Pratibha Pages

17 Model Questions 1. Who replaced Thaawarchand Which Asian city to held Gehlot as Leader of House in Rajya Sabha? 1) S. Jai Shankar 2) Mansukh Mandaviya 3) Piyush Goel 4) Nirmala Sitharaman Summer Olympics twice? 5) Dharmendra Pradhan ñªëÅ]î¦ô¢Ù VöËµj 28, 2021 n e-mail:[email protected] 2. First High Court in India conducted live stream Judicial Proceedings to National International Nepal New PM create transparency in Judiciary is… 1) Gujrat 2) Telangana On 13 July 2021, Sher Bahadur ‘KALA VISHWA’ General Ramappa temple as World 3) Andhra Pradesh 4) Allahabad Heritage Site Deuba was sworn in as Nepal’s Prime On July 18, 2021 Indian Council for Minister for the fifth time. 5) Jharkhand Cultural Relations (ICCR) launched a Awareness On 25 July 2021, UNESCO (United President Bidya Devi Bhandari 3. World Malala Day observed on…… new campaign called ‘KALA VISHWA’, Nations Educational, Scientific and administered the oath of office, a day 1)1 July 2) 21 July 3) 12 July from its Mumbai centre. Rudraksh Cultural Organization) inscribed the after the country’s Supreme Court 4) 8 July 5) 30 June On this occasion, Dr. Vinay 13th-century Ramappa temple in overturned the dissolution of the 4. An Indian photojournalist was killed Sahasrabuddhe, President, ICCR said On 15 July 2021 Prime Minister Palampet, Telangana as a ‘World House of Representatives and said in Afghanistan’s Kandahar province that the campaign will help to present Narendra Modi inaugurated the Heritage Site’. that Deuba must be appointed PM. while covering the region’s escalat- traditional folk arts of India to foreign The Temple showcases the out- ing conflict for Reuters. He/ she “International Cooperation and BRICS Labour & Employment students and also be of help to the Convention centre - Rudraksh” in his standing craftsmanship of the great Ramappa temple is…. (the journalist was killed while neglected artists. parliamentary constituency Varanasi. Kakatiya dynasty. Ministers’ Meeting covering a clash between Afghan security forces and Taliban fighters) It is a special campaign under the It can accommodate 1,200 people Ramappa temple was named after New Shepard, built by Bezos' com- On 15 July 2021, the union minister Horizon Series that will be held for a constructed with the aid of the its chief sculptor Ramappa. It is one of pany Blue Origin, is designed to serve for Labour and Employment 1) Danish Siddiqui duration of six months held virtually. Japanese International Cooperation the very few temples in the world the burgeoning market for space Bhupender Yadav chaired the BRICS 2) Amrita Chaudhry Agency (JICA). named after its sculptor. tourism. Labour & Employment Ministers 3) Rohit Sardana ARMEX-21 The state-of-the-art convention cen- Aside from its architecture and elab- He was accompanied by Mark Meeting under India’s Presidency. 4) Praful Bidwai 5) Shujaat Bukhari orate carvings on the temple's walls, On 23 July 2021, Union Defence tre is being positioned as the perfect Bezos, his brother, Wally Funk, an The discussion was held on four 5. Who won the silver medal in the pillars and ceilings, the most notable Minister Rajnath Singh was flagged in venue for exhibitions, international con- 82-year-old pioneer of the space priority areas of cooperation took women's 49kg category in feature of this temple is that it was con- the Indian Army Skiing Expedition, ventions and even concerts. race. Wally Funk became the oldest- place namely, Promoting Social Weightlifting in Tokyo Olympics? structed using bricks that are so light ARMEX-21, in New Delhi. It also meets all environmental stan- ever person to fly in space. An 18- Security Agreements amongst BRICS 1) Vandna Gupta that they can float on water. The ARMEX-21 was conducted in dards and qualifies for Level 3 status year-old student Dutch teenager Nations; Formalisation of Labour 2) Laishram Monika Devi the mountain ranges of the Himalayan under the Centre’s Green Rating for Jeff Bezos Space visit Oliver Daemen became the world's Markets; Participation of Women in 3) Mirabai Chanu youngest space traveller accompa- the Labour Force; and Gig and region to promote the adventure activi- Integrated Habitat Assessment 4) Shailaja Pujari On 20 July 2021, Amazon founder Jeff nied them. Platform Workers: Role in the Labour ty in the country and the Indian Army. (GRIHA). 5) Neelam Setti Laxmi Bezos made a short journey to space, Market. The significant aspect of the The expedition was flagged off at The craft travelled at nearly three in the first crewed flight of his rocket meeting was the adoption of the 6. India will host the World Badminton Karakoram Pass in Ladakh on 10th No cases under Section 66A times the speed of sound, reaching a ship, New Shepard from a private ‘BRICS Labour & Employment Championships in ……… March and culminated at Malari in height of nearly 100 km (62 miles) On 14 July 2021, the Ministry of Home launch site near Van Horn, Texas. Ministers’ Declaration. 1) 2023 2) 2022 3) 2028 Uttarakhand on the 6th of July. above the Earth's surface. Affairs requested all states and Union 4) 2026 5) 2030 Historic Urban Landscape Project Territories to direct all police stations 7. Who is the Chief Hydrographer to under their jurisdiction not to register Others returning to the Olympics this year After the nations’ parade, Naomi the Govt. of India received the Gwalior and Orchha cities of Madhya cases under the repealed Section 66A after being cut out previously and they Osaka, the Japanese Tennis player Alexander Dalrymple award? Pradesh have been selected by Tokyo Olympics of the Information Technology Act, include Baseball and Softball. brought the ceremony close by lighting 1) Ashok Kumar 2) Ravneet Singh UNESCO under the ‘Historic Urban 2000 related to posting online Japan Emperor Naruhito officially The mascot for Summer Olympic up the Olympic Cauldron. 3) Vinay Badhwar Landscape Project’ for the inclusive comments. inaugurated the 2020 Summer 2021 is ‘MIRAITOWA’ (derived from 4) Karambir Singh and well-planned development of fast- Olympic motto amended The Supreme Court in its judgment Olympics that began on 23 July 2021 the Japanese words 'Mirai' which 5) Ram Dass Katari growing historical cities while preserv- on 24 March 2015 in the matter of in Tokyo, Japan. The event will con- means 'future' and 'towa' means 8. Who was conferred with the presti- ing the culture and heritage. On 20 July 2021, the International Shreya Singhal Vs. Union of India had clude on August 8, 2021. 'eternity'). Olympic Committee's session added a gious Olympic Laurel Award for his On 21 July 2021, MP Chief Minister struck down Section 66A of the The theme of the opening ceremony The blue and white futuristic charac- new word to the Olympic motto special contribution to sports? Shivraj Singh Chouhan virtually Information Technology Act, 2000. is “United by Emotion” and the newly ter represents the wish that the Tokyo “Communis” which means ‘Together’. 1) Thomas Bach launched this project through video The section of the law provides built Japan National Stadium hosted 2020 Olympic Games will lead to a conferencing and said that the cities The motto now reads 'Citius, Altius, 2) Jacques Rogge police power to arrest a person for the opening ceremony. future of everlasting hope in the hearts Fortius - Communis' in Latin. will be jointly developed by the 3) Muhammad Yunus posting "offensive" content online and Tokyo is the first city in Asia to hold of the people around the world. UNESCO, Government of India and In English, it reads "faster, higher, 4) Toshiro Muto 5) Claudia Bach provides for a three-year jail term. the Summer Olympic Games twice. A total of 19 Indian athletes, includ- Madhya Pradesh by focusing on their stronger - together". The Games will feature 339 events ing flag-bearers Mary Kom and Key historical and cultural improvement. Recently the Supreme Court issued The proposal to include the new a notice to the Centre on the use of in 33 different sports, encompassing a Manpreet Singh, participated in the 1-3 3-3 5-3 7-3 Six cities of South Asia, including word ‘Together’ was made by Section 66A of the IT Act. total of 46 disciplines. nation’s parade. 2-1 4-1 6-4 8-3 Ajmer and Varanasi in India are already International Olympic President karate, sport climbing, surfing and India sent a 228-strong delegation involved in this project. Orchha and SC said that it was shocking that the Thomas Bach, which was endorsed skateboarding are new sports events in Tokyo, including 119 athletes to par- For more Information see Gwalior have been included as the 7th judgment striking down the law has not by the body's Executive Board in included. Two other sports will be ticipate in 18 sports. and 8th cities. been implemented even now. April 2021. today’s Telangana Edition F F F F F F F F F F F F F F F F F F F F

÷ô¢_ ú£Oª-ÚÛ-ô¢-é°õª (Quadratic equations) l f(x) ÷ô¢_ú£÷«ú£Ù Íô³ê¶ f(x) = 0E ÷ô¢_- ú£-Oª- ÚÛ-ô¢éÙ ÍÙæ°ô¢ª. l ÷ô¢_ú£Oª-ÚÛ-ô¢é þ§ëÅ¯-ô¢é ô¢«í£Ù 2 ôÁï‡°êÂÚÛª Þœé¨-êŸÙöËº ÷#aì ÷«ô¢ª\õª ÓEo? ax + bx + c = 0, a ≠ 0 l f(x) ÷ô¢_ú£÷«ú£ øŒŠû¦uöË¶ f(x) = 0 ÷ô¢_- ú£-Oª-ÚÛ-ô¢é ÷´ö°õª Í÷±-ê¦ô³.- ⇒ x = 36 öË¶ë¯ x = − 30 ⇒ x2 − 5x + 2 = 0 7.- 5x2 − px + 12 = 0 ÷ô¢_ ú£Oª-ÚÛ-ô¢é NàŸ¤Ûé¨ 16 l ax2 + bx + c = 0 ÷ô¢_- ú£-Oª-ÚÛ-ô¢é ÷´ö°õª ∴ (x) = 36 ú£-÷«-ëÅ¯ìÙ:- 1 p  ·ôjõª -î¶ÞœÙ - Ú¨.-Oª.-/-ÞœÙ.- Íô³ê¶ Nõª÷ ÓÙêŸ? − b ± √ b2 − 4ac ú£-÷«-ëÅ¯ìÙ:- 3 5. ax2 + bx + c = 0 α, β 1) 32 2) 27 3) 18 4) 16 =  - ÷ô¢_-ú£-Oª-ÚÛ-ô¢é ÷´ö°õª 2a 2. ÖÚÛ êŸô¢-Þœ-AöËº 60÷ªÙC Në¯u-ô¢ª–õª Ñû¦oô¢ª.- î¦JöËº 1 1 þ§ëÅ]ì:- 5x2 − px + 12 = 0ìª Íô³ê¶ ,  ÷´ö°-õªÞ¥ Ñìo ÷ô¢_ ú£OªÚÛô¢éÙ... l ax2 + bx + c = 0 ÷-ô¢_- ú£-Oª-ÚÛ-ô¢é ÷´ö°õª ví£B -ò°-õªè[ª ò°L-ÚÛõ ú£ÙÜuÚÛª ú£÷«-ì-îµªiì ô¢«ð§- α β ax2 + bx + c = 0êÁ ð¼L›úh, b óŸª-õìª, ví£B ò°LÚÛ ò°õªô¢ ú£ÙÜuÚÛª ú£÷«-ì-îµªiì 1) ax2 − bx + c = 0 2) cx2 − bx − a = 0 a = 5, b = − p, c = 12 α β α + β = −  , Íô³ê¶ 1750 2 a þ»÷³tìª ›úÚÛ-JÙ# îµ³êŸhÙ ô¢«.- ìª ÷³Üu- 3) cx2 + bx − a = 0 4) cx2 + bx + a = 0 5x − px + 12 = 0 NàŸ¤Ûé¨ =- 16 c ÷ªÙvA ú£ï£„-óŸª-E-CÅÚ¨ Nô¦-üŒÙÞ¥ ÍÙCÙ-à¦ô¢ª.- Íô³ê¶ b2 − 4ac = 16 αβ =  þ§-ëÅ]ì:- ax2 + bx + c = 0 ÷ô¢_ ú£Oª-ÚÛ-ô¢é ÷´ö°õª a Î êŸô¢-Þœ-A-öËºE ò°õªô¢ ú£ÙÜu? (−p)2 − 4(5)(12) = 16 = α, β l α, β 1) 45 2) 40 3) 38 4) 35 - ÷´-ö°-õªÞ¥ Ñìo ÷ô¢_- ú£-Oª-ÚÛ-ô¢éÙ − b c p2 − 240 = 16 x2 − (α + β)x + αβ = 0 þ§ëÅ]ì: = 60 ⇒ α + β = , αβ =  - êŸô¢-Þœ-A-öËºE Në¯u-ô¢ª–õ ú£ÙÜu - a a p2 = 16 + 240 = 256 l ax2 + bx + c = 0, (a, b, c ∈ R) ÷-ô¢_- = x  êŸô¢-Þœ-A-öËºE ò°õªô¢ ú£ÙÜu Íìª-ÚÁÙè-…. 1 1 p = √256 = ± 16 (D) = b2 − 4ac ,  ÷´ö°-õªÞ¥ Ñìo ÷ô¢_- ú£-Oª-ÚÛ-ô¢éÙ ú£-Oª-ÚÛ-ô¢é NàŸ¤Ûé¨ ò°L-ÚÛõ ú£ÙÜu =- (60 − x) α β ú£-÷«-ëÅ¯ìÙ:- 4 2 ∴ p = 16 i)- b − 4ac = 0 Í-ô³ê¶, ÷´ö°õª ú£÷«ì x ÷ªÙC ò°õªô¢ª ›úÚÛ-JÙ-#ì þ»÷³t 1 1 1 1 =- x2 −  +  x +  ×  = 0 î¦ú£h÷ ú£ÙÜuõª.- =- ô¢«.x (60 − x) (α β ) α β ii) b2 − 4ac > 0, b2 − 4ac ð¼MúÃ, ÏêŸô¢ ð¼æ© í£K¤Ûõ - ÚÛ-#aêŸ ÷ô¢_-îµªiê¶ (60 − x) ÷ªÙC ò°L-ÚÛõª ›úÚÛ-JÙ-#ì þ»÷³t α + β 1 ô¢àŸô³êŸ ÷´ö°õª NGÅìo ÍÚÛ-ô¢-é©óŸª ú£ÙÜuõª.- ⇒ x2 −  x +  = 0 =- ô¢«.(60 − x)x ( αβ ) αβ úˆšï°àÂ. ô¦ëÅ¯ÚÛ”ù£g iii) b2 − 4ac > 0, b2 − 4ac ví£ê¶uÚÛÙ - ÚÛ-#aêŸ ÷ô¢_-ú£ÙÜu ›úÚÛ-JÙ-#ì îµ³êŸhÙ þ»÷³t =- ô¢«.-1750 ⇒ αβx2 − (α + β)x + 1 = 0 Ú¥ÚÛð¼ê¶, ÷´ö°õª NGÅìo ÚÛô¢-é©óŸª ú£ÙÜuõª.- Nù£óŸª Eí£±éªõª x(60 − x) + (60 − x)x = 1750 ÷«uëÇ]îµªæ¨ÚÂq c − b iv)- b2 − 4ac < 0 Í-ô³ê¶ ÷´ö°õª ÚÛLpêŸ ⇒  x2 −  x + 1 = 0 60x − x2 + 60x − x2 = 1750 a a (Imaginary) ( ) ÍòÅ°uú£ ví£øŒoõª ú£ÙÜuõª 2 ⇒ 120x − 2x = 1750 48 Ú¨.-Oª.- ë]«ô¦Eo ví£î¦-ï£°C-øŒöËº ví£óŸ«-é¨Ù-àŸ-è¯-EÚ¨ cx2 bx 2 1. ax2 + bx + c = 0 2 48 ⇒  +  + 1 = 0 ⇒ cx + bx + a = 0 - ÷ô¢_ ú£Oª-ÚÛ-ô¢é ÷´ö°õ ⇒ 60x − x = 875 a a ÷«-CJ ví£øŒoõª í£è[-÷ÚÛª í£æ¨dì ú£÷ªóŸªÙ (t1) =  îµ³êŸhÙ î¦æ¨ ÷ô¦_õ îµ³ê¦h-EÚ¨ ú£÷«-ì-îµªiê¶ Ú¨ÙC- ⇒ x2 − 60x + 875 = 0 18 + x ú£-÷«-ëÅ¯ìÙ:- 4 î¦-æ¨öËº ÔC EáÙ? 2 48 1. ÖÚÛ -·ôjõª 360 Ú¨.-Oª.- ë]«ô¦Eo ú£÷ª-î¶-ÞœÙêÁ ví£óŸ«- ⇒ x − 35x − 25x + 875 = 0 Ú¨.-Oª.- ë]«ô¦Eo ví£î¦-ï£„-EÚ¨ ÍGÅ-÷³-ÜÙÞ¥ 6.- 2x2 + 3x − 5 = 0 ÷ô¢_- ú£-Oª-ÚÛ-ô¢é ÷´ö°õª α, β; 1) b2 + ab = 2ac 2) a2 + bc = 2ab é¨-ú£ªhÙC.- ·ôjõª -î¶-Þ¥Eo 6 Ú¨.-Oª/-ÞœÙ.- êŸT_›úh, Î ⇒ x(x − 35) − 25 (x − 35) = 0 ví£óŸ«-é¨Ù-àŸ-è¯-EÚ¨ í£è[-÷ÚÛª í£æ¨dì ú£÷ªóŸªÙ 2x2 + 7x + k = 0 ÷ô¢_- ú£-Oª-ÚÛ-ô¢é ÷´ö°õª 3) c2 + ab = 2bc 4) b2 + ab = ac 2 ⇒ (x − 35) − (x − 25) = 0 48 α − 1, β − 1 Íô³ê¶ k Nõª÷ ÓÙêŸ? 2. x2 − 5x + 10 = 0 α, β ë]«ô¦Eo ví£óŸ«-é¨Ù-àŸ-è¯-EÚ¨ Íë]-ìÙÞ¥ ÷ªôÁ (t2) =  - ÷´ö°õª Íô³ê¶ ÞœÙåõ ú£÷ªóŸªÙ í£è[ª-êŸªÙC.- Íô³ê¶ Î ·ôjõª î¶ÞœÙ- ⇒ x − 35 = 0 öË¶ë¯ x − 25 = 0 18 − x 1) 0 2) 1 3) 2 4) 3 1 1 t + 2 = t 2  `-  Nõª÷? ÓÙêŸ? sÚ¨.-Oª/-ÞœÙ.õöËºz ⇒ x = 35 öË¶ë¯ x = 25 ë]-ê¦hÙøŒÙ ví£Ú¥ô¢Ù, 1 2 þ§-ëÅ]ì: 2x + 3x − 5 = 0 ÷-ô¢_- ú£-Oª-ÚÛ-ô¢é ÷´ö°õª α β 48 48 1) 30 2) 32 3) 36 4) 40 = 35 25 = α, β 1 1 1 êŸ-ô¢-Þœ-A-öËºE ò°õªô¢ ú£ÙÜu - öË¶ë¯ ⇒  + 2 =  1) −  2) 2 3)  4)  þ§-ëÅ]ì:- ·ôjõª -î¶ÞœÙ =- x Ú¨.-Oª.-/-ÞœÙ.- Íìª-ÚÁÙè….- ú£-÷«-ëÅ¯ìÙ:- 4 18 + x 18 − x b 3 2 2 5 α + β = −  = −  = 360 48 + 36 + 2x 48 2 ·ôjõª ví£óŸ«-é¨Ùà¶ îµ³êŸhÙ ë]«ô¢Ù - Ú¨.-Oª.- 3. EøŒaõ Fæ¨öËº îµ«æ°ôÂ í£è[÷ î¶ÞœÙ 18 Ú¨.-Oª/-ÞœÙ.- ⇒  =  a 2 3. x − px + q = 0 ÷´ö°õª α, β Íô³ê¶ ·ôjõª 360 Ú¨.-Oª.- ë]«ô¢Ù ví£óŸ«-é¨ÙàŸè¯EÚ¨ 18 + x 18 − x c 5 α3β2 + α2β2 = Î í£è[÷ ìD-ví£-î¦-ï£„-EÚ¨ ÍGÅ-÷³-ÜÙÞ¥ 48 Ú¨.-Oª.- αβ =  = −  .-....-.- 360 84 + 2x 48 a 2 1) p2q 2) pq2 3) p2q2 4) pq í£çË¶d- Ú¥õÙ =- - ÞœÙ.- ë]«ô¢Ù ví£óŸ«-é¨Ù-àŸ-è¯-EÚ¨ í£çË¶d ú£÷ªóŸªÙ, ÍÙê¶ ⇒  =    x ë]«ô¦Eo ìDví£î¦-ï£„-EÚ¨ î¦õªÞ¥ ví£óŸ«-é¨Ù-àŸ-è¯-EÚ¨ 18 + x 18 − x 2x2 + 7x + k = 0 ÷ô¢_- ú£-Oª-ÚÛ-ô¢é ÷´ö°õª 4. 2 + √ 7, 2 − √ 7 ÷´ö°õª Ñìo ÷ô¢_- ú£-Oª-ÚÛ-ô¢éÙ? ·ôjõª -î¶-Þ¥Eo 6 Ú¨.-Oª/-ÞœÙ. êŸT_›úh, Î ë]«ô¦Eo í£çË¶d Ú¥õÙ ÚÛÙçË¶ 2 ÞœÙåõª ÓÚÛª\÷.- Íô³ê¶ ìD ⇒ (18 − x) (42 + x) = 24(18 + x) =- α − 1, β − 1 1) x2 + 4x + 3 = 0 2) x2 − 4x − 3 = 0 2 360 ví£î¦ï£° î¶Þœ-Ù ÓÙêŸ? sÚ¨.-Oª.-/-ÞœÙ.-õöËºz ⇒ 756 + 18x − 42x − x = 432 + 24x c k 3) x2 + 4x − 3 = 0 4) x2 − 4x + 3 = 0 ví£óŸ«-é¨Ù-àŸ-è¯-EÚ¨ í£çË¶d- Ú¥õÙ =-  ÞœÙ.- 2 (α − 1) (β − 1) =  =  x − 6 1) 4 2) 6 3) 8 4) 10 ⇒ x + 48x − 324 = 0 a 2 5. ÖÚÛ í£K¤ÛöËº ôÁï‡°-êÂÚÛª Þœé¨êŸÙ, ÎÙÞœxÙöËº ÷#aì 2 ë]ê¦hÙøŒÙ ví£Ú¥ô¢Ù, ⇒ x + 54x − 6x − 324 = 0 k 30. 2 þ§ëÅ]ì:- ⇒ αβ − α − β + 1 =  ÷«ô¢ª\õ îµ³êŸhÙ - ÍêŸ-è…Ú¨ Þœé¨-êŸÙöËº 360 360 ⇒ (x + 54) (x − 6) = 0 2 ÷«ô¢ª\õª šíJT, ÎÙÞœxÙöËº 3 ÷«ô¢ª\õª êŸT_ê¶  =  + 2 → t x − 6 x í£è[÷ 1 ⇒ x = −54 6 k 190 →→→→ söË¶ë¯z ⇒ αβ − (α + β) + 1 =  î¦æ¨ õñÌÄÙ ÷«ô¢ª\õª.- Íô³ê¶ ôÁï‡°êÂÚÛª 360 360 + 2x A ← 48 → B ∴ ìD ví£î¦-ï£°-î¶ÞœÙ (x) = 6 Ú¨.-Oª.-/-ÞœÙ.- 2 Þœé¨-êŸÙöËº ÷#aì ÷«ô¢ª\õª ÓEo? ⇒  =  Ú¨.-Oª. x − 6 x ← ú£-÷«-ëÅ¯ìÙ:- 2 5 3 k 1) 15 2) 16 3) 18 4) 17 t2 ⇒ −  − −  + 1 =  ⇒ 360x = (x − 6) (360 + 2x) 4. ÖÚÛ ÷ô¢_- ú£-Oª-ÚÛ-ô¢é ÷´ö°õ îµ³êŸhÙ 5, î¦æ¨ õñÌÄÙ 2 ( 2 ) 2 6.- 3 Ú¨.-Oª.-/-ÞœÙ.- î¶ÞœÙêÁ ví£÷-ï‡°-ú£ªhìo ìCöËº ÖÚÛ A, B = 48 ⇒ 360x = 360x + 2x2 − 2160 − 12x þ§–û¦õ ÷ªëÅ]u- ë]«ô¢Ù - Ú¨.-Oª.- 2 Íô³ê¶ Î ÷ô¢_ ú£Oª-ÚÛ-ô¢éÙ? 5 3 k í£è[÷ 24 Ú¨.-Oª.- ë]«ô¦Eo ví£î¦-ï£„-EÚ¨ î¦õªÞ¥, = 18 ⇒ −  +  + 1 =  ⇒ 2x2 − 12x − 2160 = 0 EøŒaõ Fæ¨öËº í£è[÷ î¶ÞœÙ - Ú¨.-Oª/-ÞœÙ.- 1) x2 − 5x + 2 = 0 2) x2 − 5x − 2 = 0 2 2 2 ÍGÅ-÷³-ÜÙÞ¥ ví£óŸ«-é¨Ù-àŸ-è¯-EÚ¨ 6 ÞœÙåõ = x ⇒ x2 − 6x − 1080 = 0 ìD ví£î¦ï£° î¶ÞœÙ - Íìª-ÚÁÙè….- 3) x2 + 5x + 2 = 0 4) x2 + 7x + 5 = 0 − 5 + 3 + 2 k ú£÷ªóŸªÙ í£æ¨dÙC.- Íô³ê¶ EøŒaõ Fæ¨öËº í£è[÷ ⇒  =  ⇒ x2 − 36x + 30x − 1080 = 0 ví£î¦-ï£„-EÚ¨ î¦õªÞ¥ í£è[÷ ví£óŸ«-é¨Ù-à¶-å-í£±pè[ª ë¯E þ§-ëÅ]ì:- ÷´ö°õª =- α, β Íìª-ÚÁÙè…. 2 2 î¶ÞœÙ ÓÙêŸ? sÚ¨.-Oª.-/-ÞœÙ.õöËºz 1) 7 2) 8 3) 9 4) 10 ⇒ x(x − 36) + 30 (x − 36) = 0 î¶ÞœÙ = 18 + x Ú¨.-Oª.-/-ÞœÙ.- α + β = 5, αβ = 2 k ⇒  = 0 ⇒ k = 0 ⇒ (x − 36) (x + 30) = 0 ví£î¦-ï£„-EÚ¨ ÍGÅ-÷³-ÜÙÞ¥ í£è[÷ ví£óŸ«-é¨Ù-à¶-å-í£±pè[ª α, β ÷´ö°-õªÞ¥ Ñìo ÷ô¢_ ú£Oª-ÚÛ-ô¢éÙ 2 ú£÷«ëÅ¯û¦õª = (18 − x) 2 ú£-÷«-ëÅ¯ìÙ:- 1 ⇒ x − 36 = 0 öË¶ë¯ x + 30 = 0 ë¯E î¶ÞœÙ - Ú¨.-Oª/-ÞœÙ.- =- x − (α + β)x + αβ = 0 1-1 2-3 3-2 4-2 5-4 6-3

GH with India’s policy of Neighbourhood 17 First’ and vision of Security and Growth Who is the president of for all in the Region (SAGAR). World Universities Summit Vice President of India M. Venkaiah Naidu addressed the inaugural session of the World Universities Summit organised by O.P. Jindal University International Criminal Court? Sonipat, Haryana, virtually between ñªëÅ]î¦ô¢Ù VöËµj 28, 2021 n e-mail:[email protected] 21-23 July 2021. He asked the universities to become thought leaders in finding solutions to National International global challenges including climate change, poverty and pollution. Educational documents using General Awareness World's fastest train The theme of the summit was The institute would focus on the con- others. Upon successful completion of blockchain technology China unveiled the world's fastest train "Universities of the Future: Building servation and research in India’s rich tan- the training, these trained teachers that runs at 600 km per hour. On 20 Maharashtra decided to issue educa- Institutional Resilience, Social gible heritage while offering research, shall be designated as ‘Innovation July 2021, the state media said that the Piotr tional documents using blockchain tech- Responsibility and Community Impact". development and dissemination of knowl- Ambassadors’. The trained teachers maglev train would only take 2.5 hours Hofmanski nology. On the eve of World Youth Skills edge, excellence in the education of its will become mentors and guide these to travel from Beijing to Shanghai by 11th Mekong-Ganga Cooperation day on 15 July 2021, the state declared students and activities associated with young students to pursue innovation train - a journey of more than 1,000 km. Meeting that one million diploma certificates will the heritage that contributes to the cultur- and entrepreneurship in line with the Using electromagnetic force, the be issued using this technology. al, scientific and economic life of India. National Education Policy (NEP). On 21 July 2021, the 11th Mekong- maglev train "levitates" above the track The technology suppresses the Ganga Cooperation Meeting was host- School Innovation Ambassador with no contact between body and rail. forgery of documents and the work of New Generation Akash Missile ed by Cambodia. Union External Training Program Affairs Minister S Jaishankar participat- verification. Singapore, Malta and On 21st July 2021, DRDO successfully Quad group to help Afghanistan expand trade, build transit links and ed in this eve via video conference. Bahrain are the only countries using this On 16 July 2021, Union Education tested the New Generation Akash The USA, Afghanistan, Pakistan and strengthen business-to-business ties. technology. Maharashtra will be the first Minister Dharmendra Pradhan and Missile (Akash-NG) a Surface to Air The Mekong Ganga Cooperation Uzbekistan will set up a new quadrilat- Indian state and the world’s largest user Tribal Affairs Minister Arjun Munda Missile from Integrated Test Range (MGC) stands on a strong foundation eral diplomatic platform that promotes ‘TTX-2021’ of Blockchain for educational certificates. launched the "School Innovation (ITR) off the coast of Odisha. of shared geographical, historical and long-term peace, trade and stability in civilizational ties between six countries Ambassador Training Program" for During the test, the missile demon- The defence officials of India, Sri Lanka 'Indian Institute of Heritage' Afghanistan focused on enhancing of India, Cambodia, Thailand, 50,000 school teachers. The teachers strated the high manoeuvrability and the Maldives held the Trilateral regional connectivity. Myanmar, Laos and Vietnam. On 19 July 2021, Union Minister for will be selected from CBSE and required for neutralising fast and agile Tabletop Exercise ‘TTX-2021’ in a virtual On 16 July 2021, the Joe Biden Culture G. Kishan Reddy in a written Eklavya Model Residential Schools. aerial threats. The missile system was manner between 14 and 15 July 2021. It aims to facilitate closer contacts administration declared that the four reply in the Lok Sabha said that the The program aims at training school developed by the Defence Research The interaction between the three among people inhabiting these two nations recognized the historic opportu- government of India decided to set up teachers in innovation, entrepreneur- Development Laboratory (DRDL), neighbouring countries in the Indian (Ganga and Mekong) major civilisa- nity to open flourishing interregional the ‘Indian Institute of Heritage’ at ship, IPR, design thinking, product Hyderabad in collaboration with other Ocean Region (IOR) has grown signifi- tional river basins and enhancing coop- trade routes and intend to cooperate to Noida, Gautam Buddha Nagar. development, idea generation, among DRDO laboratories. cantly in recent years, in consonance eration in a cult.

Others popularly known as 67 Minutes Snehakunja Trust has protected Model Questions 1) India 2) USA 3) Russia 4) Audrey Azoulay Mandela day. Nelson Mandela was sensitive wetland and coastal ecosys- 1. The MH-60R helicopters, the all- 4) China 5) Iran 5) Tedros Adhanom Ghebreyesus Cannes Film Festival 2021 the South African President who tems in the Western Ghats and the weather maritime helicopter 6. World Day for International Justice 10. Sparkassen chess trophy won fought for 67 years for social justice Karnataka coast for 45 years with a On 17 July 2021, Cannes Film Festival designed to support multiple mis- observed on… by… and democracy. focus on community-based restoration 2021 was ended in the South of sions imported from…. 1) 7 July 2) 12 July 3)17 July 1) Vladimir Kramnik and conservation. The virtual award France. The top award Palme d'Or con- UNDP Equator Prize 2021 1) UK 2) France 3) Japan 4) 25 July 5) 1 July 2) Garry Kasparov ferred on Julia Ducournau for "Titane" ceremony is scheduled for 4 October 4) Germany 5) USA 7. 52nd International Film Festival of 3) Magnus Carlsen (France). Best director award declared Aadhimalai Pazhangudiyinar Producer 2021 and the winners receive 2. Cleopas Sipho Dlamini was appoint- India (IFFI) will be held in ..… from 4) Viswanathan Anand to Leos Carax "Annette" (France), Company Limited (APPCL) and $10,000 prize money. ed as the new prime minister of… 20th Nov to 28th Nov 2021. 5) Fabiano Caruana Snehakunja Trust are among the 10 whereas the Best actor award was Spelling Bee 1) Hyderabad 2) Mumbai given to Caleb Landry Jones for awardees of the prestigious Equator 1) kingdom of Brunei 2) Israel 11. 2032 Summer Olympics and Zaila Avant-garde, a 14-year-old from 3) Kolkata 4) Bengaluru 5) Goa "Nitram" (USA). Prize for their work in the field of con- 3 )Kingdom of Eswatini 4) Samoa Paralympic Games to be hosted New Orleans, Louisiana, was crowned 8. A Joint military exercise “Mustafa by… The Best actress award was given to servation and biodiversity. 5) Slovakia the winner of the 2021 Scripps Kemal Ataturk 2021” was held Renate Reinsve for "Worst Person in The UNDP (United Nations 3. World Youth Skills Day observed on.. 1) Paris, France National Spelling Bee on 8 July 2021. between...... 2) Brisbane, Australia the World" (Norway). Indian Director Development Programme) gives a She is the first African American win- 1) 8 July 2) 21 July 3) 15 July 1) Turkey & Azerbaijan 3) Los Angeles, USA Payal Kapadia’s ‘A Night of Knowing biennial award, Equator Prize to rec- ner in the bee’s 96-year history. 4) 9 July 5) 24 July Nothing’ won the Oeil d’or (Golden ognize community efforts to reduce 2) India & Azerbaijan 4) Riyadh, Saudi Arabia Avant-garde correctly spelt the word 4. 2022 Olympic winter games to be Eye) award for best documentary. poverty through the conservation and 3) Pakistan & Azerbaijan “Murraya,” a genus of tropical Asiatic hosted by… 5) Lisbon, Portugal sustainable use of biodiversity. 4) Turkey & Pakistan Nelson Mandela International Day and Australian trees having pinnate 1) Sochi (Russia) 2) Beijing (China) Key APPCL is run by indigenous people 5) India & Pakistan Nelson Mandela International Day is leaves and flowers with imbricated 3) Pyeongchang (South Korea) 1-5 4-2 7-5 10-4 from the Nilgiri Biosphere Reserve in 9. Who is the present president of the observed on 18th July every year. The petals, to win the championship over 4) Milan/ Cortina d'Ampezzo (Italy) 2-3 5-3 8-1 11-2 Tamil Nadu and its work improved International Criminal Court? day plays a significant role in honour- Indian American Chaitra Thummala, 5) Vancouver (Canada) 3-3 6-3 9-3 ing the legacy of Nelson Mandela. livelihood across 147 villages by pro- 12, of Frisco, Texas. Another Indian 1) Guy Ryder 5. Which nation successfully tested For more Information see The theme for this year is “One cessing and marketing a diverse American Bhavana Madini, 13, from Tsirkon (Zircon) hypersonic cruise 2) Qu Dongyu hand can feed Another”. This day is range of forest produce and crops. New York, placed third in the Bee. missile? 3) Piotr Hofmanski today’s AP Edition F F F F F F F F F F F F F F F F F F F F