GH
Oxygen Express
Indian Railway launched the ‘Oxygen
Express’ in response to its fight against
Covid-19. On 22 April 2021, the first
Oxygen Express carrying 100 tonnes of
Liquid Medical Oxygen (LMO) tankers
started from Visakhapatnam of Andhra
Pradesh to Maharashtra.
The tankers were transported
through Ro-Ro service of Indian
Railways.
The LMO supplied by Rashtriya Ispat
Nigam Ltd (RINL) plant in
Visakhapatnam.
The Indian Railways and Indian Air
Force( IAF) have been deployed to
reduce the travel time of oxygen
tankers and assured states of the
Central government’s full support in
the fight against the pandemic.
SVAMITVA
On 24 April 2021 Prime Minister
Narendra Modi launched the distribu-
tion of e-property cards under the
SVAMITVA scheme on the National
Panchayati Raj Day virtually.
SVAMITVA stands for Survey of
Villages and Mapping with Improvised
Technology in Village Areas.
Under the scheme, the entire village
properties are surveyed by drone and
property cards are distributed to the
owners.
On this eve, 4.09 lakh people were
given such e- property cards in more
than 5,000 villages. The scheme
infused a new confidence in the villages
as property documents remove uncer-
tainty and reduce the chances of prop-
erty disputes while protecting the poor
from exploitation and corruption.
The scheme will cover around 6.62
Lakh villages of the entire country dur-
ing 2021-2025.
The pilot phase of the scheme was
implemented during 2020-21 in the
States of Maharashtra, Karnataka,
Haryana, Uttar Pradesh, Uttarakhand,
Madhya Pradesh and select villages of
Punjab and Rajasthan.
‘Samudra Setu-II’
On 30 April 2021, the Indian Navy
launched operation ‘Samudra Setu-II’
to bring oxygen-filled cryogenic con-
tainers to India from abroad.
The Mission deployed warships that
will undertake shipment of liquid oxy-
gen filled cryogenic containers and
associated medical equipment in sup-
port of nation's fight against Covid-19.
Indian Naval ships including Kolkata,
Kochi, Talwar, Tabar, Trikand,
Jalashwa and Airavat have been
deployed to participate in the mission.
Operation Samudra Setu-I was
launched last year by the Navy to bring
back the Indian citizens stranded in
neighbouring countries, amidst COVID
19 outbreak.
SUPACE
On 6 April 2021, the Supreme Court
unveiled its Artificial Intelligence (AI)
portal SUPACE, designed to make
research easier for judges, thereby
easing their workload.
It is a tool that collects relevant facts
and laws and makes them available to
a judge.
1. Nikol Pashinyan was resigned as
the Prime Minister of……..
1) Ujbekistan 2) Azerbaijan
3) Romania 4) Armenia
5) Kazakhstan
2. Claude Joseph was appointed as
the new Prime Minister of ......
1) Georgia 2) Fiji 3) Haiti
4) Gambia 5) Austria
3. Who became first Indian woman
climber to scale Mt Annapurna, the
10th highest peak in the world?
1) Arunima Sinha
2) Malavath Purna
3) Priyanka Mohite
4) Santosh Yadav 5) Dicky Dolma
4. World Malaria Day is observed on
...... The 2021 theme is “Reaching
the Zero Malaria target"
1) 20th April 2) 22nd April
3) 25th April 4) 1st May
5) 4th May
5. The RT-PCR test is a laboratory
test that can identify the virus that
causes COVID-19. In this context,
RT-PCR stands for ......
1) Real Transcription- Polymerase
Chain Reaction
2) Reverse Transport- Polymerase
Chain Reaction
3) Reverse Transcription-
Polymerase Count Reaction
4) Roll Transcription- Polymerase
Chain Reaction
5) Reverse Transcription-
Polymerase Chain Reaction
6. First Indian and Asian woman con-
ferred with the ‘WILD Innovator
Award' is ......
1) Dr Krithi K Karanth
2) Dr Mayuri Yeole
3) Dr Kavitha Amirneni
4) Dr Navneet Kaur
5) Dr Rama Narasimhan
7. Which Marathi film won the best for-
eign language feature at the Moscow
International Film Festival 2021?
1) Dhurala 2) Vijeta 3) Puglya
4) Kesari 5) Tattad
8. 2022 AFC Women's Asian Cup foot-
ball to be hosted by ......
1) China 2) India 3) Indonesia
4) Japan 5) Iran
9. The book “How to Avoid a Climate
Disaster: The Solutions We Have
and the Breakthroughs We Need”
written by ......
1) James Hansen 2) Elon Musk
3) S K Sateesh
4) Amitav Ghosh 5) Bill Gates
ñªëÅ]î¦ô¢Ù  5, 2021 n e-mail:[email protected]
17
National
Oscar best picture
award conferred on..?
Writer
Amara Veeraswamy
Subject Expert
GeneralAwareness
Chandler Good Government
Index (CGGI)
India has been ranked 49th in the
Chandler Good Government Index
(CGGI) 2021 among 104 countries in
terms of government capabilities and
outcomes.
The Chandler Institute of
Governance, having base in Singapore
released the Chandler Good
Government Index (CGGI) on 26 April
2021.
The index was topped by Finland.
The second and third positions are
marked by Switzerland and Singapore
respectively.
The index ranking was calculated by
considering 7 pillars. They are
Leadership and foresight, Strong insti-
tutions, Robust laws and policies,
Attractive market place, Financial
stewardship, helping people rise and
Global influence and Reputation.
India Russia 2+2
On 26 April 2021, India and Russia
agreed to establish a "2+2 ministerial
dialogue" between foreign and defence
ministers to add further momentum to
the bilateral strategic partnership.
PM Modi and Russian president
Putin noted the ongoing cooperation
between the two countries to fight the
global pandemic. The approval for
emergency use of Sputnik-V vaccine in
India was appreciated by President
Putin.
Russia now became part of a small
group of countries with whom India has
2+2 dialogue of foreign and defence
ministers. India has such mechanism
with the USA, Japan and Australia.
SCRI
On 27 April 2021, India, Japan and
Australia launched the Supply Chain
Resilience Initiative (SCRI) to build
resilient supply chains in the Indo-
Pacific region.
In a move to counter China’s domi-
nance of supply chain in the Indo-
Pacific region, the trade ministers of
India, Japan and Australia launched
SCRI in a virtual trilateral ministerial
meeting.
India’s trade minister Piyush Goyal
participated the meeting.
Varuna 2021
The 19th edition of the Indian and
French Navy bilateral exercise
‘VARUNA-2021’ was conducted in the
Arabian Sea from 25th to 27th April
2021.
The three-day exercise had seen
high tempo-naval operations at sea,
including advanced air defence and
anti-submarine exercises, intense fixed
and rotary wing flying operations,
tactical manoeuvres, surface and anti-
air weapon firings, underway replen-
ishment and other maritime security
operations.
Trends in Military
Expenditure 2020
The Stockholm International Peace
Research Institute (SIPRI) released
the report titled ‘Trends in World
Military Expenditure 2020’ on 26 April
2021.
As per the report, India was the third
biggest military spender in the world in
2020. The list was topped by the
USA and China. India’s total expendi-
ture on the military for 2020 was $ 72.9
billion.
The report also observed that
despite the Covid-19 pandemic, the
military spending across the world rose
to $1,981 billion in 2020, registering an
increase of 2.6 percent as compared
with figures for 2019.
National Panchayati Raj Day
National Panchayati Raj Day
observed on 24 April. The annual cel-
ebration is done to commemorate the
day on which the 73rd Constitutional
Amendment was passed in 1992. The
act came into effect on April 24, 1993.
Dr. Manmohan Singh, the former
Prime Minister of India declared the
first National Panchayati Raj Day on
24 April in the year 2010.
Oscar Awards
On 25 April 2021, the 93rd edition of
Oscars Awards took place in Union
station and Dolby Theatre in Los
Angeles, California, U.S.A.
The best Picture award conferred
on Nomadland and the Best Director
Award conferred on Chloe Zhao
(Nomadland)
Best Actor award declared to
Anthony Hopkins (The Father). Best
Actress award conferred on Frances
McDormand (Nomadland).
Daniel Kaluuya was conferred with
Best supporting Actor award (Judas
and the Black Messiah) and Yuh-jung
Youn got best supporting Actress
award (Minari).
Emerald Fennell was conferred with
Best Original Screen play award
(Promising Young Woman).
Best Documentary Feature award
declared to ‘My Octopus Teacher’.
The Award ‘Animated Film” con-
ferred to “Soul” and Best International
Feature Film conferred on “Another
Round”, the Danish Film.
Best Music (Original Score) award
had given to “Soul” and Best Music
(Original Song) award conferred on
“Fight For You”.
International
Model Questions
Others
For more Information see
today’s Telangana Edition
Key
1-4 2-3 3-3 4-3 5-5
6-1 7-3 8-2 9-5
1. Ú¨ÙC-î¦-æ¨ö˺ í£J-í£²ô¢g ÷ô¢_ú£ÙÜu Ú¥EC ÔC?1) 144 2) 169 3) 324 4) 0.25
þ§ëÅ]ì: 144 =- 122, 12 ú£ï£°á ú£ÙÜu Ú¥ñæ¨d 144
í£J-í£²ô¢g ÷ô¢_ ú£ÙÜu Í÷±-꟪ÙC.-169 =- 132, 13 ú£ï£°á ú£ÙÜu Ú¥ñæ¨d 169
í£J-í£²ô¢g ÷ô¢_-ú£ÙÜu Í÷±-꟪ÙC.-324 =- 182, 18 ú£ï£°á ú£ÙÜu Ú¥ñæ¨d 324
í£J-í£²ô¢g ÷ô¢_-ú£ÙÜu Í÷±-꟪ÙC0.25 =- 0.52, 0.5 ú£ï£°á ú£ÙÜu Ú¥ë]ª. Ú¥ñæ¨d0.25 í£J-í£²ô¢g ÷ô¢_-ú£ÙÜu Ú¥ë]ª.- ú£-÷«-ëůìÙ:- 4
2. îµ³ë]æ¨ 25 ò˶ú‡ ú£ÙÜuõ îµ³êŸhÙ ÓÙêŸ?1) 576 2) 625 3) 676 4) 500
þ§ëÅ]ì: 1 + 3 + 5 + 7 + ..... (n ú£Ù-Üuõª) = n2
1 + 3 + 5 + 7 + ..... (25 ú£ÙÜuõªz =- 252
=- 25 × 25 =- 625
ú£÷«-ëůìÙ:- 2Þœ÷ª-EÚÛ: ÖÚÛ ÍÙ·Ú ú£ÙÜuö˺x ÍA-#ìo í£J-í£²ô¢g
÷ô¢_ ú£ÙÜu =- 1 (12)
·ôÙè[Ù-·Úõ ú£ÙÜuö˺x ÍA-#ìo í£J-í£²ô¢g ÷ô¢_-ú£ÙÜu =- 16 (42)
÷´è[Ù-·Úõ ú£ÙÜuö˺x ÍA-#ìo í£J-í£²ô¢g ÷ô¢_-ú£ÙÜu =- 100 (102)
û¦õªÞœÙ·Úõ ú£ÙÜuö˺x ÍA-#ìo í£J-í£²ô¢g ÷ô¢_-ú£ÙÜu =- 1024 (322)
Íô³-ë]Ù-·Úõ ú£ÙÜuö˺x ÍA-#ìo í£J-í£²ô¢g ÷ô¢_-ú£ÙÜu =- 10,000 (100-2)
ÖÚÛ ÍÙ·Ú ú£ÙÜuö˺x ÍA-šíë]Ì í£J-í£²ô¢g ÷ô¢_-ú£ÙÜu =- 9 (32)
·ôÙè[Ù-·Úõ ú£ÙÜuö˺x ÍA-šíë]Ì í£J-í£²ô¢g ÷ô¢_-ú£ÙÜu =- 81 (92)
÷´è[Ù-·Úõ ú£ÙÜuö˺x ÍA-šíë]Ì í£J-í£²ô¢g ÷ô¢_-ú£ÙÜu =- 961 (312)
û¦õª-ÞœÙ-·Úõ ú£ÙÜuö˺x ÍA-šíë]Ì í£J-í£²ô¢g ÷ô¢_-ú£ÙÜu =- 9801 (99-2)
Íô³-ë]Ù-·Úõ ú£ÙÜuö˺x ÍA-šíë]Ì í£J-í£²ô¢g ÷ô¢_ ú£ÙÜu =- 99856 (3162)
3. 122, 132 ÷ªëÅ]u Ñìo í£²ô¦gÙ-Ú¥õ ú£ÙÜu?1) 24 2) 25 3) 26 4) 27
þ§ëÅ]ì: n2, (n + 1)2 (n ÖÚÛ ú£ï£°á ú£ÙÜu) ÷ªëÅ]u Ñìoí£²ô¦gÙ-Ú¥õ ú£ÙÜu =- 2n
122, 132 ÷ªëÅ]u- Ñìo í£²ô¦gÙ-Ú¥õ ú£ÙÜu =- 2 × 12 =- 24 ú£-÷«-ëůìÙ:- 1
4. 92 + 402 = x2 Íô³ê¶ x Nõª÷ ÓÙêŸ?1) 51 2) 49 3) 41 4) 59
þ§-ëÅ]ì: 92 + 402 = x2
⇒ 81 + 1600 = x2
⇒ 1681 = x2
⇒ x = √1681 ⇒ = √
412 = 41
∴ x = 41 ú£-÷«-ëůìÙ:- 3Þœ-÷ª-EÚÛ: a2 + b2 = c2 (a, b, cõª ú£ï£°á ú£ÙÜuõªzÍô³ê¶ (a, b, c)E šíjëǯ-ÞœJ-óŸªû vAÚÛÙ ÍÙæ°ô¢ª.-Ñë¯: (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17)
îµ³ë]-ö˵j-ìN.-
√
5. 2275 + √841 = ?
1) 46 2) 48 3) 47 4) 52
√
√
þ§-ëÅ]ì: 2275 + √841 = 2275 + 29
(... √841 = 29)
= √2304 = √
482 = 48
ú£-÷«-ëůìÙ:- 2
√
√
√
√
6. 10 + 25 + 108 + 154 + √225 = ?
1) 4 2) 6 3) 8 4) 9
√
√
√
√
þ§-ëÅ]ì: 10 + 25 + 108 + 154 + √225
√
√
√
√
= 10 + 25 + 108 + 154 + 15
√
√
√
√
= 10 + 25 + 108 + 169
√
√
√
= 10 + 25 + 108 + 13
√
√
√
√
√
= 10 + 25 + 121 = 10 + 25 + 11
√
√
= 10 + 36 = √10 + 6
= √16 = 4 ú£-÷«-ëůìÙ:- 1
7. ÷´è[ª ÷ô¢ªú£ í£²ô¦gÙ-Ú¥õ ÷ô¦_õ îµ³êŸhÙ 434
Íô³ê¶ Î ú£ÙÜuõ îµ³êŸhÙ ÓÙêŸ? 1) 45 2) 42 3) 39 4) 36
þ§-ëÅ]ì: ÷´è[ª ÷ô¢ªú£ í£²ô¦gÙ-Ú¥õª =
x, x + 1, x + 2 Íìª-ÚÁÙè….-x2 + (x + 1)2 + (x + 2)2 = 434
⇒ x2 + x2 + 2x + 1 + x2 + 4x + 4 = 434
⇒ 3x2 + 6x + 5 = 434
⇒ 3x2 + 6x + 5 − 434 = 0
⇒ 3x2 + 6x − 429 = 0
⇒ x2 + 2x −143 = 0
⇒ x2 + 13x − 11x − 143 = 0
⇒ x(x + 13) − 11(x + 13) = 0
⇒ (x + 13) (x − 11) = 0
⇒ x + 13 = 0 öË¶ë¯ x − 11 = 0
⇒ x = −13 öË¶ë¯ x = 11
⇒ x = 11 (x = −13 í£²ô¢g ú£ÙÜu Ú¥ë]ªz∴ x = 11
x + 1 = 11 + 1 = 12
x + 2 = 11 + 2 = 13
÷-ô¢ªú£ í£²ô¦gÙ-Ú¥õ îµ³êŸhÙ = x + (x + 1z(x + 2)
= 11 + 12 + 13 = 36
ú£-÷«-ëůìÙ:- 48. x = 0.
3 Íô³ê¶ 2x2 =
1) 0.1 2) 0.
2 3) 0.
6 4) 0.
9
þ§-ëÅ]ì: x = 0.3
3 − 0 3 1= = =
9 9 3
1 2 1x2 = () =
3 9
1 22x2 = 2 × = = 0.2222...
9 9
= 0.2 ú£-÷«-ëůìÙ:- 2
9. ÖÚÛ Dô¢+-àŸ-꟪-ô¢-vþ§-Ú¥ô¢ ð»õÙ ð»è[÷±, î�µè[-õªp-ìÚÛª 1
1 - ·ôåªx ÑÙC.- Î ð»õÙ î�µjø‹õuÙ 1.-4406 2
šï°Ú¥dô¢ªx Íô³ê¶ Î ð»õÙ ð»è[÷± ÓÙêŸ? sOªå-ô¢xö˺z1) 167 2) 127 3) 147 4) 137
þ§-ëÅ]ì: ÖÚÛ Dô¢+-àŸ-꟪-ô¢-vþ§-Ú¥ô¢ ð»õÙî�µè[õªp (b) = x Íìª-ÚÁÙè…
1 3ð»è[÷± (l) = 1 b = b
2 2
3= x
2
D-ô¢+-àŸ-꟪-ô¢-vþ§-Ú¥ô¢ ð»õÙ î�µjø‹õuÙ =- l × b
3 3= x × x = x2
2 2
3ë]-ê¦hÙøŒÙ ví£Ú¥ô¢Ù x2 = 1.4406 šï°Ú¥dô¢ªx
2
3 x2 = 1.4406 × 10000 àŸ.-Oª.-2
= 14406 àŸ.-Oª.-2
⇒ x2 = 14406 × àŸ.-Oª.- 3
=- 9604 àŸ.-Oª.-⇒ x = √
9604 Oª. = 98 Oª.-
3 3ð»õÙ ð»è[÷± (l) = x = × 98 = 147 Oª.
2 2
ú£-÷«-ëůìÙ:- 3√
10. √
1225 + 0.0615 +- x = 35.25 Íô³ê¶ x
Nõª÷ ÓÙêŸ?1) 0.1 2) 0.01 3) 0.001 4) 0.0001
√
þ§-ëÅ]ì: √1225 + 0.0615 + x = 35.25
√
⇒ 35 + 0.0615 + x = 35.25
√
⇒ 0.0615 + x = 35.25 − 35
√
⇒ 0.0615 + x = 0.25
⇒ 0.0615 + x = (0.25)2
⇒ 0.0615 + x = 0.0625
⇒ x = 0.0625 − 0.0615 ⇒ x = 0.0010
∴ x = 0.001 ú£-÷«-ëůìÙ:- 311. îµ³ë]æ¨ 10 ú£ï£°á ú£ÙÜuõ ÷ô¦_õ îµ³êŸhÙ ÓÙêŸ?
1) 325 2) 345 3) 365 4) 385
þ§-ëÅ]ì: 12 + 22 +- 32 ...... -+ n2
n(n + 1)(2n + 1)=
6
12 + 22 + 32 + ...... + 102
10(10 + 1)(2 × 10 + 1)=-
6
10 × 11 × 21= = 385
6 ú£-÷«-ëůìÙ:- 4
Þœ-÷ª-EÚÛ:-n2(n + 1)2
13 + 23 +- 33 + ...... +- n3 = 4
(or)
n2(n + 1)2∑ n3 =
4
(or)
îµ³-ë]æ¨ n ú£ï£°á ú£ÙÜuõ íÆ£ªû¦õ îµ³êŸhÙ n2(n + 1)2
= 4
n(n + 1) 2= []
2
= (∑ n)2
12. îµ³ë]æ¨ 4 ú£ï£°á ú£ÙÜuõ íÆ£ªû¦õ îµ³êŸhÙ ÓÙêŸ?1) 64 2) 100 3) 81 4) 144
þ§-ëÅ]ì:- 13 + 23 + 33 + 43
= (1 + 2 + 3 + 4)2
= 102 = 100
ú£-÷«-ëůìÙ:- 2
ô¢àŸô³êŸúˆšï°àÂ. ô¦ëůÚÛ”ù£g Nù£óŸª Eí£±éªõª
÷«uëÇ]æ̈ÚÂq
ð¼æ© í£K¤Ûõví£ê¶uÚÛÙ
÷«-CJ ú£÷ª-ú£uõª
ú£ÙÝ°u ÷u÷ú£–÷³Ý°uÙø‹õª
F x2 =- y Í-ô³ê¶ √y = x Í-÷±-꟪ÙC.- ÍÙç˶
x ÷ô¢_Ù y Í-ô³ê¶ y ÷ô¢_-÷´õÙ x Í-÷±-꟪ÙC.-F n Í-û¶C ÖÚÛ ú£ï£°á ú£ÙÜu Íô³ê¶ n2 í£J-í£²ô¢g
÷ô¢_ú£ÙÜu sÚÛ#aêŸ ÷ô¢_-ú£ÙÜuz Í÷±-꟪ÙC.-í£J-í£²ô¢g ÷ô¢_ú£ÙÜu-õÚÛª Ñë¯--ô¢é:- 1, 4, 9, 16,
25, 36, 49...
Þœ÷ª-EÚÛ: 1.42 = 1.96, 142 = 196 õö˺1.96 í£-J-í£²ô¢g ÷ô¢_ú£ÙÜu Ú¥ë]ª (Not a perfect
square number).
196 í£J-í£²ô¢g ÷ô¢_-ú£ÙÜu (Perfect square
number).
F îµ³-ë]æ¨ n ò˶ú‡ ú£ÙÜuõ îµ³êŸhÙ Óõx-í£±pè[« ÚÛ#aêŸ÷ô¢_-ú£ÙÜu Í÷±-꟪ÙC.-1 + 3 + 5 + 7 + ...... (n ú£Ù-Üuõªz =- n2
n(n+1) (2n+1)F 12 + 22 + 32 + ...... + n2 =
6
sö˶ë¯zn(n+1) (2n+1)
∑ n2 = 6
sö˶ë¯zîµ³ë]æ¨ n ú£-á ú£ÙÜuõ ÷ô¦_õ îµ³êŸhÙ
n(n+1) (2n+1)=
6
ÍòÅ°uú£ ví£øŒoõª
ú£÷«ëůû¦õª1-4 2-1 3-2 4-3 5-2 6-2 7-3 8-1
11 x
2
x
5 5 1 11. a = , b = Íô³ê¶ + = .....
3 4 a2 b2
1) 4 2) 3 3) 2 4) 1
2. Ú¨ÙC-î¦-æ¨E áêŸ-í£-ô¢-àŸÙè….-i) 62 + 82 = ? a) 625
ii) 82 + 152 = ? b) 169
iii) 72 + 242 = ? c) 100
iv) 52 + 122 = ? d) 289
1) i-c, ii-d, iii-a, iv-b 2) i-c, ii-b, iii-a, iv-d
3) i-c, ii-b, iii-a, iv-d 4) i-d, ii-c, iii-b, iv-a
√
√
√
3. 21 + 13 + 7 + √4 = ?
1) 25 2) 5 3) 9 4) 12
4. 412, 422 ÷ªëÅ]u Ñìo í£²ô¦gÙ-Ú¥õª ÓEo?1) 84 2) 86 3) 82 4) 88
5. x = 0.2 Íô³ê¶ 3x2 =
1) 1.2 2) 1.
3 3) 1.
8 4) 1.
9
6. Ú¨ÙC-î¦-æ¨ö˺ šíjëǯ-Þœ-J-óŸªû vAÚÛÙ Ú¥EC ÔC?1) (3, 4, 5) 2) (10, 12, 13)
3) (10, 24, 26) 4) (9, 12, 15)
7. ÷´è[ª ÷ô¢ªú£ í£²ô¦gÙ-Ú¥õ îµ³êŸhÙ 110. Íô³ê¶Î ú£ÙÜuõ îµ³êŸhÙ ÓÙêŸ?1) 15 2) 21 3) 18 4) 24
8. û¦õªÞœª ÍÙ·Úõ ÍA šíë]Ì í£J-í£²ô¢g ÷ô¢_-ú£ÙÜuÚÛª,÷´è[Ù-·Úõ ÍA šíë]Ì í£J-í£²ô¢g ÷ô¢_-ú£Ù-ÜuÚÛª ÷ªëÅ]uòÅ˶ë]-ÙêŸ?1) 8840 2) 8904 3) 8841 4) 8740
Dr Krithi K Karanth
F F F F F F F F F F F F F F F F F F F F
šíjëǯ-ÞœJ-óŸªû vAÚÛÙ ÍE î�¶æ̈E ÍÙæ°ô¢ª?šíjëǯ-ÞœJ-óŸªû vAÚÛÙ ÍE î�¶æ̈E ÍÙæ°ô¢ª?šíjëǯ-ÞœJ-óŸªû vAÚÛÙ ÍE î�¶æ̈E ÍÙæ°ô¢ª?šíjëǯ-ÞœJ-óŸªû vAÚÛÙ ÍE î�¶æ̈E ÍÙæ°ô¢ª?šíjëǯ-ÞœJ-óŸªû vAÚÛÙ ÍE î�¶æ̈E ÍÙæ°ô¢ª?šíjëǯ-ÞœJ-óŸªû vAÚÛÙ ÍE î�¶æ̈E ÍÙæ°ô¢ª?šíjëǯ-ÞœJ-óŸªû vAÚÛÙ ÍE î�¶æ̈E ÍÙæ°ô¢ª?šíjëǯ-ÞœJ-óŸªû vAÚÛÙ ÍE î�¶æ̈E ÍÙæ°ô¢ª?šíjëǯ-ÞœJ-óŸªû vAÚÛÙ ÍE î�¶æ̈E ÍÙæ°ô¢ª?šíjëǯ-ÞœJ-óŸªû vAÚÛÙ ÍE î�¶æ̈E ÍÙæ°ô¢ª?šíjëǯ-ÞœJ-óŸªû vAÚÛÙ ÍE î�¶æ̈E ÍÙæ°ô¢ª?
GH
48th Chief Justice of India
On 24 April 2021, Justice N.V.
Ramana sworn in as the 48th Chief
Justice of India by President Ram
Nath Kovind at Rashtrapati Bhavan.
He will hold the post for sixteen
months, until 26 August 2022.
During his tenure in the Supreme
Court, Justice Ramana has been a
part of many significant rulings. Some
among them are setting up of special
courts for fast-tracking criminal cases
against MPs and MLAs, bringing the
CJI’s office amenable to the Right to
Information Act and lifting Internet
restrictions in Jammu and Kashmir.
Corona Warriors Scheme
On 30 April 2021, the government
of Madhya Pradesh launched the
Corona Warriors Scheme. The gov-
ernment will take the responsibility of
family members of health workers
who have passed away while on
Corona duty.
Their families will be given a relief
of Rs.50 lakhs by the state govern-
ment.
The state government also declared
that the Covid vaccine will be admin-
istered free of cost to those above 18
years of age.
‘Climate VulnerabilityAssessment for Adaptation Plan’
On 17 April 2021, the report titled
‘Climate Vulnerability Assessment for
Adaptation Planning in India Using a
Common Framework’ was released
by Department of Science and
Technology (DoST), Government of
India.
Prof Ashutosh Sharma, the secre-
tary of DoST said that the National cli-
mate vulnerability assessment has
identifies 8 eastern states as highly
vulnerable to climate change. They
are Jharkhand, Mizoram, Odisha,
Chhattisgarh, Assam, Bihar,
Arunachal Pradesh, and West Bengal.
These states, mostly in the eastern
part of the country, require prioritiza-
tion of adaptation interventions.
Himachal Pradesh, Telangana,
Sikkim and Punjab have been cate-
gorised as lower-middle vulnerable
states. Uttarakhand, Haryana, Tamil
Nadu, Kerala, Nagaland, Goa and
Maharashtra have been categorised
as states with low vulnerability.
Trial of Python-5 Air to AirMissile
On 27 April 2021, Tejas, the India's
indigenous Light Combat Aircraft,
added the 5th generation Python-5
Air-to-Air Missile (AAM) in its air-to-air
weapons capability successfully.
The trials were also aimed to vali-
date enhanced capability of already
integrated Derby Beyond Visual
Range (BVR) AAM on Tejas.
The test firing at Goa completed a
series of missile trials to validate its
performance under extremely chal-
lenging scenarios.
Derby missile achieved direct hit on
a high-speed manoeuvring aerial tar-
get and the Python missiles also
achieved 100% hits, thereby validat-
ing their complete capability.
The Python-5 is the newest mem-
ber of the Israeli Python family of
short-range air-to-air missiles
Govt. of Delhi means
Lt Governor
On 27 April 2021, the Government of
National Capital Territory of Delhi
(Amendment) Act, 2021 came in to
force which gives primacy to the
Lieutenant Governor (L-G) over the
elected government.
According to the legislation, the
"government" in Delhi means the
"Lieutenant Governor" and the city
government will now have to seek the
opinion of the Lieutenant Governor
before taking any executive action.
Lok Sabha on 22 March and Rajya
Sabha on 24 March 2021 passed the
above legislation.
Earth Day
22 April is Earth Day, an international
event celebrated around the world to
pledge support for environmental pro-
tection. This year’s theme for Earth
Day is ‘Restore Our Earth’. The year
2021 marks the 51st anniversary of the
annual celebrations.
In 2009, the United Nations desig-
nated April 22 as ‘International Mother
Earth Day’.
The Earth Day aims to build the
world’s largest environmental move-
ment to drive transformative change
for people and the planet.
Yudhvir Memorial Award
On 30 April 2021, the 29th Yudhvir
Memorial Award was presented to
Hyderabad-based gynaecologist,
Dr. Evita Fernandez in recognition of
her service for the cause of women’s
healthcare and empowerment.
Vice President of India M Venkaiah
Naidu on this eve stressed the need to
accelerate the target 3.1 of
Sustainable Development Goals
(SDGs) set by the UNO that aims to
reduce the global maternal mortality
ratio by less than 70 per 100,000 live
births by 2030.
ñªëÅ]î¦ô¢Ù  5, 2021 n e-mail:[email protected]
17
National
Yudhvir Memorial Award
was presented to ..?
Writer
Amara Veeraswamy
Subject Expert
GeneralAwareness
World Press Freedom Index 2021
On 20 April 2021, the World Press
Freedom Index 2021 was published by
the international journalism not-for-profit
body, Reporters Without Borders (RSF).
In the index, India got 142 rank,
while Norway topped the index.
India has been listed under coun-
tries considered “bad” for journalism
and is among the most dangerous
places in the world for journalists.
The Index ranks countries and
regions according to the level of free-
dom available to journalists. The report
said few forces in India created an
environment of intimidation for journal-
ists who are critical of the government
by labelling them as “anti-national” or
“anti-state”.
The last rank position of 180 is
marked by Eritrea.
The parameters include pluralism,
media independence, media environ-
ment and self-censorship, legislative
framework, transparency and the qual-
ity of the infrastructure that supports
the production of news and information.
‘Leaders’ Summit on Climate’
‘Leaders’ Summit on Climate’ held
between 22-23 April 2021 was hosted
by the President of the U.S.A. Joe
Biden.
The two-day conference coincides
with the 5th anniversary of the opening
of the Paris Agreement on climate
change for signature.
The summit was held to strengthen
the cooperation among the nations to
tackle the climate change issues. The
leaders from 40 nations participated in
the summit.
The dignitaries discussed climate
action, nature-based solutions, climate
security and technological innovations
for clean energy.
The theme of the summit is “Our
Collective Sprint to 2030”.
Henley Passport Index
On 15 April 2021, the Henley Passport
Index released its list of the most pow-
erful passports.
India stands at number 84 in the list,
as the Indian citizens can visit Visa
Free or Visa-on-Arrival in over 58
places.
Japan and Singapore hold the top
two spots in the index respectively,
while Germany and South Korea share
the third spot.
Each country’s passport gives its cit-
izens different freedom and different
access.
The index ranks the passport as
per their mobility score, the higher the
score the better the passport and vice-
versa. Countries are ranked by the
number of passports they accept visa-
free or with visa on arrival.
International
Others
1. International Dance Day observed on
1) 1 April 2) 20 April 3) 18 April
4) 29 April 5) 4 May
2. What is the name of China's first
Mars Rover?
1) Nihao 2) Xiexie
3) Zhurong 4) Bu keqi 5) Zao
3. Kim Boo Kyum was nominated as
the prime minister of ......
1) South Korea 2) China
3) North Korea 4) Vietnam
5) Thailand
4. Who is appointed as the Associate
Attorney General of the USA, mak-
ing her the first Indian-American to
serve in this role?
1) Marcia Fudge 2) Uzra Zeya
3) Vanita Gupta 4) Mala Adiga
5) Neera Tanden
5. Shaheen-1A the nuclear-capable
surface to the surface ballistic mis-
sile was test-fired by ......
1) Israel 2) UK 3) USA
4) Pakistan 5) UAE
6. Who became India’s 68th Chess
Grandmaster?
1) Baskaran Adhiban
2) Sameer
3) Arjun Kalyan
4) Surya Shekhar Ganguly
5) Abhijeet Gupta
7. Which nation’s troops would be
withdrawn from Afghanistan by 11
September 2011?
1) Russia 2) UAE 3) USA
4) India 5) Japan
8. Which nation’s space agency
Roscosmos announced that it will
launch its own space station in
2025?
1) UK 2) Poland 3) Russia
4) USA 5) Germany
9. 2021 Barcelona Open Tennis
Tournament clinched by ......
1) Novak Djokovic
2) Rafael Nadal
3) Roger Federer
4) Dominic Thiem
5) Stan Wawrinka
10. Organisation for the Prohibition of
Chemical Weapons (OPCW) select-
ed whom as its external auditor for a
three-year term starting 2021?
1) Sunil Arora 2) Arvind Saxena
3) Rajiv Mehrishi
4) N.K.Singh 5) GC Murmu
11. ICC Women’s World Cup 2022 to
be hosted by ......
1) India 2) Pakistan
3) Australia 4) New Zealand
5) West Indies
12. Who assumed charge as the 24th
Chief Election Commissioner of
India?
1) K.K.Venugopal 2) Rajiv Kumar
3) Sushil Chandra
4) Amitabh Kanth
5) Pramod Chandra Mody
For more Information see
today’s AP Edition
Model Questions
Key
1-4 2-3 3-1 4-3 5-4 6-3
7-3 8-3 9-2 10-5 11-4 12-3
Dr. Evita Fernandez
1. Ú¨ÙC-î¦-æ¨ö˺ í£J-í£²ô¢g ÷ô¢_ú£ÙÜu Ú¥EC ÔC?1) 144 2) 169 3) 324 4) 0.25
þ§ëÅ]ì: 144 =- 122, 12 ú£ï£°á ú£ÙÜu Ú¥ñæ¨d 144
í£J-í£²ô¢g ÷ô¢_ ú£ÙÜu Í÷±-꟪ÙC.-169 =- 132, 13 ú£ï£°á ú£ÙÜu Ú¥ñæ¨d 169
í£J-í£²ô¢g ÷ô¢_-ú£ÙÜu Í÷±-꟪ÙC.-324 =- 182, 18 ú£ï£°á ú£ÙÜu Ú¥ñæ¨d 324
í£J-í£²ô¢g ÷ô¢_-ú£ÙÜu Í÷±-꟪ÙC0.25 =- 0.52, 0.5 ú£ï£°á ú£ÙÜu Ú¥ë]ª. Ú¥ñæ¨d0.25 í£J-í£²ô¢g ÷ô¢_-ú£ÙÜu Ú¥ë]ª.- ú£-÷«-ëůìÙ:- 4
2. îµ³ë]æ¨ 25 ò˶ú‡ ú£ÙÜuõ îµ³êŸhÙ ÓÙêŸ?1) 576 2) 625 3) 676 4) 500
þ§ëÅ]ì: 1 + 3 + 5 + 7 + ..... (n ú£Ù-Üuõª) = n2
1 + 3 + 5 + 7 + ..... (25 ú£ÙÜuõªz =- 252
=- 25 × 25 =- 625
ú£÷«-ëůìÙ:- 2Þœ÷ª-EÚÛ: ÖÚÛ ÍÙ·Ú ú£ÙÜuö˺x ÍA-#ìo í£J-í£²ô¢g
÷ô¢_ ú£ÙÜu =- 1 (12)
·ôÙè[Ù-·Úõ ú£ÙÜuö˺x ÍA-#ìo í£J-í£²ô¢g ÷ô¢_-ú£ÙÜu =- 16 (42)
÷´è[Ù-·Úõ ú£ÙÜuö˺x ÍA-#ìo í£J-í£²ô¢g ÷ô¢_-ú£ÙÜu =- 100 (102)
û¦õªÞœÙ·Úõ ú£ÙÜuö˺x ÍA-#ìo í£J-í£²ô¢g ÷ô¢_-ú£ÙÜu =- 1024 (322)
Íô³-ë]Ù-·Úõ ú£ÙÜuö˺x ÍA-#ìo í£J-í£²ô¢g ÷ô¢_-ú£ÙÜu =- 10,000 (100-2)
ÖÚÛ ÍÙ·Ú ú£ÙÜuö˺x ÍA-šíë]Ì í£J-í£²ô¢g ÷ô¢_-ú£ÙÜu =- 9 (32)
·ôÙè[Ù-·Úõ ú£ÙÜuö˺x ÍA-šíë]Ì í£J-í£²ô¢g ÷ô¢_-ú£ÙÜu =- 81 (92)
÷´è[Ù-·Úõ ú£ÙÜuö˺x ÍA-šíë]Ì í£J-í£²ô¢g ÷ô¢_-ú£ÙÜu =- 961 (312)
û¦õª-ÞœÙ-·Úõ ú£ÙÜuö˺x ÍA-šíë]Ì í£J-í£²ô¢g ÷ô¢_-ú£ÙÜu =- 9801 (99-2)
Íô³-ë]Ù-·Úõ ú£ÙÜuö˺x ÍA-šíë]Ì í£J-í£²ô¢g ÷ô¢_ ú£ÙÜu =- 99856 (3162)
3. 122, 132 ÷ªëÅ]u Ñìo í£²ô¦gÙ-Ú¥õ ú£ÙÜu?1) 24 2) 25 3) 26 4) 27
þ§ëÅ]ì: n2, (n + 1)2 (n ÖÚÛ ú£ï£°á ú£ÙÜu) ÷ªëÅ]u Ñìoí£²ô¦gÙ-Ú¥õ ú£ÙÜu =- 2n
122, 132 ÷ªëÅ]u- Ñìo í£²ô¦gÙ-Ú¥õ ú£ÙÜu =- 2 × 12 =- 24 ú£-÷«-ëůìÙ:- 1
4. 92 + 402 = x2 Íô³ê¶ x Nõª÷ ÓÙêŸ?1) 51 2) 49 3) 41 4) 59
þ§-ëÅ]ì: 92 + 402 = x2
⇒ 81 + 1600 = x2
⇒ 1681 = x2
⇒ x = √1681 ⇒ = √
412 = 41
∴ x = 41 ú£-÷«-ëůìÙ:- 3Þœ-÷ª-EÚÛ: a2 + b2 = c2 (a, b, cõª ú£ï£°á ú£ÙÜuõªzÍô³ê¶ (a, b, c)E šíjëǯ-ÞœJ-óŸªû vAÚÛÙ ÍÙæ°ô¢ª.-Ñë¯: (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17)
îµ³ë]-ö˵j-ìN.-
√
5. 2275 + √841 = ?
1) 46 2) 48 3) 47 4) 52
√
√
þ§-ëÅ]ì: 2275 + √841 = 2275 + 29
(... √841 = 29)
= √2304 = √
482 = 48
ú£-÷«-ëůìÙ:- 2
√
√
√
√
6. 10 + 25 + 108 + 154 + √225 = ?
1) 4 2) 6 3) 8 4) 9
√
√
√
√
þ§-ëÅ]ì: 10 + 25 + 108 + 154 + √225
√
√
√
√
= 10 + 25 + 108 + 154 + 15
√
√
√
√
= 10 + 25 + 108 + 169
√
√
√
= 10 + 25 + 108 + 13
√
√
√
√
√
= 10 + 25 + 121 = 10 + 25 + 11
√
√
= 10 + 36 = √10 + 6
= √16 = 4 ú£-÷«-ëůìÙ:- 1
7. ÷´è[ª ÷ô¢ªú£ í£²ô¦gÙ-Ú¥õ ÷ô¦_õ îµ³êŸhÙ 434
Íô³ê¶ Î ú£ÙÜuõ îµ³êŸhÙ ÓÙêŸ? 1) 45 2) 42 3) 39 4) 36
þ§-ëÅ]ì: ÷´è[ª ÷ô¢ªú£ í£²ô¦gÙ-Ú¥õª =
x, x + 1, x + 2 Íìª-ÚÁÙè….-x2 + (x + 1)2 + (x + 2)2 = 434
⇒ x2 + x2 + 2x + 1 + x2 + 4x + 4 = 434
⇒ 3x2 + 6x + 5 = 434
⇒ 3x2 + 6x + 5 − 434 = 0
⇒ 3x2 + 6x − 429 = 0
⇒ x2 + 2x −143 = 0
⇒ x2 + 13x − 11x − 143 = 0
⇒ x(x + 13) − 11(x + 13) = 0
⇒ (x + 13) (x − 11) = 0
⇒ x + 13 = 0 öË¶ë¯ x − 11 = 0
⇒ x = −13 öË¶ë¯ x = 11
⇒ x = 11 (x = −13 í£²ô¢g ú£ÙÜu Ú¥ë]ªz∴ x = 11
x + 1 = 11 + 1 = 12
x + 2 = 11 + 2 = 13
÷-ô¢ªú£ í£²ô¦gÙ-Ú¥õ îµ³êŸhÙ = x + (x + 1z(x + 2)
= 11 + 12 + 13 = 36
ú£-÷«-ëůìÙ:- 48. x = 0.
3 Íô³ê¶ 2x2 =
1) 0.1 2) 0.
2 3) 0.
6 4) 0.
9
þ§-ëÅ]ì: x = 0.3
3 − 0 3 1= = =
9 9 3
1 2 1x2 = () =
3 9
1 22x2 = 2 × = = 0.2222...
9 9
= 0.2 ú£-÷«-ëůìÙ:- 2
9. ÖÚÛ Dô¢+-àŸ-꟪-ô¢-vþ§-Ú¥ô¢ ð»õÙ ð»è[÷±, î�µè[-õªp-ìÚÛª 1
1 - ·ôåªx ÑÙC.- Î ð»õÙ î�µjø‹õuÙ 1.-4406 2
šï°Ú¥dô¢ªx Íô³ê¶ Î ð»õÙ ð»è[÷± ÓÙêŸ? sOªå-ô¢xö˺z1) 167 2) 127 3) 147 4) 137
þ§-ëÅ]ì: ÖÚÛ Dô¢+-àŸ-꟪-ô¢-vþ§-Ú¥ô¢ ð»õÙî�µè[õªp (b) = x Íìª-ÚÁÙè…
1 3ð»è[÷± (l) = 1 b = b
2 2
3= x
2
D-ô¢+-àŸ-꟪-ô¢-vþ§-Ú¥ô¢ ð»õÙ î�µjø‹õuÙ =- l × b
3 3= x × x = x2
2 2
3ë]-ê¦hÙøŒÙ ví£Ú¥ô¢Ù x2 = 1.4406 šï°Ú¥dô¢ªx
2
3 x2 = 1.4406 × 10000 àŸ.-Oª.-2
= 14406 àŸ.-Oª.-2
⇒ x2 = 14406 × àŸ.-Oª.- 3
=- 9604 àŸ.-Oª.-⇒ x = √
9604 Oª. = 98 Oª.-
3 3ð»õÙ ð»è[÷± (l) = x = × 98 = 147 Oª.
2 2
ú£-÷«-ëůìÙ:- 3√
10. √
1225 + 0.0615 +- x = 35.25 Íô³ê¶ x
Nõª÷ ÓÙêŸ?1) 0.1 2) 0.01 3) 0.001 4) 0.0001
√
þ§-ëÅ]ì: √1225 + 0.0615 + x = 35.25
√
⇒ 35 + 0.0615 + x = 35.25
√
⇒ 0.0615 + x = 35.25 − 35
√
⇒ 0.0615 + x = 0.25
⇒ 0.0615 + x = (0.25)2
⇒ 0.0615 + x = 0.0625
⇒ x = 0.0625 − 0.0615 ⇒ x = 0.0010
∴ x = 0.001 ú£-÷«-ëůìÙ:- 311. îµ³ë]æ¨ 10 ú£ï£°á ú£ÙÜuõ ÷ô¦_õ îµ³êŸhÙ ÓÙêŸ?
1) 325 2) 345 3) 365 4) 385
þ§-ëÅ]ì: 12 + 22 +- 32 ...... -+ n2
n(n + 1)(2n + 1)=
6
12 + 22 + 32 + ...... + 102
10(10 + 1)(2 × 10 + 1)=-
6
10 × 11 × 21= = 385
6 ú£-÷«-ëůìÙ:- 4
Þœ-÷ª-EÚÛ:-n2(n + 1)2
13 + 23 +- 33 + ...... +- n3 = 4
(or)
n2(n + 1)2∑ n3 =
4
(or)
îµ³-ë]æ¨ n ú£ï£°á ú£ÙÜuõ íÆ£ªû¦õ îµ³êŸhÙ n2(n + 1)2
= 4
n(n + 1) 2= []
2
= (∑ n)2
12. îµ³ë]æ¨ 4 ú£ï£°á ú£ÙÜuõ íÆ£ªû¦õ îµ³êŸhÙ ÓÙêŸ?1) 64 2) 100 3) 81 4) 144
þ§-ëÅ]ì:- 13 + 23 + 33 + 43
= (1 + 2 + 3 + 4)2
= 102 = 100
ú£-÷«-ëůìÙ:- 2
ô¢àŸô³êŸúˆšï°àÂ. ô¦ëůÚÛ”ù£g Nù£óŸª Eí£±éªõª
÷«uëÇ]æ̈ÚÂq
ð¼æ© í£K¤Ûõví£ê¶uÚÛÙ
÷«-CJ ú£÷ª-ú£uõª
ú£ÙÝ°u ÷u÷ú£–÷³Ý°uÙø‹õª
F x2 =- y Í-ô³ê¶ √y = x Í-÷±-꟪ÙC.- ÍÙç˶
x ÷ô¢_Ù y Í-ô³ê¶ y ÷ô¢_-÷´õÙ x Í-÷±-꟪ÙC.-F n Í-û¶C ÖÚÛ ú£ï£°á ú£ÙÜu Íô³ê¶ n2 í£J-í£²ô¢g
÷ô¢_ú£ÙÜu sÚÛ#aêŸ ÷ô¢_-ú£ÙÜuz Í÷±-꟪ÙC.-í£J-í£²ô¢g ÷ô¢_ú£ÙÜu-õÚÛª Ñë¯--ô¢é:- 1, 4, 9, 16,
25, 36, 49...
Þœ÷ª-EÚÛ: 1.42 = 1.96, 142 = 196 õö˺1.96 í£-J-í£²ô¢g ÷ô¢_ú£ÙÜu Ú¥ë]ª (Not a perfect
square number).
196 í£J-í£²ô¢g ÷ô¢_-ú£ÙÜu (Perfect square
number).
F îµ³-ë]æ¨ n ò˶ú‡ ú£ÙÜuõ îµ³êŸhÙ Óõx-í£±pè[« ÚÛ#aêŸ÷ô¢_-ú£ÙÜu Í÷±-꟪ÙC.-1 + 3 + 5 + 7 + ...... (n ú£Ù-Üuõªz =- n2
n(n+1) (2n+1)F 12 + 22 + 32 + ...... + n2 =
6
sö˶ë¯zn(n+1) (2n+1)
∑ n2 = 6
sö˶ë¯zîµ³ë]æ¨ n ú£-á ú£ÙÜuõ ÷ô¦_õ îµ³êŸhÙ
n(n+1) (2n+1)=
6
ÍòÅ°uú£ ví£øŒoõª
ú£÷«ëůû¦õª1-4 2-1 3-2 4-3 5-2 6-2 7-3 8-1
11 x
2
x
5 5 1 11. a = , b = Íô³ê¶ + = .....
3 4 a2 b2
1) 4 2) 3 3) 2 4) 1
2. Ú¨ÙC-î¦-æ¨E áêŸ-í£-ô¢-àŸÙè….-i) 62 + 82 = ? a) 625
ii) 82 + 152 = ? b) 169
iii) 72 + 242 = ? c) 100
iv) 52 + 122 = ? d) 289
1) i-c, ii-d, iii-a, iv-b 2) i-c, ii-b, iii-a, iv-d
3) i-c, ii-b, iii-a, iv-d 4) i-d, ii-c, iii-b, iv-a
√
√
√
3. 21 + 13 + 7 + √4 = ?
1) 25 2) 5 3) 9 4) 12
4. 412, 422 ÷ªëÅ]u Ñìo í£²ô¦gÙ-Ú¥õª ÓEo?1) 84 2) 86 3) 82 4) 88
5. x = 0.2 Íô³ê¶ 3x2 =
1) 1.2 2) 1.
3 3) 1.
8 4) 1.
9
6. Ú¨ÙC-î¦-æ¨ö˺ šíjëǯ-Þœ-J-óŸªû vAÚÛÙ Ú¥EC ÔC?1) (3, 4, 5) 2) (10, 12, 13)
3) (10, 24, 26) 4) (9, 12, 15)
7. ÷´è[ª ÷ô¢ªú£ í£²ô¦gÙ-Ú¥õ îµ³êŸhÙ 110. Íô³ê¶Î ú£ÙÜuõ îµ³êŸhÙ ÓÙêŸ?1) 15 2) 21 3) 18 4) 24
8. û¦õªÞœª ÍÙ·Úõ ÍA šíë]Ì í£J-í£²ô¢g ÷ô¢_-ú£ÙÜuÚÛª,÷´è[Ù-·Úõ ÍA šíë]Ì í£J-í£²ô¢g ÷ô¢_-ú£Ù-ÜuÚÛª ÷ªëÅ]uòÅ˶ë]-ÙêŸ?1) 8840 2) 8904 3) 8841 4) 8740
F F F F F F F F F F F F F F F F F F F F
šíjëǯ-ÞœJ-óŸªû vAÚÛÙ ÍE î�¶æ̈E ÍÙæ°ô¢ª?šíjëǯ-ÞœJ-óŸªû vAÚÛÙ ÍE î�¶æ̈E ÍÙæ°ô¢ª?šíjëǯ-ÞœJ-óŸªû vAÚÛÙ ÍE î�¶æ̈E ÍÙæ°ô¢ª?šíjëǯ-ÞœJ-óŸªû vAÚÛÙ ÍE î�¶æ̈E ÍÙæ°ô¢ª?šíjëǯ-ÞœJ-óŸªû vAÚÛÙ ÍE î�¶æ̈E ÍÙæ°ô¢ª?šíjëǯ-ÞœJ-óŸªû vAÚÛÙ ÍE î�¶æ̈E ÍÙæ°ô¢ª?šíjëǯ-ÞœJ-óŸªû vAÚÛÙ ÍE î�¶æ̈E ÍÙæ°ô¢ª?šíjëǯ-ÞœJ-óŸªû vAÚÛÙ ÍE î�¶æ̈E ÍÙæ°ô¢ª?šíjëǯ-ÞœJ-óŸªû vAÚÛÙ ÍE î�¶æ̈E ÍÙæ°ô¢ª?šíjëǯ-ÞœJ-óŸªû vAÚÛÙ ÍE î�¶æ̈E ÍÙæ°ô¢ª?šíjëǯ-ÞœJ-óŸªû vAÚÛÙ ÍE î�¶æ̈E ÍÙæ°ô¢ª?