𝟎 B) √ 𝟐𝟗 𝟖𝟑𝟏 C) √ 𝟐𝟑 𝟖𝟑𝟎 D) √ 𝟐𝟑 24. If (x + 1)² + (x + 2)² = 16, then what is the value of 4x² + 12x + 40? ;fn (x + 1)² + (x + 2)² = 16, rks 4x² + 12x + 40 dk eku D;k gS\ (a) 52 (b) 62 (c) 56 (d) 74 SSC CHSL TIER – I 2022 25. If 𝒂 + 𝒃 = 𝟏𝟏 and 𝒂𝒃 = 𝟏𝟓, then 𝒂𝟐 + 𝒃𝟐 is equal to: यदि 𝒂 + 𝒃 = 𝟏𝟏 और 𝒂𝒃 = 𝟏𝟓 है , तो 𝒂𝟐 + 𝒃𝟐 का मान बताइए। (a) 90 (b) 91 (c) 93 (d) 92 26. If a + b = 24 and 8ab = 256, then what is the value of 3a² + 3b²? ;fn a + b = 24 and 8ab = 256, rks 3a² + 3b² gS\ (a) 1536 (b) 1024 (c) 512 (d) 1636 SSC CHSL TIER – I 2022 27. If x–y = 25 and xy = 78, then what is the value of x² + y²? ;fn x–y = 25 vkSj xy = 78 gS] rks x² + y² dk eku D;k gksxk\ (a) 625 (b) 781 (c) 103 (d) 756 28. The difference between two numbers is 43 and their product is 50. Find the sum of their squares. िो संख्याओं के बीच का अंतर 43 और उनका गुणिफि 50 है । उनके वगों का योग ज्ञात कीक्जए। (a) 1947 (b) 1946 (c) 1948 (d) 1949 𝒙 𝒚 29. If x+y = 18 and xy = 9, then find ( + )? 𝒚 𝒙 यदि x+y = 18 और xy = 9 है , तो ( + )ज्ञात कीक्जए? 𝒙 𝒚 𝒚 𝒙 (SSC SELECTION POST XII GRADUATE LEVEL 2024) Telegram Channel : https://t.me/mathsbygaganpratap A) 38 B) 32 C) 36 D) 34 30. If 𝟑𝒙 + 𝟑𝒚 = 𝟏𝟎 & 𝟑𝒙+𝒚 = 𝟓, then find 𝟑𝒙−𝒚 + 𝟑𝒚−𝒙 ? यदि 𝟑𝒙 + 𝟑𝒚 = 𝟏𝟎 & 𝟑𝒙+𝒚 = 𝟓 है , तो 𝟑𝒙−𝒚 + 𝟑𝒚−𝒙 ज्ञात कीक्जये? A) 10 B) 18 C) 20 D) None 31. If p + q = 7 and p² + q² = 25, then find the value of pq. ;fn p + q = 7 and p² + q² = 25, rks pq dk eku Kkr dhft,A (a) 12 (b) 24 (c) 36 (d) 18 SSC CHSL TIER – I 2022 32. The sum of two numbers is 28 and the sum of their squares is 528. Find the square root of the product of both the numbers? िो संख्याओं का योग 28 है और उनके वगों का योग 528 है । िोनों संख्याओं के गण ु नफि का वगगमि ू ज्ञात कीक्जए? SSC CPO 2024 A) 8√𝟐 B) 2√𝟐 C) 4√𝟐 D) 6√𝟐 33. If a – b = 5 and a2 + b2 = 45, then what is the value of ab? ;fn a – b = 5 vkSj a2 + b2 = 45 gS] rks ab dk eku D;k gksxk\ (a) 20 (b) 10 (c) 25 (d) 15 34. If 3a+2b = 49 and ab = 8, then the value of 9𝒂𝟐 + 4𝒃𝟐 will be: यजि 3a+2b = 49 और ab = 8 है, तो 9𝒂𝟐 + 4𝒃𝟐 का मान होगा: a)2305 b)2301 c)2497 d)2137 35. If 2p + 5q = 12 and pq = 3, find the value of 4p² + 25q². ;fn 2p + 5q = 12 vkSj pq = 3, rks 4p² + 25q² dk eku Kkr dhft,A (a) 64 (b) 24 (c) 84 (d) 44 SSC CHSL TIER – I 2022 36. If (7x – 10y) = 8 and xy = 5, then what is the value of 49x² + 100y² ? ;fn (7x – 10y) = 8 vkSj xy = 5 gS] rks 49x² + 100y² dk eku D;k gksxk\ (a) 764 (b) 632 (c) 623 (d) 746 37. If 49a² + 25b² = 30 and ab = 1, a, b > 0, then the value of (7a + 5b) is: ;fn 49a² + 25b² = 30 vkSj ab = 1tgk¡ a, b > 0 gS] rks (7a + 5b) dk eku D;k gksxk\ (a) 14 Telegram Channel : https://t.me/mathsbygaganpratap  (b) 8 (c) 12 (d) 10 38. If 9𝒂 + 𝒃 = 25 and ab = 4, then the value of 3a+b will be: 𝟐 𝟐 यजि 9𝒂𝟐 + 𝒃𝟐 = 25 और ab = 4 है, तो 3a + b का मान होगा: 𝟐 𝟏 a)6 b)7 c)7 d)6 𝟓 𝟒 39. If 𝒂𝟐 + 𝒃𝟐 = 𝟐𝟖𝟗, ab=120, (a>b), then (𝒂𝟐 − 𝒃𝟐 ) is equal to: यदि 𝒂𝟐 + 𝒃𝟐 = 𝟐𝟖𝟗, ab=120, (a>b), तो (𝒂𝟐 − 𝒃𝟐 ) ककसके बराबर होगा? A) 171 B) 187 C) 191 D) 161 40. If x – y = 13 and xy = 19, then the value of 𝒙𝟐 − 𝒚𝟐 is: यजि x – y = 13 और xy = 19 है, तो 𝒙𝟐 − 𝒚𝟐 का मान है : a) 13√𝟐𝟔𝟗 b)91√𝟓 c)39√𝟑𝟏 d)26√𝟗𝟕 41. If a + 4b = 19 and 2ab = 17, then the value of |𝒂 − 𝟒𝒃| is: यजि a + 4b = 19 और 2ab = 17, तो |𝒂 − 𝟒𝒃| का मान है: a)13 b)15 c)16 d)14 42. If a + b = 11 and a – b = 8, then find the value of 'ab'. ;fn a + b = 11 vkSj a – b = 8 gS] rks 'ab' dk eku Kkr djsaA (a) 16.5 (b) 13.25 (c) 15.45 (d) 14.25 43. If (3p – 5m) = 5 and pm = 6, then what is the value of (9p² – 25m²)? ;fn (3p – 5m) = 5 vkSj pm = 6 gS] rks (9p² – 25m²) dk eku D;k gksxk\ (a) 5 385 (b) 30 10 (c) 5 385 (d)  10 44. If x + y = √𝟏𝟑 and x - y = √𝟏𝟏, then the value of xy (x2 + y2) is: यजि x + y = √13 और x - y = √11, तो xy (x2 + y2) का माि ज्ञात कीजिये : 1. 10 2. 6 3. √6 4. √10 (SSC SELECTION POST XI 2023) 45. If x + y = 10 and xy = 4, then what is the value of x4 + y4? (Mains 2017) ;fn x + y = 10 vkSj xy = 4 gS] rks x4 + y4 dk eku D;k gS\ (a) 8464 (b) 8432 (c) 7478 (d) 6218 46. If 𝒂 + 𝒃 = √𝟏𝟐 & 𝒂 − 𝒃 = √𝟖, then find 𝒂 + 𝒃 ?𝟒 𝟒 यदि 𝒂 + 𝒃 = √𝟏𝟐 & 𝒂 − 𝒃 = √𝟖 है , तो 𝒂𝟒 + 𝒃𝟒 ज्ञात कीक्जये? A) 94 B) 96 C) 95 D) 98 47. If 𝒙 = 𝟏 − 𝒚 & 𝒙𝟐 = 𝟐 − 𝒚𝟐 , 𝒕𝒉𝒆𝒏 𝒙𝟒 + 𝒚𝟒 =? (a) 𝟗⁄𝟐 (b) 𝟑⁄𝟐 (c) 𝟕⁄𝟐 (d) 𝟓⁄𝟐 Telegram Channel : https://t.me/mathsbygaganpratap 48. If 𝒙 + 𝒚 = 𝟏𝟗, 𝒙𝒚 = 𝟗, then find 𝒙√𝒚 + 𝒚√𝒙? यदि 𝒙 + 𝒚 = 𝟏𝟗, 𝒙𝒚 = 𝟗, तो 𝒙√𝒚 + 𝒚√𝒙 ज्ञात कीक्जए? A) 10 B) 12 C) 15 D) 21 49. If 𝒙𝟐 − 𝒚𝟐 = 𝟗, 𝒙𝒚 = 𝟑, then find x+y? A) ±√𝟔 + 𝟑√𝟏𝟑 C) ±√𝟓 + 𝟏𝟑√𝟑 B) ±√𝟒 + 𝟑√𝟏𝟑 D) ±𝟏𝟗 50. If a + b = 24 and a2 + b2 = 306, where a > b, then the value of 4a - 5b is: ;fn a + b = 24 vkSj a2 + b2 = 306 gS] tgka] a > b gS] rks 4a - 5b dk eku Kkr djsaA (a) 18 (b) 20 (c) 12 (d) 15 51. If x+y = 27 and x²+y² = 425, then the value of (x-y)² will be: ;fn x+y = 27 vkSj x²+y² = 425, gS] rks (x-y)² dk eku Kkr djsAa (a) 225 (b) 169 (c) 121 (d) 144 52. If x–2y=3 and 2xy = 5, then find the value of (x+2y)². ;fn x–2y=3 vkSj 2xy = 5 gS] rks (x+2y)² dk eku Kkr djsAa (a) 29 (b) 27 (c) 30 (d) 28 53. If a3+b3=5824 and a+b=28, then(a-b)2+ab is equal to: (CPO 2019) a) 208 b) 152 c) 180 d)236 54. If a3+b3=432 and a+b=12, then(a+b)2-3ab is equal to: (2018 PRE) a) 42 b) 52 c) 36 d) 38 55. If a³ = b³ + 988 and a – b = 4, then what is the value of 2a² + 2ab + 2b²? ;fn a³ = b³ + 988 vkSj a – b = 4, rks 2a² + 2ab + 2b² dk eku D;k gS\ (a) 516 (b) 494 (c) 500 (d) 247 SSC CHSL TIER – I 2022 56. If 𝒂𝟑 − 𝒃𝟑 = 𝟖𝟗𝟗 and 𝒂 − 𝒃 = 𝟑𝟏, then (𝒂 − 𝒃)𝟐 + 𝟑𝒂𝒃 is equal to: यदि 𝒂𝟑 − 𝒃𝟑 = 𝟖𝟗𝟗 तथा 𝒂 − 𝒃 = 𝟑𝟏, तो (𝒂 − 𝒃)𝟐 + 𝟑𝒂𝒃 का माना है : A) 35 B) 31 C) 16 D) 29 57. 𝟎. 𝟎𝟎𝟖𝑿𝟑 + 𝟎. 𝟎𝟐𝟕𝒀𝟑 = 𝟏𝟐𝟓 & 𝟎. 𝟐𝑿 + 𝟎. 𝟑𝒀 = 𝟐𝟓, then find (𝟎. 𝟐𝑿 + 𝟎. 𝟑𝒀)𝟐 − 𝟎. 𝟏𝟖𝑿𝒀? यदि 𝟎. 𝟎𝟎𝟖𝑿𝟑 + 𝟎. 𝟎𝟐𝟕𝒀𝟑 = 𝟏𝟐𝟓 & 𝟎. 𝟐𝑿 + 𝟎. 𝟑𝒀 = 𝟐𝟓 है , तो (𝟎. 𝟐𝑿 + 𝟎. 𝟑𝒀)𝟐 − 𝟎. 𝟏𝟖𝑿𝒀 ज्ञात कीक्जये? A) 5 C) 125 B) 25 D) 10 Telegram Channel : https://t.me/mathsbygaganpratap 58. What is the value of (a–b)³ – a³ + b³? (a–b)³ – a³ + b³ dk eku D;k gS\ (a) 3ab(a–b) (b) –3ab(a+b) (c) –3ab(a–b) (d) 3ab(a+b) SSC CHSL TIER – I 2022 𝒙 𝒚 59. ( + ) 𝟑 =? (2019 PRE) 𝟑 𝟓 𝒙𝟑 𝒙𝟐 𝒚 𝒙𝒚𝟐 𝒚𝟑 𝒙𝟑 𝒙𝟐 𝒚 𝒙𝒚𝟐 𝒚𝟑 a) + + + b) + + + 𝟐𝟕 𝟐𝟓 𝟐𝟓 𝟏𝟐𝟓 𝟐𝟕 𝟏𝟓 𝟐𝟓 𝟏𝟐𝟓 𝒙𝟑 𝒙𝟐 𝒚 𝒙𝒚𝟐 𝒚𝟑 𝒙𝟑 𝒙𝟐 𝒚 𝒙𝒚𝟐 𝒚𝟑 c) + + + d) + + + 𝟐𝟓 𝟐𝟓 𝟐𝟓 𝟏𝟐𝟓 𝟏𝟕 𝟏𝟓 𝟐𝟓 𝟏𝟐𝟓 60. (𝟑𝒂 − 𝟒𝒃)𝟑 is equal to? (𝟑𝒂 − 𝟒𝒃)𝟑 ककसके बराबर है ? A) 𝟐𝟕𝒂𝟑 − 𝟔𝟒𝒃𝟑 B) 𝟐𝟕𝒂𝟑 − 𝟔𝟒𝒃𝟑 − 𝟏𝟎𝟖𝒂𝟐 𝒃 + 𝟏𝟒𝟒𝒂𝒃𝟐 C) 𝟗𝒂𝟐 − 𝟏𝟔𝒃𝟐 D) 𝟗𝒂𝟐 − 𝟐𝟒𝒂𝒃 + 𝟏𝟔𝒃𝟐 61. Simplify the given expression/fn, x, O;atd dks ljy dhft,A (5x + 8y) (25x² + 64y² – 40xy) (a) 125x³ – 51y³ (b) 25x³ + 64y³ (c) 125x³ + 512y³ (d) 25x³ – 64y³ (SSC CGL 2022) 62. The value of 27𝒂𝟑 − 𝟐√𝟐 𝒃𝟑 𝒊𝒔 equal to:- (2019 PRE) 27a3 - 2√𝟐𝒃𝟑 का मान......के बराबर है। a) (3a-√2b)(9𝒂𝟐 − 𝟐𝒃𝟐 + 𝟔√𝟐𝒂𝒃) b) (3a-√2b)(9𝒂𝟐 + 𝟐𝒃𝟐 + 𝟔√𝟐𝒂𝒃) c) (3a-√2b)(9𝒂𝟐 + 𝟐𝒃𝟐 + 𝟑√𝟐𝒂𝒃) d) (3a-√2b)(9𝒂𝟐 − 𝟐𝒃𝟐 − 𝟑√𝟐𝒂𝒃) 63. Simplify the following. (𝒙 − 𝟑𝒚)𝟑 + 𝟐𝟕(𝒚𝟑 − 𝒙𝒚𝟐 )? ननम्नलिखित को सरि कीक्जये. (𝒙 − 𝟑𝒚)𝟑 + 𝟐𝟕(𝒚𝟑 − 𝒙𝒚𝟐 ) (SSC SELECTION POST XII HIGHER SECONDARY LEVEL) A) 𝒙𝟑 − 𝟑𝒙𝟐 𝒚 B) 𝒙𝟑 − 𝟗𝒙𝟐 𝒚 C) 𝒙𝟑 − 𝟐𝟕𝒚𝟑 − 𝟗𝒙𝟐 𝒚 D) 𝒙𝟑 − 𝟐𝟕𝒚𝟑 − 𝟗𝒙𝟐 𝒚 + 𝟐𝟕𝒙𝒚𝟐 + 𝟐𝟕𝒚𝟐 − 𝟐𝟕𝒚𝟐 𝟓 𝟐𝟓 64. If b=5, determine the value of an expression ( + 𝟓𝒃)( − 𝟐𝟓 + 𝟐𝟓𝒃𝟐 ) using an identity? 𝒃 𝒃𝟐 यदि b=5, तो एक समानता का उपयोग करके ब्यंजक ( + 𝟓𝒃)( 𝟐 − 𝟐𝟓 + 𝟐𝟓𝒃𝟐 ) का मान ननर्ागररत करें ? 𝟓 𝟐𝟓 𝒃 𝒃 A) 25726 B) 15625 C) 15438 D) 25636 SSC CGL 2023 PRE 65. If a = 17, b =13, then find the value of the expression (a 3 − b3 − 3a 2b + 3ab2 ). यदि a = 17, b = 13 है , तो व्यंजक (a 3 − b3 − 3a 2b + 3ab 2 ) का मान ज्ञात कीक्जए । (a) –64 (b) –27000 (c) 27000 (d) 64 SSC CGL 2023 PRE Telegram Channel : https://t.me/mathsbygaganpratap  (x3 −y3 )(x+y) 66. Simplify the given expression. fn, x, O;atd dks ljy dhft,A x2 +xy+y2 (a) x – y 2 2 (b) x + y (c) x + y 2 2 (d) x – y 67. What is the coefficient of x in the expansion of (3x–4)³ ? (3x–4)³ ds foLrkj esa x dk xq.kkad Kkr djsaA (a) –144 (b) –108 (c) 108 (d) 144 68. The coefficient of 𝒙𝟐 𝒊𝒏 (𝟐𝒙 + 𝒚)𝟑 𝒊𝒔: − (𝟐𝒙 + 𝒚)𝟑 , में 𝒙𝟐 का गुणांक है :- a) 12𝒚𝟐 b) 12y c) 8 d) 12 𝟏 𝟑 69. What is the constant term in the expansion of (𝟓𝒙𝟐 − ) ? 𝒙 𝟏 𝟑 (𝟓𝒙𝟐 − ) ds foLrkj eas vpj in (constant term) Kkr djsAa 𝒙 (a) 5 (b) –15 (c) 15 (d) 75 𝒙² ³ 70. What is the coefficient of x² in the expansion of (𝟓– ) ? 𝟑 𝒙² ³ (𝟓– ) ds foLrkj eas X² dk xq.kkad Kkr djsaA 𝟑 𝟐𝟓 (a) − 𝟑 (b) –25 𝟓 (c) − 𝟑 (d) 25 71. What is the coefficient of y2 in the expansion of (√𝟐𝒚𝟐 − 𝟓√𝟑)𝟑 ? O;atd (√𝟐𝒚𝟐 − 𝟓√𝟑)𝟑 ds foLrkj esa y2 dk xq.kkad Kkr djsaA (a) −𝟐𝟐𝟓√𝟐 (b) −𝟑𝟎√𝟑 (c) 𝟐𝟐𝟓√𝟐 (d) 𝟑𝟎√𝟑 72. If 8 + 2px² – 36x – 27x³ = (2 – 3x)³, then what is the value of p? ;fn 8 + 2px² – 36x – 27x³ = (2 – 3x)³ rks p dk eku Kkr djsAa (a) 27 (b) 54 (c) 9 (d) –27 73. The coefficient of x3y in (x–2y) × (5x + y)3 is: (x–2y) × (5x + y)3 eas x3y dk xq.kkad (coefficient) Kkr djsaA Telegram Channel : https://t.me/mathsbygaganpratap  (a) 75 (b) –150 (c) 250 (d) –175 74. If x4 + y4 = x2y2, then the value of x6 + y6 is: यजि x4 + y4 = x2y2 है , तो x6 + y6 का माि क्या होगा? (a) 1 (b) 3 (c) 2 (d) 0 (SSC CPO 2023) 75. If A + B = 12 and AB = 17, what is the value of A3 + B3? (2019 PRE) यदि A + B = 12 और AB = 17 है, तो A³ + B³ का मान क्‍या होगा? (A) 1116 (B) 1106 (C) 1166 (D) 1213 76. If a+b =4 and ab=-21, then what is the value of 𝒂𝟑 + 𝒃𝟑 ? यदि a+b =4 और ab=-21, तो 𝒂𝟑 + 𝒃𝟑 का मान क्या है ? A) 370 B) 158 C) 185 D) 316 77. If 5x + y = 17 and xy = 6, then what is the value of 125x³ + y³? ;fn 5x + y = 17 vkSj xy = 6 rks 125x³ + y³ dk eku D;k gS\ (a) 3383 (b) 1530 (c) 3183 (d) 4913 SSC CHSL TIER – I 2022 78. If (𝟐𝟐 − 𝒎)(𝒎 − 𝟏𝟗) = 𝟓, then find (𝒎 − 𝟏𝟗)𝟑 + (𝟐𝟐 − 𝒎)𝟑 ? यदि (𝟐𝟐 − 𝒎)(𝒎 − 𝟏𝟗) = 𝟓 है , तो (𝒎 − 𝟏𝟗)𝟑 + (𝟐𝟐 − 𝒎)𝟑 ज्ञात कीक्जये? A) -18 B) 18 C) 20 D) -20 79. If 𝒂𝟑 + 𝒃𝟑 = 𝟑𝟓 & 𝒂𝒃 = 𝟔, then find a+b? यदि 𝒂𝟑 + 𝒃𝟑 = 𝟑𝟓 & 𝒂𝒃 = 𝟔, तो a+b ज्ञात कीक्जए? A) 5 B) 8 C) -8 D) 2 80. If 𝒙𝒚 = −𝟔 & 𝒙𝟑 + 𝒚𝟑 = 𝟏𝟗 (x and y are integers), then 𝟏 𝟏 what is the value of + ? 𝒙−𝟏 𝒚−𝟏 यदि 𝒙𝒚 = −𝟔 & 𝒙𝟑 + 𝒚𝟑 = 𝟏𝟗 (x और y पूर्ाांक हैं), तो का मान क्या है ? 𝟏 𝟏 + 𝒙−𝟏 𝒚−𝟏 A) 2 B) 1 C) -1 D) -2 81. If x-y =4 and xy = 3, then what is the value of x³-y³ ? ;fn x–y = 4 vkSj xy = 3 gS] rks x³ – y³ dk eku Kkr djsaA Telegram Channel : https://t.me/mathsbygaganpratap  (a) 88 (b) 28 (c) 100 (d) 64 82. If x – y = 25 and xy = 444, compute the value of x3 – y3. यदि x - y = 25 और xy = 444 है , तो x3 - y3 के मान की गणना करें । SSC CPO 2024 A) 48925 B) 42985 C) 28495 D) 26725 𝟕 𝟏 𝟏 𝟏𝟒 83. If x – y = 𝟒 and 𝒙 − 𝒚 = 𝟑 , then x³ – y³ is equal to : 𝟕 𝟏 𝟏 𝟏𝟒 ;fn x – y = vkSj − = gS] rks x³ – y³ dk eku Kkr djsaA 𝟒 𝒙 𝒚 𝟑 𝟒𝟑𝟑 (a) 𝟑𝟐 𝟒𝟑𝟑 (b) 𝟔𝟒 𝟐𝟏𝟕 (c) 𝟔𝟒 𝟐𝟏𝟕 (d) 𝟑𝟐 84. If (a + b) = 16 and a³ + b³ = 1456, then what is the value of ab? ;fn (a + b) = 16 and a³ + b³ = 1456, rks ab dk eku D;k gS\ (a) 50 (b) 48 (c) 64 (d) 55 SSC CHSL TIER – I 2022 85. If 3a + 2b = 27 and 27a3 + 8b3 = 1458, then find 2ab. यदि 3a + 2b = 27 और 27a3 + 8b3 = 1458, तो 2ab का मान ज्ञात कीदिए। (a) 72 (b) 70 (c) 77 (d) 75 86. If a− b = 27 and 𝒂𝟑 −𝒃𝟑 = 5427, then the value of ab will be: यजि a − b = 27 और 𝒂𝟑 −𝒃𝟑 = 5427, तो ab का मान होगा: a)-176 b)-110 c)-152 d)-140 𝟔𝟒 𝟑 𝟏𝟐𝟓 𝟑 𝟒 𝟓 87. If 𝒂 − 𝒃 = 𝟑𝟖𝟕 & 𝒂 − 𝒃 = 𝟑, then find 10ab? 𝟐𝟕 𝟔𝟒 𝟑 𝟒 यदि 𝒃 = 𝟑𝟖𝟕 & 𝒂 − 𝒃 = 𝟑 है , तो 10ab ज्ञात कीक्जये? 𝟔𝟒 𝟑 𝟏𝟐𝟓 𝟑 𝟒 𝟓 𝒂 − 𝟐𝟕 𝟔𝟒 𝟑 𝟒 A) 210 C) 220 B) 230 D) 240 88. If x + y = 13 and 𝒙𝟐 + 𝒚𝟐 = 101, then the value of 𝒙𝟑 + 𝒚𝟑 will be: यजि x + y = 13 और 𝒙𝟐 + 𝒚𝟐 = 101, तो 𝒙𝟑 + 𝒚𝟑 का मान होगा: (a) 767 (b) 949 (c) 793 (d) 871 𝟕 𝟑𝟏 89. If a + b =𝟑, 𝒂𝟐 + 𝒃𝟐 = 𝟗 , then find 27(𝒂𝟑 + 𝒃𝟑 ) =? a)117 b)154 c)126 d)168 90. If 𝒂𝟐 + 𝒃𝟐 = 𝟗𝟓and ab=13, (a>0, b>0) then the value of (𝒂𝟑 + 𝒃𝟑 ) is: यदि𝒂𝟐 + 𝒃𝟐 = 𝟗𝟓 और ab=13, (a>0, b>0) है तो (𝒂𝟑 + 𝒃𝟑 ) का मान है : A) 861 B) 968 C) 1100 D) 902 Telegram Channel : https://t.me/mathsbygaganpratap 91. If 16x² + y² = 48 and xy = 2, x, y > 0, then the value of (64x³ + y³) is: ;fn 16x² + y² = 48 vkSj xy = 2, x, y > 0 gS] rks (64x³ + y³) dk eku Kkr djsaA (a) 320 (b) 340 (c) 300 (d) 240 92. If a2+b2=135 and ab=7, (a>0, b>0) then the value of (a3-b3) is: यदि a2+b2=135 और ab=7, (a>0, b>0) है तो (a3-b3) का मान है : A) 1562 B) 1408 C) 1420 D) 1350 93. If x² + y² = 45 and x – y = 5 then what is the value of x³ – y³? ;fn x² + y² = 45 vkSj x – y = 5 gS] rks x³ – y³ dk eku Kkr djsaA (a) 150 (b) 250 (c) –25 (d) 275 𝟏 𝟏 94. If a3 + b3 = 218 and a + b = 2, then the value of + is : 𝒂 𝒃 (Mains 2018) 𝟏 𝟏 यदि a3 + b3 = 218 और a + b = 2 है, तो + का मान है: 𝒂 𝒃 𝟐 𝟐 𝟏 𝟏 (a) (b) – (c) (d) – 𝟑𝟓 𝟑𝟓 𝟏𝟕 𝟏𝟐 95. If x + y = 12 and xy = 27, x > y, then the value of (x3−y3) is: ;fn x + y = 12 vkSj xy = 27, x > y, rks (x3−y3) dk eku D;k gS\ (a) 720 (b) 702 (c) 724 (d) 710 96. If x + y = 17 and xy = 25, x > y, then the value of (x3−y3) is: ;fn x + y = 17 vkSj xy = 25, x > y, rks (x3−y3) dk eku D;k gS\ (a) 792√𝟐𝟏 (b) 702√𝟐𝟏 (c) 724√𝟐𝟑 (d) none 97. If 2x + 3y = 4 and 4x2 + 9y2 =64, then what is the value of 8 x3 + 27y3. ;fn 2x+3y = 4 vkSj 4x2 + 9y2 = 64, rks 8x3+27y3 dk eku D;k gS\ (a) 352 (b) 325 (c) 235 (d) 253 98. If x² + 4y² = 53 and x – 2y = 5, then what is the value of x³ – 8y³? ;fn x² + 4y² = 53 vkSj x – 2y = 5 gS] rks x³ – 8y³ dk eku Kkr djsaA (a) –85 (b) 335 (c) 155 (d) 85 99. If x + y = 14 and 𝒙𝟑 + 𝒚𝟑 = 1064, then the value of 𝒙𝟐 − 𝒚𝟐 will be: (x > y) यजि x + y = 14 और 𝒙𝟑 + 𝒚𝟑 = 1064 है, तो 𝒙𝟐 − 𝒚𝟐 का मान होगा: (x > y) a)84 b)112 c)70 d)78 100. If 𝒂𝟑 − 𝒃𝟑 = 𝟔𝟎𝟐 & 𝒂 − 𝒃 = 𝟐, then find the value of (𝒂𝟐 + 𝒃𝟐 )? यदि 𝒂𝟑 − 𝒃𝟑 = 𝟔𝟎𝟐 & 𝒂 − 𝒃 = 𝟐, तो (𝒂𝟐 + 𝒃𝟐 ) का मान ज्ञात कीक्जए? ( IB ACIO 2023) A) 156 B) 240 C) 202 D) 260 Telegram Channel : https://t.me/mathsbygaganpratap 101. If 𝒂 − 𝒃 = 𝟒 and 𝐚𝟑 − 𝐛𝟑 = 𝟖𝟖, then find the value of 𝐚𝟐 − 𝐛𝟐. यदि 𝒂 − 𝒃 = 𝟒 और 𝐚𝟑 − 𝐛𝟑 = 𝟖𝟖 है , तो 𝐚𝟐 − 𝐛𝟐 का मान क्या होगा? (a) 𝟔 √𝟔 (b) 𝟗√𝟔 (c) 𝟕√𝟔 (d) 𝟖√𝟔 102. If 2a – b = 3 and 8a3 – b3 = 999, then find the value of 4a2 – b2. यदि 2a – b = 3 और 8a3 – b3 = 999 है, तो 4a2 – b2 का मान ज्ञात कीदिए। (a) 63 (b) 65 (c) 61 (d) 67 103. If 2 p + r = 21, and pr = 38, then find the value of p³ - r ;fn p + r = 21, vkSj pr = 38, rks p³ - r³ dk eku Kkr dhft,A (a) 6538 (b) 6102 (c) 6113 (d) 6851 SSC CHSL TIER – I 2022 104. If x³ + y³ = 416 and x + y = 8, then find x 4 + y4. ;fn x³ + y³ = 416 vkSj x + y = 8 gS] rks x4 + y4 dk eku Kkr dhft,A (a) 3002 (b) 3204 (c) 3004 (d) 3104 105. If a + b = p, ab = q, then (a4 + b4) is equal to : ;fn a + b = p, ab = q gS] rks (a4 + b4) dk eku Kkr dhft,A (a) p4 – 2p²q² + q² (b) p4 – 4p²q² + 2q² (c) p4 – 4p²q + q² (d) p4 – 4p²q + 2q² 106. If 𝟖𝒂𝟑 + 𝟐𝟕𝒃𝟑 = 𝟏𝟔 & 𝟐𝒂 + 𝟑𝒃 = 𝟒, then find the value of 𝟏𝟔𝒂𝟒 + 𝟖𝟏𝒃𝟒 ? यदि 𝟖𝒂𝟑 + 𝟐𝟕𝒃𝟑 = 𝟏𝟔 & 𝟐𝒂 + 𝟑𝒃 = 𝟒 है , तो 𝟏𝟔𝒂𝟒 + 𝟖𝟏𝒃𝟒 का मान ज्ञात कीक्जए? A) 26 B) 30 C) 28 D) 32 107. If x + y = 4 and 𝒙𝟑 + 𝒚𝟑 = 12, then the value of 𝒙𝟒 + 𝒚𝟒 will be: यजि x + y = 4 और 𝒙𝟑 + 𝒚𝟑 = 12 है, तो 𝒙𝟒 + 𝒚𝟒 का मान होगा: 𝟏𝟒𝟔 𝟏𝟑𝟏 𝟏𝟒𝟑 𝟏𝟐𝟕 a) b) c) d) 𝟗 𝟗 𝟗 𝟗 108. If 𝒂𝟑 − 𝒃𝟑 = 260 , a−b = 8 then 𝒂𝟒 + 𝒃𝟒 = ? a)1682.5 b)1628.5 c)1862.5 d)1268.5 109. If 𝟐𝟓𝒂𝟐 + 4𝒃𝟐 = 124 , ab =3 then 𝟏𝟐𝟓𝒂𝟑 −8𝒃𝟑 = ? a)1322 b)1264 c)1232 d)1268 110. If a2 + b2 = 69 and a4 + b4 = 3409, then the value of a3 + b3 is : यदि a2 + b2 = 69 और a4 + b4 = 3409है, तो a3 + b3 का मान है: (a) 506 (b) 407 (c) 429 (d) 473 111. If 5x + 9y = 5 and 125𝒙𝟑 + 729𝒚𝟑 = 120 then the value of the product of x and y? यजि 5x + 9y = 5 तथा 125𝒙𝟑 + 729𝒚𝟑 = 120 है तो x और y का गुणनफि होगा ? A) 1/9 B) 1/135 C) 1/45 D) 1/75 112. If x – y = 4 and x³ – y³ = 316, y > 0 then the value of x4 – y4 is : ;fn x – y = 4 vkSj x³ – y³ = 316 gS] y > 0 gS] rks x4 – y4 dk eku Kkr djsaA Telegram Channel : https://t.me/mathsbygaganpratap  (a) 2482 (b) 2320 (c) 2500 (d) 2401 113. If 𝒙𝟑 = 𝟏𝟏𝟔 + 𝒚𝟑 and x = 4 + y, then find ( x+ y)? 𝟏𝟓 𝟏𝟎√𝟑 𝟏𝟎 A) B) C) 10√𝟑 D) √𝟔 𝟕 √𝟑 114. If a + b = 2 and ab = 4, then find the value of a 4 + b4 + ab3 + ba3. ;fn a + b = 2 rFkk ab = 4 gS] rks a4 + b4 + ab3 + ba3 dk eku Kkr dhft,A (a) 18 (b) –16 (c) –32 (d) 24 115. If 𝒙 + 𝒚 = 𝟑, 𝒙𝟐 + 𝒚𝟐 = 𝟕, 𝒕𝒉𝒆𝒏 𝒇𝒊𝒏𝒅 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒙𝟔 + 𝒚𝟔 =? यदि 𝒙 + 𝒚 = 𝟑, 𝒙𝟐 + 𝒚𝟐 = 𝟕 है , तो 𝒙𝟔 + 𝒚𝟔 का मान ज्ञात कीक्जये? A) 322 C) 321 B) 342 D) 329 𝟔𝟓 𝟏 116. If 16x² + y² = and xy = , x, y > 0, then what is the value of (64x³ + y³)? 𝟑𝟔 𝟏𝟖 𝟔𝟓 𝟏 ;fn 16x² + y² = vkSj xy = , x, y > 0 gS] rks (64x³ + y³) dk eku D;k gksxk\ 𝟑𝟔 𝟏𝟖 𝟏𝟗 (a) 𝟒 𝟐𝟕 (b) 𝟒 𝟐𝟕 (c) 𝟖 𝟏𝟗 (d) 𝟖 𝟑 𝟒 117. If 3x + 2y = 15 & xy = 6, then find 𝒙𝟑 + 𝒚𝟑 ? 𝟐 𝟗 यदि 3x + 2y = 15 और xy = 6, तो 𝒙𝟑 + 𝒚𝟑 ज्ञात कीजिए? (ICAR Technician 2022) 𝟑 𝟒 𝟐 𝟗 A) 98.6 B) 97.5 C) 95.8 D) 92.5 𝟑 𝟏 𝒚³ 118. If 2x – y = 2 and xy = , then what is the value of (x³– )? 𝟐 𝟐 𝟖 𝟑 𝟏 𝒚³ ;fn 2x – y = 2 vkSj xy = gS] rks (x³– ) dk eku Kkr djsa\ 𝟐 𝟐 𝟖 𝟏𝟑 (a) 𝟐 𝟏𝟑 (b) 𝟖 𝟏𝟑 (c) 𝟒 𝟏𝟑 (d) 𝟗 𝟏 119. If (4a–3b) = 1, ab = , where a > 0 and b > 0, what is the value of (64a³ + 27b³)? 𝟐 𝟏 ;fn (4a–3b) = 1, ab = , tgk¡ a > 0 vkSj b > 0 gS] rks (64a³ + 27b³) dk eku D;k gS\ 𝟐 (a) 15 (b) 25 Telegram Channel : https://t.me/mathsbygaganpratap  (c) 30 (d) 35 𝟐 𝒙²+𝒚² 120. If (𝒙𝟑 + 𝒚 ) = (x²+y²), then the value of 𝟑 𝟑 x  0, y  0, is: 𝒙𝒚 𝟐 𝒙²+𝒚² ;fn (𝒙𝟑 + 𝒚𝟑 )𝟑 = (x²+y²), rks x  0, y  0 dk eku D;k gksxk\ 𝒙𝒚 (a) 2/3 (b) x²+y (c) 1 (d) x+y² 121. If a³ + 3a² + 3a = 63, then the value of a² + 2a is: ;fn a³ + 3a² + 3a = 63, rks a² + 2a dk eku gS& (a) 22 (b) 19 (c) 15 (d) 8 SSC CHSL TIER – I 2022 122. x, y are two positive numbers such that x > y. If x4 + y4 = 706 and xy = 15, then the value of 2x + 3y is: x,y nks ,slh /kukRed la[;k,¡ gSa fd x > y gSA ;fn x4 + y4 = 706 vkSj xy =15 gS] rks 2x + 2y dk eku Kkr djasA (a) 19 (b) 20 (c) 18 (d) 15 123. The sum of two numbers is 59 and their product is 1150. Find the sum of their squares. nks la[;kvksa dk ;ksx 59 gS vkSj mudk xq.kuQy 1150 gSA muds oxksZa dk ;ksx Kkr dhft,A (a) 1176 (b) 1181 (c) 1183 (d) 1178 124. If the difference between two numbers is 5 and the difference their cubes is 1850, then the difference between their squares is: ;fn nks la[;kvksa dk varj 5 gS vkSj muds ?kuksa dk varj 1850 gS] rks muds oxksZa ds e/; fdruk varj gksxk\ (a) 5 482 (b) 5 483 (c) 5 484 (d) 5 485 𝒂𝟑 −𝒃³ 𝟑𝒂𝒃 125. If a = 26 and b = 22, then the value of − is _______. 𝒂𝟐 −𝒃² 𝒂+𝒃 𝒂𝟑 −𝒃³ 𝟑𝒂𝒃 ;fn a = 26 vkSj b = 22 gS] rks − dk eku -------------------- gSA 𝒂𝟐 −𝒃² 𝒂+𝒃 (a) 5/3 (b) 13/11 (c) 1/3 Telegram Channel : https://t.me/mathsbygaganpratap  (d) 11/13 (SSC CGL 2022) 126. On simplification, 𝒙𝟑 −𝒚𝟑 𝒚[(𝒙−𝒚)𝟐 +𝟑𝒙𝒚] (𝒙+𝒚)𝟐 −(𝒙−𝒚)𝟐 ÷ × is equal to : 𝒙[(𝒙+𝒚)𝟐 −𝟑𝒙𝒚] 𝒙𝟑 +𝒚𝟑 𝒙𝟐 −𝒚𝟐 𝒙𝟑 −𝒚𝟑 𝒚[(𝒙−𝒚)𝟐 +𝟑𝒙𝒚] (𝒙+𝒚)𝟐 −(𝒙−𝒚)𝟐 ÷ × का मान ज्ञात कीदिए । 𝒙[(𝒙+𝒚)𝟐 −𝟑𝒙𝒚] 𝒙𝟑 +𝒚𝟑 𝒙𝟐 −𝒚𝟐 𝟏 𝟏 a) 4 b) 1 c) d) 𝟐 𝟒 𝒙𝟑 +𝒚𝟑 (𝒙+𝒚)𝟐 −𝟑𝒙𝒚 (𝒙+𝒚)𝟐 +(𝒙−𝒚)𝟐 127. If P = (𝒙−𝒚)𝟐 ,𝑸 = and R = , then what is the value of (P÷Q) ×R? (2019 PRE) +𝟑𝒙𝒚 𝒙𝟑 −𝒚𝟑 𝒙𝟐 −𝒚𝟐 𝒙𝟑 +𝒚𝟑 (𝒙+𝒚)𝟐 −𝟑𝒙𝒚 (𝒙+𝒚)𝟐 +(𝒙−𝒚)𝟐 यदि P = (𝒙−𝒚)𝟐 +𝟑𝒙𝒚 ,𝑸 = और R = , है तो (P÷Q) ×R का मान क्या है ? 𝒙𝟑 −𝒚𝟑 𝒙𝟐 −𝒚𝟐 𝟐 𝟐 𝟐 𝟐 a) 2xy b) 2(𝒙 + 𝒚 ) c) 𝒙 + 𝒚 d) 𝟒𝒙𝒚 128. Simplify the given expression: fn, x, O;atd dks ljyhÑr dhft,& (𝒂+𝒙)(𝒂𝒙𝟐 −𝒙³) 𝒂²−𝒂𝒙+𝒙² (𝒂𝟐 −𝟐𝒂𝒙+𝒙𝟐 )(𝒂–𝒙) ( × )÷ ,ax 𝒂³+𝒙³ 𝒂²𝒙²+𝒙𝟒 (𝒂𝟒 −𝒙𝟒 ) 𝒂+𝒙 (a) 𝒂−𝒙 (b) a²–x² 𝒂−𝒙 (c) 𝒂+𝒙 (d) a4 – x4 𝒙𝟒 −𝒚𝟒 𝒙 (𝐱+𝐲)𝟐 −𝟒𝐱𝐲 129. If x=4.5 and y = 1.5, then the value of × (𝐱+𝐲)𝟐 ÷ (𝐱+𝐲)𝟐 is: (𝐱+𝐲)𝟑 −𝟑𝐱𝐲(𝐱 + 𝐲) +𝟐𝐱𝐲 −𝟑𝐱𝐲 𝒙𝟒 −𝒚𝟒 𝒙 (𝐱+𝐲)𝟐 −𝟒𝐱𝐲 ;fn x = 4-5 vkSj y = 1-5 gS] rks × (𝐱+𝐲)𝟐 ÷ (𝐱+𝐲)𝟐 dk eku fdruk gksxk\ (𝐱+𝐲)𝟑 −𝟑𝐱𝐲(𝐱 + 𝐲) +𝟐𝐱𝐲 −𝟑𝐱𝐲 1.6 2.2.5 3. 3 4. 1.5 ( ICAR Technician 2023) 𝒙𝟐 +𝟑𝒙+𝟗 𝒙𝟑 −𝟐𝟕 (𝒙−𝟒)𝟐 −𝟏 130. If x = 3.5, then what is the value of ÷ × =? 𝒙𝟐 −𝟐𝟓 𝒙𝟐 +𝟑𝒙−𝟏𝟎 𝒙𝟐 −𝟒 𝒙𝟐 +𝟑𝒙+𝟗 𝒙𝟑 −𝟐𝟕 (𝒙−𝟒)𝟐 −𝟏 ;fn x = 3-5 gks] rks ÷ × dk eku fdruk gksxk\ 𝒙𝟐 −𝟐𝟓 𝒙𝟐 +𝟑𝒙−𝟏𝟎 𝒙𝟐 −𝟒 1. 2/9 2. 2/11 3. 1/4 4. 1/5 ( ICAR Technician 2023) {(𝒎𝟐 +𝒏𝟐 )(𝒎−𝒏)−(𝒎−𝒏)³} 131. The value of is: (𝒎𝟐 𝒏−𝒎𝒏²) {(𝒎𝟐 +𝒏𝟐 )(𝒎−𝒏)−(𝒎−𝒏)³} dk eku D;k gS\ (𝒎𝟐 𝒏−𝒎𝒏²) (a) m + n (b)m – n (c) 2 (d) m/n 132. If x (x – 4) = 2, then 𝒙 – 88𝒙𝟑 – 13 = ? 𝟔 (a) – 6 (b) – 4 (c) – 5 (d) – 2 133. If 2𝒂𝟐 – a – 2 = 0, then find 8𝒂𝟔 – 13𝒂𝟑 – 3 =? a)1 b)2 c)0 d)5 134. 𝟐 𝟓 𝑰𝒇 𝒙 − 𝟐𝒙 + 𝟒 = 𝟎, 𝒕𝒉𝒆𝒏 𝒙 − 𝟐𝒙 + 𝟑𝟎 =? 𝟒 a) 62 b) 63 c) 64 d)60 135. If x2+3x+9=0, then x5+3x4+260=? यदि x2+3x+9=0 है तब x5+3x4+260 का मान ज्ञात करे ? a) 17 b) 23 c) 19 d) 14 𝟏 𝟏 𝟏 136.if + = , then 𝒙𝟒𝟗 − 𝟑𝟒𝟑𝒙𝟒𝟔 + 𝒙𝟑 + 𝟏𝟕 =? 𝒙 𝟕 𝒙+𝟕 a)289 b)0 d)360 d)326 Telegram Channel : https://t.me/mathsbygaganpratap  𝟏 𝟏 𝟏 137. If 𝒑 + 𝒒 = 𝒑+𝒒, then 𝒑𝟑 − 𝒒𝟑 =? a) p – q b) pq c) 0 d) 1 138. If 𝟐𝟒√𝟑𝒙𝟑 + 𝟐√𝟐𝒚𝟑 = (𝟐√𝟑𝒙 + √𝟐𝒚) (𝑨𝒙𝟐 + 𝑩𝒙𝒚 + 𝑪𝒚𝟐 ) then (𝟐𝑨 + √𝟔𝑩 − 𝑪) is equal to: अगर 𝟐𝟒√𝟑𝒙𝟑 + 𝟐√𝟐𝒚𝟑 = (𝟐√𝟑𝒙 + √𝟐𝒚) (𝑨𝒙𝟐 + 𝑩𝒙𝒚 + 𝑪𝒚𝟐 ) है , तो (𝟐𝑨 + √𝟔𝑩 − 𝑪) बराबर है : (Mains 2018) A) 10 B) 14 C) 6 D) 8 139. If 𝟐𝟓𝟎√𝟐𝒙 − 𝟓√𝟓𝒚 = (𝟓√𝟐𝒙 − √𝟓𝒚) × (𝑨𝒙𝟐 + 𝑩𝒙𝒚 + 𝑪𝒚𝟐 ), then the value of (A+C-√𝟏𝟎𝑩) is: 𝟑 𝟑 यदि 𝟐𝟓𝟎√𝟐𝒙𝟑 − 𝟓√𝟓𝒚𝟑 = (𝟓√𝟐𝒙 − √𝟓𝒚) × (𝑨𝒙𝟐 + 𝑩𝒙𝒚 + 𝑪𝒚𝟐 ), है तो (A+C-√𝟏𝟎𝑩) का मान है : A) 10 B) 5 C C) 𝟓√𝟐 D) 𝟐√𝟓 140. If 𝟖𝒙𝟑 − 𝟐𝟕𝒚𝟑 = (𝑨𝒙 + 𝑩𝒚)(𝑪𝒙𝟐 − 𝑫𝒚𝟐 + 𝟔𝒙𝒚), then (𝑨 + 𝑩 + 𝑪 − 𝑫)is equal to: यदि 𝟖𝒙𝟑 − 𝟐𝟕𝒚𝟑 = (𝑨𝒙 + 𝑩𝒚)(𝑪𝒙𝟐 − 𝑫𝒚𝟐 + 𝟔𝒙𝒚), तो (𝑨 + 𝑩 + 𝑪 − 𝑫) बराबर है: (2018 PRE) (a) -12 (b) 12 (c) 9 (d) 15 141. If 𝟔√𝟔 p³ + 2√𝟐q³ = (√𝟔p+√𝟐q)(Sp² + Mq² – Npq), then the positive value of √𝑺² + 𝑴² + 𝟐𝑵² is: ;fn 𝟔√𝟔 p³ + 2√𝟐q³ = (√𝟔p+√𝟐q)(Sp² + Mq² – Npq) gS] rks √𝑺² + 𝑴² + 𝟐𝑵² dk /kukRed eku D;k gS\ (a) 10 (b) 8 (c) 9 (d) 12 142. If 𝒙𝟔 − 𝟓𝟏𝟐𝒚𝟔 = (𝒙𝟐 + 𝑨𝒚𝟐 )(𝒙𝟒 − 𝑩𝒙𝟐 𝒚𝟐 + 𝑪𝒚𝟒 ), then what is the value of (A+B-C)? (CPO 2019) ;fn x6 – 512y6 = (x2 + Ay2) (x4 – Bx2y2 + Cy4) gS] rks (A + B – C) dk eku Kkr dhft, (a) – 80 (b) – 72 (c) 72 (d) 48 143. If 8(x + y)³ – 27(x–y)³ = (5y–x) (Ax² + By² + Cxy), then what is the value of (A + B – C)? ;fn 8(x + y)³ – 27(x–y)³ = (5y–x) (Ax² + By² + Cxy) gS] rks (A + B – C) dk eku Kkr djsAa (a) 16 (b) –26 (c) 36 (d) –16 144. If (x + y)³ + 27(x – y)³ = (Ax – 2y)(Bx² + Cxy + 13y²), then the value of A – B – C is: ;fn (x + y)³ + 27(x – y)³ = (Ax – 2y)(Bx² + Cxy + 13y²) gS] rks A – B – C dk eku Kkr djsAa (a) 27 (b) 20 (c) 15 (d) 13 145. Given that (2x+y)3-(x+2y)3 = (x-y) [A(x2+y2) + Bxy], the value of (2A-B) is: fn;k x;k gS fd (2x+y)3-(x+2y)3 = (x-y) [A(x2+y2) + Bxy] gS] rks (2A-B) dk eku Kkr djsAa (a) 7 (b) 6 (c) 0 (d) 1 Telegram Channel : https://t.me/mathsbygaganpratap 146. If (𝒙 + 𝟐𝒚)𝟑 + (𝟐𝒙 − 𝒚)𝟑 = (𝟑𝒙 + 𝒚)[𝑨𝒙𝟐 + 𝑩𝒚𝟐 + 𝑪𝒙𝒚], then the value of (3A-B-C):(A+B+C)? यदि (𝒙 + 𝟐𝒚)𝟑 + (𝟐𝒙 − 𝒚)𝟑 = (𝟑𝒙 + 𝒚)[𝑨𝒙𝟐 + 𝑩𝒚𝟐 + 𝑪𝒙𝒚] है , तो (3A-B-C):(A+B+C) का मान क्या है ? (ICAR Technician 2022) A) 2:5 B) 1:7 C) 5:7 D) 3:4 𝑿𝒂𝟑 −𝒀𝒃𝟑 𝑿+𝒀 147. If = (𝟎. 𝟑𝟔𝒂𝟐 + 𝟎. 𝟑𝟎𝒂𝒃 + 𝟎. 𝟐𝟓𝒃𝟐 ), then find ? 𝒁𝒂−𝑻𝒃 𝒁−𝑻 𝑿𝒂𝟑 −𝒀𝒃𝟑 यदि = (𝟎. 𝟑𝟔𝒂𝟐 + 𝟎. 𝟑𝟎𝒂𝒃 + 𝟎. 𝟐𝟓𝒃𝟐 ) है , तो ज्ञात कीक्जए? 𝑿+𝒀 𝒁𝒂−𝑻𝒃 𝒁−𝑻 A) 3.40 C) 3.39 B) 3.41 D) 12 𝟏 𝟏 𝟑 148. 𝟑 [𝒂 − ] + [𝒂 − ] =? 𝒂 𝒂 𝟏 A) 𝒂 − 𝟐 𝒂𝟑 𝟏 B) 𝒂 − 𝟑 𝒂𝟑 𝟏 C) 𝒂 + 𝟑 𝒂𝟑 𝟏 D) 𝒂 − 𝟐 𝒂𝟐 149. What is the simplified form of the following expression? fuEufyf[kr O;atd dk ljyhÑr :i D;k gS\ 𝟏 𝟑 𝟏 𝟑 (𝒙 − ) + (𝒙 + ) 𝒚 𝒚 𝟑 (a) 𝒙 (𝒙² − ) 𝒚² 𝟑 (b) –2x(𝒙² + ) 𝒚² 𝟑 (c) 2x(𝒙² − ) 𝒚² 𝟑 (d) 2x(𝒙² + ) 𝒚² 150. Simplify the given expression. 3 3  2  2 fn, x, O;atd dk eku Kkr djsaA  x −  −x+   x  x  4 (a) −4  3x + 3   x   4 (b) −4  3x − 3   x  𝟒 (c) −𝟒 (𝒙 + ) 𝒙𝟑  4  (d) 2x − 3   x  (𝒙+𝟑)𝟑 +(𝒙−𝟑)𝟑 151. Simplify the given expression: ? 𝒙𝟐 +𝟐𝟕 (𝒙+𝟑)𝟑 +(𝒙−𝟑)𝟑 दिए गए ब्यंजक को सरि बनाएं: 𝒙𝟐 +𝟐𝟕 A) 3x Telegram Channel : https://t.me/mathsbygaganpratap B) x C) 4x D) 2x 152. Find the square root of (𝟑 + √𝟓)𝟑 + (𝟑 − √𝟓)𝟑 ? (𝟑 + √𝟓)𝟑 + (𝟑 − √𝟓)𝟑 का वगगमूि ज्ञात कीक्जये? A) 9 B) 12 C) 14 D) 6 153. If (3x + 2 y)3 + (3x-2y)3 =3kx (3x2+4y2), then the value of k will be: ;fn (3x + 2 y)3 + (3x-2y)3 =3kx (3x2+4y2), gS] rks k dk eku Kkr djsaA (a) 18 (b) 9 (c) 3 (d) 6 154. If (2x+3y)³ – (2x–3y)³ = 3y[Ax²+By²], then what is the value of (A–B)? ;fn (2x+3y)³ – (2x–3y)³ = 3y[Ax²+By²] gS] rks (A–B) dk eku D;k gksxk\ (a) 12 (b) 9 (c) 3 (d) 6 𝟏 155. If (4x+2y)³ + (4x–2y)³ = 16(Ax³+Bxy²), then what is the value of (√𝑨² + 𝑩²)? 𝟐 𝟏 ;fn (4x+2y)³ + (4x–2y)³ = 16(Ax³+Bxy²), rks (√𝑨² + 𝑩²) dk eku D;k gS\ 𝟐 (a) 8 (b) 3 (c) 5 (d) 7 156. If (𝟑𝒙 + 𝟐𝒚)𝟑 − (𝟐𝒙 + 𝟑𝒚)𝟑 = 𝑴(𝒙𝟑 − 𝒚𝟑 ) + 𝑵𝒙𝒚(𝒙 − 𝒚), then find (M-N)? यदि (𝟑𝒙 + 𝟐𝒚)𝟑 − (𝟐𝒙 + 𝟑𝒚)𝟑 = 𝑴(𝒙𝟑 − 𝒚𝟑 ) + 𝑵𝒙𝒚(𝒙 − 𝒚) है , तो (M-N) ज्ञात कीक्जये? A) 1 B) 7 C) 4 D) 8 𝒙𝟑 + 𝟑𝒙 𝟐𝟑𝟒 157. If = then 𝒙𝟐 +5=? 𝟑𝒙𝟐 + 𝟏 𝟏𝟎𝟗 a)31 b)41 c)38 d)46 𝟔𝟒𝒙𝟑 + 𝟏𝟎𝟖𝒙 𝟏𝟒𝟔𝟑 158. If = then (𝟖𝒙 − 𝟒𝟑)𝟐 ? 𝟏𝟒𝟒𝒙𝟐 + 𝟐𝟕 𝟕𝟑𝟒 a)64 b)81 c)100 d)121 159. If x = 2 + √𝟑, then find the value of x4 – 8x3 + 16x2. यदि x = 2 + √𝟑 है , तो x4 – 8x3 + 16x2 का मान ज्ञात कीजिए। (a) – 1 (b) 1 (c) 0 (d) 2 𝟑 160. If x = √𝟓 + 𝟐, then the value of 𝒙𝟑 − 𝟔𝒙𝟐 + 𝟏𝟐𝒙 − 𝟏𝟐 is equal to: यदि x = √𝟓 + 𝟐 है , तो 𝒙𝟑 − 𝟔𝒙𝟐 + 𝟏𝟐𝒙 − 𝟏𝟐 का मान है ? 𝟑 Telegram Channel : https://t.me/mathsbygaganpratap  (a) 0 (b) 2 (c) 1 (d) – 1 161. If √𝒙 = √𝟑 − √𝟓, then the value of 𝒙𝟐 – 16x +6 is: यदि √𝒙 = √𝟑 − √𝟓, है , तो 𝒙𝟐 – 16x +6 का मान है ? (a) 0 (b) 4 (c) 2 (d) – 2 162. If x = 2 + 22/3 + 21/3, then what is the value of x3 – 6x2 + 6x+18? (a) 30 (b) 20 (c) 10 (d) 22 𝟐 𝟏 163. If 𝟕 + 𝟕𝟑 + 𝟕𝟑 , then which of the options below is correct? 𝟐 𝟏 यदि 𝟕 + 𝟕𝟑 + 𝟕𝟑 , तो नीचे दिए गए ववकल्पों में से कौन सा ववकल्प सही है ? ( IB ACIO 2023) A) 𝒙𝟑 + 𝟐𝟏𝒙𝟐 − 𝟏𝟐𝟔𝒙 − 𝟐𝟓𝟐 = 𝟎 B) 𝒙𝟑 + 𝟐𝟏𝒙𝟐 − 𝟏𝟐𝟔𝒙 + 𝟐𝟓𝟐 = 𝟎 C) 𝒙𝟑 − 𝟐𝟏𝒙𝟐 − 𝟏𝟐𝟔𝒙 + 𝟐𝟓𝟐 = 𝟎 D) 𝒙𝟑 − 𝟐𝟏𝒙𝟐 + 𝟏𝟐𝟔𝒙 − 𝟐𝟓𝟐 = 𝟎 𝟑 𝟑 𝟑 [(𝒂−𝟏)𝟑 −𝟓] 164. If 𝒂 = √𝟐 + √𝟑 + 𝟏, 𝒕𝒉𝒆𝒏 (𝒂−𝟏)𝟑 =? (a) 165 (b) 162 (c) 163 (d) 164 165. If x + y = 1 and xy(xy – 2) = 16, then the value of 𝒙𝟒 + 𝒚𝟒 =? यदि x + y = 1 और xy(xy – 2) = 16, तो 𝒙𝟒 + 𝒚𝟒 का मान है ? (a) 23 (b) 27 (c) 39 (d) 33 166. 𝟑 𝟕 𝟐 𝒙 + 𝟒𝒙 − 𝟖 = 𝟎, 𝒕𝒉𝒆𝒏 𝒙 + 𝟔𝟒𝒙 =? a)96 b)128 c)216 d)108 𝒙𝟓 +𝟖 167. If 𝒙𝟐 + 𝒙 = 𝟏, then find ? 𝒙+𝟏 𝒙𝟓 +𝟖 यदि 𝒙𝟐 + 𝒙 = 𝟏 है , तो ज्ञात कीक्जये? 𝒙+𝟏 A) 3 C) 2 B) 5 D) 4 168. If x+1=𝒙𝟐 and x>0, then 2𝒙𝟒 is (CAT 2017) (a) 6+4√𝟓 (b) 3+5√𝟓 (c) 5+3√𝟓 (d) 7+3√𝟓 −𝟐 𝟐 𝒃 169. The term to be added to 𝟏𝟔𝟗𝒂 + 𝟏. 𝟒𝟒𝒃 + 𝟐𝟕 to make a perfect square? 𝒂 𝟏𝟔𝟗𝒂−𝟐 + 𝟏. 𝟒𝟒𝒃𝟐 + 𝟐𝟕 को पूणग वगग बनाने के लिए इसमे कौन स पि जोड़ा जाना चादहए? 𝒃 𝒂 a) 1.2ab b) 3.2b𝒂−𝟏 c) 4.5𝒂−𝟏 𝒃 d) 4.2b𝒂−𝟏 𝟏 170. For what value(s) of k will the expression p + √𝒑 + k² be a perfect square? 𝟗 𝟏 k ds fdl eku@fdu ekuksa ds fy, O;atd p + √𝒑 + k² ,d iw.kZ oxZ gksxk\ 𝟗 𝟏 (a) k=± 𝟖 𝟏 (b) k=± 𝟗 𝟏 (c) k=± 𝟐𝟏 𝟏 (d) k=± 𝟏𝟖 171. If √𝒙𝟐 + 𝟑𝒙 + 𝟑𝟖 + √𝒙𝟐 + 𝟑𝒙 − 𝟏𝟕 = 11 then, Find √𝒙𝟐 + 𝟑𝒙 + 𝟑𝟖 − √𝒙𝟐 + 𝟑𝒙 − 𝟏𝟕 =? a)4 b)5 c)6 d)7 Telegram Channel : https://t.me/mathsbygaganpratap 172. If √𝟖𝒙𝟑 + 𝟓𝟑𝒙𝟐 − 𝟕𝟏𝒙 + 𝟔𝟎 + √𝟖𝒙𝟑 + 𝟓𝟑𝒙𝟐 − 𝟕𝟏𝒙 − 𝟗𝟑 =17, then find √𝟖𝒙𝟑 + 𝟓𝟑𝒙𝟐 − 𝟕𝟏𝒙 + 𝟔𝟎 − √𝟖𝒙𝟑 + 𝟓𝟑𝒙𝟐 − 𝟕𝟏𝒙 − 𝟗𝟑 =? a) 8 b) 7 c) 10 d) 9 𝟑 If √𝒕 + 𝟒𝟎 − √𝒕 − 𝟐𝟎 = 5, then 𝟑 173. 𝟑 𝟑 𝟑 √(𝒕 + 𝟒𝟎)𝟐 + √(𝒕 − 𝟐𝟎)𝟐 + √(𝒕 + 𝟒𝟎)(𝒕 − 𝟐𝟎) =? (a) 14 (b) 12 (c) 10 (d) 18 𝟑 174. If p=999, then the value of √𝒑(𝒑𝟐 + 𝟑𝒑 + 𝟑) + 𝟏 is a) 1000 b) 999 c) 998 d) 1002 𝟑 175. If p=101, then the value of √𝒑(𝒑𝟐 − 𝟑𝒑 + 𝟑) − 𝟏 is a) 100 b) 101 c) 102 d) 1000 176. If p = 38, then the value of p(p² + 3p + 3) is_______. ;fn p = 38 gS] rks p(p² + 3p + 3) dk eku Kkr dhft,A (a) 39313 (b) 59319 (c) 39318 (d) 59318 𝒎(𝒎𝟐 +𝟑𝒎+𝟑)+𝟏 177. Find the value of when m = 87. 𝒎(𝒎+𝟐)+𝟏 𝒎(𝒎𝟐 +𝟑𝒎+𝟑)+𝟏 ;fn m = 87 gS] rks dk eku Kkr dhft,A 𝒎(𝒎+𝟐)+𝟏 (a) 88 (b) 87 (c) 90 (d) 96 178. What is the value of 64x3 + 38x2y + 20xy2 + y3, when x = 3 and y = -4? x = 3 और y = -4 होिे पर 64x3 + 38x2y + 20xy2 + y3 का माि ज्ञात कीजिए: (a) 1236 (b) 488 (c) 536 (d) 1256 SSC CGL 2023 PRE 179. What is the value of (27x3 − 58x2y + 31xy2 − 8y3), when x = −5 and y = −7? x = -5 और y = -7 होिे पर (27x3 - 58x2y + 31xy2 - 8y3) का माि ज्ञात कीजिए? 1924 (b) −1924 (c) −1926 (d) 1926 SSC CGL 2023 PRE 180. If x + y = 14, then the value of x³ + y³ + 42xy is: ;fn x + y = 14 gS] rks x³ + y³ + 42xy dk eku----------------- gSA (a) 2744 (b) 2644 (c) 2742 (d) 271 181. If x + 3y = 6, what is the value of x3 +27y2 + 54xy ? ;fn x+3y = 6] rks x3 + 27y3+54xy dk eku D;k gS\ (a) 216 (b) 258 (c) 264 (d) 220 182. If y = 2x + 1, then what is the value of (8x³ – y³ + 6xy)? ;fn y = 2x + 1 gS] rks (8x³ – y³ + 6xy) dk eku Kkr djsAa (a) –15 (b) 1 Telegram Channel : https://t.me/mathsbygaganpratap  (c) –1 (d) 15 √𝟐 183. If x = √𝟐 + 1 and y = , then what is the value of (x–2y–1) (x²+4y²+2xy–2x–2y+1)? 𝟑 √𝟐 ;fn x = √𝟐 + 1 vkSj y = gS] rks (x–2y–1) (x²+4y²+2xy–2x–2y+1) dk eku D;k gS\ 𝟑 𝟑𝟖√𝟐 (a) 𝟐𝟕 𝟒√𝟐 (b) 𝟑 𝟏𝟑√𝟐 (c) 𝟗 𝟒𝟎√𝟐 (d) 𝟐𝟕 𝒙𝟐 +𝒂𝒙+𝒂𝟐 (𝒙𝟐 −𝒂𝒙+𝒂𝟐 ) 184. if 4x + 3a = 0 then what is the value of 𝒙𝟑 −𝒂𝟑 − 𝒙𝟑 +𝒂𝟑 𝒙𝟐 +𝒂𝒙+𝒂𝟐 (𝒙𝟐 −𝒂𝒙+𝒂𝟐 ) ;fn 4x + 3a = 0 rks − dk eku D;k gksxk\ 𝒙𝟑 −𝒂𝟑 𝒙𝟑 +𝒂𝟑 𝟑𝟐 𝟕 𝟒 𝟐𝟒 (A) − (B) (C) − (D) 𝟕𝒂 𝒂 𝟕𝒂 𝟕𝒂 185. If x = -y±√𝒙𝒚 + 𝟏𝟔 = (𝟒𝟖 + 𝒚𝟑 )𝟏/𝟑 , then find the value of x – y? 𝟏 यजि x = -y±√𝒙𝒚 + 𝟏𝟔 = (𝟒𝟖 + 𝒚𝟑 )𝟑 है, तो x – y का मान ज्ञात कीजिये? A) 6 C) 3 B) 2 D) 𝟑 𝟐𝟕 𝟏 𝟐𝟕 186. If 𝒙𝟑 + = (𝒂𝟑 + 𝒃𝟑 ) and 3x + = (𝒂𝟑 − 𝒃𝟑 ), then find 6(𝒂𝟐 − 𝒃𝟐 )=? 𝒙 𝟐 𝒙𝟑 𝟐 𝟖 𝟗 (a) 4 (b) 1 (c) (d) 𝟑 𝟒 𝟑 𝟑 187. If 𝒑 = √𝒂 + √𝒂𝟐 + 𝒃𝟑 + √𝒂 − √𝒂𝟐 + 𝒃𝟑 , then what is 𝒑𝟑 + 𝟑𝒃𝒑 equal to? यदि 𝒑 = √𝒂 + √𝒂𝟐 + 𝒃𝟑 + √𝒂 − √𝒂𝟐 + 𝒃𝟑 , तो 𝒑𝟑 + 𝟑𝒃𝒑 ककसके बराबर है ? (CDS-1 2024) 𝟑 𝟑 A) -2a B) a C) 2a D) 3a 188. If 𝒙𝟐 = 𝟏𝟕𝒙 + 𝒚, 𝒚𝟐 = 𝒙 + 𝟏𝟕𝒚 𝒂𝒏𝒅 𝒙 ≠ 𝒚, then find √𝒙𝟐 + 𝒚𝟐 + 𝟏? यजि 𝒙𝟐 = 𝟏𝟕𝒙 + 𝒚, 𝒚𝟐 = 𝒙 + 𝟏𝟕𝒚 और 𝒙 ≠ 𝒚, तो √𝒙𝟐 + 𝒚𝟐 + 𝟏 ज्ञात कीजिये ? A)15 B)16 C)17 D)18 189. If 𝒂 + 𝒃 = 𝟏 𝒂𝒏𝒅 𝒂𝟐 + 𝒃𝟐 = 𝟐 𝒂𝒏𝒅 𝒕𝒉𝒆𝒏 𝒇𝒊𝒏𝒅 𝒂𝟓 + 𝒃𝟓 = ? यजि 𝒂 + 𝒃 = 𝟏 और 𝒂𝟐 + 𝒃𝟐 = 𝟐 तो 𝒂𝟓 + 𝒃𝟓 ज्ञात कीजिए? 𝟏𝟕 𝟏𝟗 𝟑𝟕 𝟕 (a) (b) (c) (d) 𝟒 𝟒 𝟖 𝟐 190. If 𝒙 + 𝒚 = 𝟏𝟗 & 𝒙𝒚 = 𝟗, then find 𝒙√𝒙 + 𝒚√𝒚? यदि 𝒙 + 𝒚 = 𝟏𝟗 & 𝒙𝒚 = 𝟗 है , तो 𝒙√𝒙 + 𝒚√𝒚 ज्ञात कीजिये? A) 80 B) 100 C) 125 D) 110 Telegram Channel : https://t.me/mathsbygaganpratap 191. Let a and b be two positive real numbers such that a √𝒂+b√𝒃=32 and a√𝒃+b√𝒂=31. What is the 𝟓(𝒂+𝒃) value of ? 𝟕 (CDS 2019) a और b िो र्नात्मक वास्तववक संख्याएँ हैं, जैसे कक a√𝒂+b√𝒃=32 और a√𝒃+b√𝒂=31| का मान क्या है 𝟓(𝒂+𝒃) 𝟕 (a) 5 (b) 7 (c) 9 (d) Cannot be determined 192. If x = √𝟏𝟎 + √𝟏𝟏 , y = √𝟏𝟎 − √𝟏𝟏, then value of 7x² – 50xy + 7y² = _______. ;fn x = √𝟏𝟎 + √𝟏𝟏 , y = √𝟏𝟎 − √𝟏𝟏, rks 7x² – 50xy + 7y² dk eku Kkr dhft,A (a) 386 (b) 344 (c) 704 (d) 1360 193. What is the value of the following expression? fuEufyf[kr O;atd dk eku D;k gksxk\ (𝒃+𝒄) 𝒙𝒂 (𝒂+𝒃) 𝒙𝒃 𝒙𝒄 (𝒂+𝒄) 2²( 𝒃 ) × 3²( 𝒄 ) × 6–2( 𝒂 ) 𝒙 𝒙 𝒙 (a) 1 (b) 0 (c) 4 (d) 9 Telegram Channel : https://t.me/mathsbygaganpratap