Union government notified new rules defining

domicile for the Union Territory of Jammu and

Kashmir (J&K)

According to this, any person residing in

Jammu and Kashmir for 15 years, children of

officials working in the Union Territory for

minimum 10 years and migrants who fulfill

the stated conditions can be eligible for

domicile.

The order also said that any studied for a

period of seven years and appeared in class

10th/12th examination in an educational

institution located in the UT of J&K also

eligible for domicile.

The definition also include children of

Central Government, All India Services

Officers, officials of PSUs etc served in

Jammu and Kashmir for a total period of 10

years or children on parents who fulfill any of

the conditions in sections also eligible for

domicile.

Persons registered as a migrant by the

Relief and Rehabilitation Commissioner

(Migrants) in the UT of J&K, will also be

included in the definition.

Multi-feed Oxygen Manifold

(MOM)

The Andhra Pradesh government came

forward to purchase the ‘portable Multi-feed

Oxygen Manifold’ (MOM), a novel contraption

developed by naval personnel in

Visakhapatnam, that would help meet any

emergency requirement of oxygen supply to

coronavirus patients.

Using this unique device, one cylinder

could be used to supply oxygen to six patients

simultaneously, enabling critical care man-

agement to a larger number of Covid-19

patients with the existing limited resources.

PMCARES

Prime Minister Narendra Modi announced the

constitution of the PM's Citizen Assistance

and Relief in Emergency Situations

(PM-CARES) fund. This will be a dedicated

national fund with the primary objective of

dealing with any kind of emergency or

distress situation, like posed by the COVID-19

pandemic. The account number for the PM

CARES fund is 2121PM20202 with IFSC

code SBIN0000691. The SWIFT code is

SBININBB104 and the UPI id is

pmcares@sbi. Prime Minister is the

Chairman of this trust and its Members

include Defence Minister, Home Minister

and Finance Minister. Citizens and

organisations can go to the website

pmindia.gov.in and donate to PM CARES

Fund. The fund will enable micro-donations

allowing a large number of people will be able

to contribute with smallest of denominations.

Donations to this fund will be exempted from

income tax under section 80(G).

n email: help@eenadupratibha.netøŒEî¦ô¢Ù 11 Ôví‡öËÀ 2020 -

Amara Veeraswamy

Subject Expert

Writer

1. List of Important Days given. The wrong

combination is….

1) World Autism Awareness Day - 2 April

2) World Theatre Day - 30 March

3) World Tuberculosis Day - 24 March

4) International Day of Forests - 21 March

5) World Water Day - 22 March

2. Which state launched PRAGYAAM app to

issue e-passes to everyone associated

with delivery of essential services amid

lockdown?

1) Andhra Pradesh 2) Tamil Nadu

3) Jharkhand 4) Gujarat

5) Manipur

3. B.P. Kanungo was reappointed as…

1) Comptroller and Auditor General of

India

2) Deputy Governor of RBI

3) Chief Information Commissioner

4) Governor of Jammu and Kashmir

5) Health Secretary

4. Indian Army launched which operation to

insulate the 1.3 million strong force from

coronavirus infection?

1) Operation No 2) Operation Carona

3) Operation ARMY

4) Operation Namaste

5) Operation No Shake hand

5. Aadhaar-PAN linking date extended to …

1) 30 June 2020 2) 30 April 2021

3) 31 Dec 2020 4) 30 July 2020

5) 1 July 2020

6. Which nation officially joined as the 30th

member of NATO (of North Atlantic Treaty

Organization)?

1) USA 2) France

3) North Macedonia 4) Switzerland

5) Japan

7. World athletics championships scheduled

to be held at ……….postponed to 2022.

1) Rome, Italy 2) Tokyo, Japan

3) Eugene, USA 4) Canberra, Australia

5) London, UK

8. National Cyber Research, Innovation and

capacity centre was inaugurated at..

1) Mumbai 2) Delhi 3) Jaipur

4) Hyderabad 5) Pune

9. International Conference on Banana 2020

was held in..

1) Andhra Pradesh 2) Karnataka

3) Kerala 4) Tamil Nadu

5) Assam

10. ‘Missing in Action: The Prisoners Who

Never Came Back’ written by..

1) Savita Chhabra 2) Shashi Thorror

3) Chander Suta Dogra

4) John Maxwell Coetzee

5) Nitu Bhattacharya

KEY

1-2 2-3 3-2 4-4 5-1 6-3 7-3 8-4 9-4 10-3

Model Quesitons

Virtual G20 Leaders' Summit

An Extraordinary Virtual G20 Leaders'Summit was convened on 26 March 2020 todiscuss the challenges posed by theoutbreak of the COVID-19 pandemic and to

forge a global coordinated response.

PM Narendra Modi thanked the King ofSaudi Arabia for convening this extraordi-nary session of G20. He called on the G20 tocome out with a concrete action plan to fightthe global pandemic.

At the meeting, G20 Leaders agreed totake all necessary measures to contain thepandemic and protect people. They alsosupported strengthening of the WorldHealth Organization (WHO)’s mandate inthe fight against pandemics, includingdelivery of medical supplies, diagnostictools, treatments, medicines and vaccines.

He added that 90% of the COVID-19cases and 88% of deaths were in G20countries even as they share 80% of worldGDP and 60% of world population.

Aarogya Setu

On 2 April 2020, the ministry of electronics

and IT launched a mobile app called Aarogya

Setu, which will help people in identi-

fying the risk of getting affected by the Corona

Virus.

The app is available in 11 languages and

has been launched on both Andriod and ioS.

It was developed through Public-Private

Partnership under guidance of National

Informatics Center (NIC). The app uses smart

phones’ location data and Bluetooth to see if

a user has been near a Covid-19 infected

person. The app will share user data with the

government in case anyone has been in

contact with a person who has tested positive

for corona virus.

World Bank helps India

World Bank approved fast-track $1 billion

India COVID-19 Emergency Response and

Health Systems Preparedness Project to help

India prevent, detect, and respond to the

COVID-19 pandemic and strengthen its

public health preparedness.

This is the largest ever health sector

support from the World Bank to India.

The fund is part of the World Bank’s first

group of projects, amounting to $1.9 billion

that will assist 25 countries.

The emergency financing is being given to

support better screening, contact tracing and

laboratory diagnostics in the country. It will

also be used to procure personal protective

equipment and set up new isolation wards in

the country.

Mega merger of Banks

The merger of ten state-run banks into four

came into force from 1 April 2020. The

branches of merging banks will operate as of

the banks in which these have been

amalgamated.

Oriental Bank of Commerce and United

Bank of India merged with Punjab National

Bank.

Syndicate Bank merged with Canara Bank.

Allahabad Bank merged with Indian Bank.

Andhra Bank and Corporation Bank merged

with Union Bank of India.

Following the consolidation, there will be

seven large public sector banks (PSBs), and

five smaller ones.

Domicile of Jammu and Kashmir

General

Awareness

Exercise NCC Yogdan

National Cadet Corps (NCC) offered a

helping hand to civilian authorities in the

country’s fight against COVID-19 by

extending the services of cadets under

‘Exercise NCC Yogdan’.

It issued guidelines for temporary

employment of its cadets to augment relief

efforts and functioning of various agencies

involved in battling the pandemic.

The tasks envisaged for NCC cadets

include, manning of helpline/call centres, dis-

tribution of relief materials/medicines/

food/essential commodities; community

assistance, data management and queue &

traffic management.

According to the guidelines, cadets should

not be employed in handling of law and order

situation or for active military duties or at hot

spots.

Rs 1.7 lakh crore relief package

Union government announced a Rs.1.7 lakh

crore relief package aimed at providing a

safety net for those hit the hardest by the

Covid-19 lockdown, along with insurance

cover for frontline medical personnel.

Any health professional, who while treating

Covid-19 patients, meet with some accident,

then he/she would be compensated with an

amount of Rs.50 lakh under the scheme.

About 800 million people will get free cereals

and cooking gas apart from cash through

direct transfers for three months. The first

installment of Rs.2,000 due in 2020-21 will be

front-loaded and paid in April 2020 itself under

the PM KISAN Yojana. Higher wages under

the Mahatma Gandhi National Rural

Employment Act (MGNREGA), Rs.1,000

ex-gratia payment to nearly 30 million poor

senior citizens, widows and disabled as well

were also part of the package.

There are around 3 crore aged widows and

people in Divyang category who are

vulnerable due to economic disruption caused

by COVID-19. Government will give them

Rs.1,000 to tide over difficulties during next

three months.

The States have been asked to use the

Building and Construction Workers Welfare

Fund to provide relief to construction workers

and the first installment of Rs.2,000 under the

Pradhan Mantri Kisan Yojana will be front-

loaded to reach 87 million farmers in April.

Operation Namaste is for?

n email: help@eenadupratibha.netøŒEî¦ô¢Ù 11 Ôví‡öËÀ 2020

Straight Objective Type

1. If |Z − 1| + |Z − 3| ≤ 8, then maximum value

of |Z − 4| is where Z is a complex number.

1) 8 2) 9 3) 10 4) 2

2. If |Z1| = 2, |Z2| = 3, |Z3| = 4 and |Z1 + Z2 + Z3|

= 5 then |4 Z2 Z3 + 9 Z3 Z1 + 16 Z1 Z2| = ?

1) 14 2) 48 3) 96 4) 120

3. If Z is a complex number and P is a point π

satisfying arg Z = . Such that sum of its 4

distances from two given point (0 1) and k

(0 2) is minimum, then P must be (1 + i),3

the numerical value of k should be

1) 1 2) 2 3) 3 4) 4

4. If z is a non zero complex number then

∫50

0

arg (−|z|) dx =

1) 0 2) 50 3) 50π 4) not defined

5. The coefficient of x8 in

x2 x4 x6 x8

(1 + + + + )8

is∠2 ∠4 ∠6 ∠8

1 1 11) 1 2) 3) 4)

8 216 315

6. The remainder when 2323 is divisible by 53 is

1) 7 2) 1 3) 30 4) 0

Numerical Value Type

7. If α is a complex number such that 2α + 1 = z

1 1 1

where z = √−3 and 1 −α2 − 1 α2 1 α2 α7

= − kz then k = ........

24n

8. The fractional part of (n ∈ N) is ........15B. Eswara Rao

Subject Expert

Writer

Complex Numbers, De Moivre’s

theorem and Binomial theorem

Straight Objective Type

1. The number of skew symmetric matrices

of order 3 × 3 by using the elements of the

set A = {−3, −2, −1, 0, 1, 2, 3}

1) 76 2) 77 3) 1 4) 73

2. The number of ways in which TRUE or

FALSE examination of 20 statements can

be answered on the assumption that no

two consecutive questions are answered

the same way

1) 20 2) 21 3) 2 4) 1

3. The number of ways in which four letters

can be selected from the letters of the

word ‘MATHEMATICS’ is ......

∠111) 2) 136

(∠2)3

3) 133 4) 146

4. The probability that a teacher will give a

surprise test during any class meeting is

3/5. If a student is absent on two days.

Then the probability that be will miss

atleast one test is

9 4 21 131) 2) 3) 4)

25 25 25 25

5. If two different numbers are taken

from the set {0, 1, 2, 3, .... 10}, then the

probability that their sum as well

as absolute difference are both multiple

of 4 is

6 7 12 141) 2) 3) 4)

55 55 15 55

6. The least number of times a fair coin

must be tossed. So that the probability of

getting atleast one head is atleast 0.8 is

1) 1 2) 2 3) 3 4) 4

7. If in a frequency distribution, the mean

and median are 21 and 22 respectively

then its mode is

1) 20.5 2) 22 3) 23 4) 24

Numerical Value Type

8. The number of ways of writing 98 as the

product of two positive integers is .....

9. A man alternately tossed a coin and

throws die beginning with coin. The

probability that be gets head before he

gets 5 or 6 on die is.....

Key: 1-4 2-3 3-2 4-3 5-1 6-3 7-4 8-3 9-0.75

Permutation and Combinations:

Probability: Statistics

Straight Objective Type

1. The graph of the function y = f(x) has a

unique tangent at the point (ea 0) through

which the graph passes then

log(1 + 7f(x)) − sin f(x)Lt is

x→ea 3f(x) 1

1) 1 2) 2 3) 0 4) 3

7 29 133 5n + 2n

2. Lt { + + + ...... + } =10 102 103 10n

n→∝7 3 5

1) 2) 3) 4) 010 4 4

sin 2x + 2 sin2 x − 2 sin x3. Lt =

x→0 cos x − cos2 x

1) 0 2) 1 3) −1 4) 4

4. If [x] denote the greatest integer less than

or equal to x then

[x] + [2x] + [3x] +......+ [nx]Lt =

n→∝ n2

x x x1) x 2) 3) 4)

2 3 4

5. Let f be a continuous function on R such

1 n2

that f () = sin (en). e−n2 + , then4n n2 + 1

f(0) = 1

1) 0 2) 3) 1 4) 22

6. If f(x) = minimum of {x, x2} ∀ x ∈ R, then

f(x) is

1) discontinuous at 0

2) discontinuous at 1

3) continuous on R 4) continuous at 0, 1

(cosx)12 − (cosx)

13

7. Lt = x→0 sin2x

1 1 1 11) 2) − 3) 4) −

6 6 12 12

ex2− cosx

8. Lt =x→0 x2

3 1 11) 2) 3) 1 4)

2 2 4

9. If a, b are chosen from {1, 2, 3, 4, 5, 6, 7}

randomly with replacement. The

ax + bx

probability that Lt ()2/x

= 7 is..x→0 2

1 2 3 41) 2) 3) 4)

49 49 49 49

xtan 2x − 2x tanx 10. Lt =

x→0 (1 − cos 2x)2

1 11) 2 2) −2 3) 4) −

2 2

Numerical Value Type

1 911. Suppose f(n + 1) = { f(n) + }, n ∈ N

2 f(n)

if f(n) > 0, ∀ n ∈ N then Lt f(n) = ......n→∝

sin(πcos2 x)12. Lt = ..........

x→0 x2

Key: 1-2 2-3 3-4 4-2 5-3 6-3 7-4 8-1 9-2

10-3 11-3 12-3.14

Limits and Continuity

Straight Objective Type

1. The negation of −s v (− r ^ s) is equiva-

lent to

1) s v (r v ~ s) 2) s ^ r

3) s ^ (−r) 4) s ^ (r ^ (−s))

2. P ^ (−P) ⇒ P is

1) a tautology 2) a contradiction

3) a tautology and a contradiction

4) Neither a tautology nor contradiction

3. If a , b, c are in A P : b, c, d are in G P

and c, d, e are in H P if a = 2, e =18 then

sum of all possible values of C is

1) −6 2) 6 3) 12 4) 0

4. If a, b, c are positive real numbers such

that their product is 64. Then minimum

value of b is

1) 4 2) 3 3) 2 4) 1

5. If 100 times, the 100th term of A.P with

non zero common difference equals the

50 times its 50th term then 150th term of

the A.P is

1) 150 2) 0

3) −150 4) 150 times its 50th term

6. For any three positive real numbers a, b, c

9(25a2 + b2) + 25 (c2 − 3ac) = 15b

(3a + c) then

1) b, c, a are in A.P

2) a, b, c are in A.P

3) a, b, c are in G.P

4) b, c, a are in G.P

7. If sets A and B have 3 and 6 elements

each then the minimum number of

elements in A U B is

1) 3 2) 6 3) 9 4) 18

8. If W denote the words in the english

dictionary. Define the relation of R by

R = {(x y) ∈ W × W / the words x and y

have at least one letter in common}then r is

1) reflexive, symmetric and not transitive

2) reflexive, symmetric and transitive

3) reflexive, not symmetric and transitive

4) not reflexive, symmetric and transitive

Numerical Value Type

9. If n (A ∩ Bc) = 5; n (B ∩ A

c) = 6,

n (A ∩ B) = 4 and (A ∪ B) = K

KThen the value of = ...........

30

10. Sum to Infinity of the series

2 6 10 141 + + + + + ......... ∞

3 32

33

34

Mathematical Reasoning: Sequence

and Series, Sets, Ralations

JEE MAINMathematics

Straight Objective Type

1. If ax2 + bx + 6 = 0 does not have two dis-

tinct real roots, where a, b ∈ R then the

least value of 3a + b is ....

1) −1 2) −2 3) −3 4) −4

2. The equations x2 + 3x + 5 = 0 and

ax2 + bx + c = 0 have a common root, if

a, b, c ∈ N then the least possible value of

a + b + c is equal to

1) 1 2) 6 3) 9 4) 12

3. Let f(x) = (1 + b2) x2 + 2bx + 1 and m(b) be

the minimum value of f(x). As b varies, the

range of m (b) is

11) [−1 1] 2) [0 ] 3) (1 2] 4) (0 1]

2

4. The set of values of x for which the

inequality [x]2 − 5[x] + 6 ≤ 0 holds good

(where [.] denote the greatest integral

function)

1) 1 ≤ x < 2 2) 2 ≤ x < 3

3) 1 ≤ x < 3 4) 2 ≤ x < 4

5. If x3 + ax + 1 = 0 and x4 + ax2 + 1 = 0

have a common root then a =

1) −2 2) 2 3) 3 4) −3

6. The number of real roots of the equation

1 3 1(x + ) + (x + ) = 0 isx x

1) 2 2) 3 3) 6 4) 0

Numerical Value Type

7. The number real roots of

(6 − x)4 + (8 − x)4 = 16 is .....

8. If both the roots of the equation x2 − 2ax +

a2 − 1 = 0 lie in the interval

(−3 4) then sum of integral parts of ‘a’ is ......

Key: 1-2 2-3 3-4 4-4 5-1 6-4 7-2 8-0

Quadratic Equation and

Expressions, Theory of Equations

Key: 1-2 2-4 3-2 4-3 5-4 6-3 7-3 8-0.06

Key: 1-2 2-1 3-4 4-1 5-2 6-1 7-2 8-1 9-0.5 10-3

The number real roots of ?