Bihar PGT Mathematics Mock Test - 4 - Bihar PGT/TGT/PRT MCQ

The students can be seen waiting for their results in the given statement. Thus, it has to be in the present continuous tense.
Option 3 is the only option that makes an appropriate fit in the given sentence. 

'किरातार्जुनीयम्' के लेखक भारवि है।

किरातार्जुनीयम् 18 सर्गो और 1030 श्लोकों का एक महाकाव्य है।

कथानक— महाभारत के वन पर्व पर आधारित है। इसमें अर्जुन द्वारा शिव तपस्या से पाशुपतास्त्र प्राप्ति का वर्णन है।

अत: विकल्प (A) सही है I

जसोदा हरि पालनैं झुलावै। 
हलरावै, दुलराइ मल्हावै, जोइ-जोइ कछु गावै॥ 

उपर्युक्त पंक्तियों में यशोदा जी के द्वारा कृष्ण को झुला झुलाना और खिलाना और गीत गाने का भाव प्रस्तुत है जिससे श्रोता के मन में एक बचपन की झलक उत्पन्न होती है अत: पंत्ति में वात्सल्य रस है।

वात्सल्य रस - वात्सल्य रस का स्थायी भाव वात्सल्यता होता है वात्सल्य रस में माता का पुत्र के प्रति प्रेम, बड़ों का बच्चों के प्रति प्रेम, और यही स्नेह और प्रेम का भाव वात्सल्य रस कहलाता है।

अत: विकल्प (B) सही है I

निर्मला हिंदी का एक सबसे महत्वपूर्ण उपन्यास है। निर्मला हिंदी के महान उपन्यासकार प्रेमचंद की रचना है। प्रेमचंद द्वारा लिखित हिंदी की अन्य महत्वपूर्ण रचनाएँ- गोदान, गबन, कफ़न, सेवासदन, कर्मभूमि रंगभूमि आदि है I

अत: विकल्प (A) सही है I

यमक शब्द का अर्थ होता है - दो, जब एक ही शब्द ज्यादा बार प्रयोग हो पर हर बार अर्थ अलग-अलग आये वहाँ पर यमक अलंकार होता है। अर्थात जिस प्रकार अनुप्रास अलंकार में किसी एक वर्ण की आवृति होती है I

अत: विकल्प (B) सही है I

The correct answer is Robert Clive.

Key Points

When Alivardi Khan died in 1756, Sirajuddaulah became the nawab of Bengal.

• The Company was worried about his power and keen on a puppet ruler who would willingly give trade concessions and other privileges.
• So it tried, though without success, to help one of Sirajuddaulah’s rivals become the nawab.
• An infuriated Sirajuddaulah asked the Company to stop meddling in the political affairs of his dominion, stop fortification, and pay the revenues.
• After negotiations failed, the Nawab marched with 30,000 soldiers to the English factory at Kassimbazar, captured the Company officials, locked the warehouse, disarmed all Englishmen, and blockaded English ships.
• Then he marched to Calcutta to establish control over the Company’s fort there.

Important Points

• On hearing the news of the fall of Calcutta, Company officials in Madras sent forces under the command of Robert Clive, reinforced by naval fleets.
• Prolonged negotiations with the Nawab followed.
• Finally, in 1757, Robert Clive led the Company’s army against Sirajuddaulah at Plassey. 
• The Battle of Plassey became famous because it was the first major victory the Company won in India.

Thus, it is clear that Robert Clive led the company's army against Sirajudallah at Plassey.

Additional Information

• James Mill was a famous economist and political philosopher from Scotland.
• The Permanent Settlement of Bengal was brought into effect by the East India Company headed by Governor-General Lord Cornwallis in 1793.
• Lord Dalhousie devised a policy that came to be known as the Doctrine of Lapse.

The logic that follows here is 

1) D is sitting to the immediate left of A.

2) C is sitting to the immediate right of B.

3) B is not sitting adjacent to A.

The final seating arrangement will be

Second to the right of D is 'E'.

Hence, the correct answer is E.

The correct answer is Todar Mal.

• As Akbar's finance minister, Raja Todar Mal has implemented a new revenue system called zabt, and a tax system called dahshala.
  • He took a careful survey of crop yields and cultivated prices for a ten-year 1570–1580 era. 
  • On this basis, the tax has been set in cash on each harvest.
  • Each province was divided into income circles with its own tax rates and an individual crop schedule.
  • There was a prevalence of this method where the Mughal administration could survey the land and keep careful records.

Important Points 

• The Akbar territory was divided into 15 Subahs for the revenue system, further subdivided into a total of 187 Sarkars across 15 subahs, and those 197 sarkars (sirkar) were subdivided into a total of 3367 Mahals or Pargana.

Given: Neptune, Planet, Moon

The logic followed here is: Neptune is a Planet, but Moon is not. Moon is a natural satellite.

Hence, option (4)  is the correct answer.

The first figure is a triangle, then there are 3 line segments inside it.

Similarly,

Circle, then there should be 3 line segments inside it.

The figure is shown below:-

Hence, Option (2) is the correct answer.

At the State level, the Council of Ministers is the executive body of the state that assists the Governor in the administration.

Important Points

The Council of Ministers consists of the Chief Minister and other ministers.

• The Chief Minister is appointed by the Governor while the other members of the council are appointed by the Governor on the advice of the Chief Minister.
• The Council of Ministers takes the policy decisions and advises the Governor on important issues.
• The council submits bills to the Assembly and initiates them.
• It gives directions to partner states and institutions of the community.
• It considers the budget of the community.
• It controls the finance of the state.
• It makes the rules and regulations for the staff.
• It submits the annual progress reports and makes the agenda of the meetings.
• It establishes the Sectorial Committees.

Thus, it is clear that the Governor appoints the Council of Ministers of a State. 

Key Points 

• The biosphere reserves are the areas meant for the conservation of biodiversity.
• These are large areas of protected land for the conservation of wildlife, plant and animal resources and traditional life of the tribals living in the area.
• The biosphere reserves help to maintain the biodiversity and culture of that area.
• A biosphere reserve may also contain other protected areas.
• The Pachmarhi Biosphere Reserve consists of one national park named Satpura and two wildlife sanctuaries named Bori and Pachmarhi

Additional Information

• There are18 biosphere reserves in India:-
  • Cold Desert, Himachal Pradesh
  • Nanda Devi, Uttrakhand
  • Khangchendzonga, Sikkim
  • Dehang-Debang, Arunachal Pradesh
  • Manas, Assam
  • Dibru-Saikhowa, Assam
  • Nokrek, Meghalaya
  • Panna, Madhya Pradesh
  • Pachmarhi, Madhya Pradesh
  • Achanakmar-Amarkantak, Madhya Pradesh-Chhattisgarh
  • Kachchh, Gujarat
  • Similipal, Odisha
  • Sundarban, West Bengal
  • Seshachalam, Andhra Pradesh
  • Agasthyamala, Karnataka-Tamil Nadu-Kerala
  • Nilgiri, Tamil Nadu-Kerala 
  • Gulf of Mannar, Tamil Nadu
  • Great Nicobar, Andaman & Nicobar Island

 replacing x and y both by 1, we get

Since a, b, c are in H.P.

Now log (a + c) + log (a – 2b + c)
= log [(a + c){(a + c) – 2b}]
= log [(a + c)² – 2b (a + c)]
= log [(a + c)² – 2 × 2ac]
= log (a – c)² or log (c – a)²
= 2 log (a – c) or 2 log (c – a)
∴ log (a + c) + log (a – 2b + c) = 2 log (c – a)

We have , 

Therefore, range of f(x) is {-1}.

The sign of the sinA and tanA in third quadrant is negative and positive.

If A and B are square matrices of same order , then , product of the matrices is not commutative.Therefore , the given result is true only when AB = BA.

As value of both determinants are equal
∴ (1×1) - (1×1) = 4x - 2
0 = 4x-2.
4x = 2.
x = 2/4 = 1/2

The correct answer is b) 8

2a² + 3b² = 35

3b² = 35 – 2a²

The maximum value on RHS is 35.

3b² ≤ 35

b² ≤ 11.66

b = 0, ± 1, ± 2, ± 3….

3b² = 35 – 2a²

Any number multiplied by 2 gives an even number. 

3b² is odd.

If b = 0, then 3b² is not odd.

If b = ± 1, then 3b² is odd.

If b = ± 2, then 3b² is even.

If b = ± 3, then 3b² is odd.

3b² = 35 – 2a²

If b = ± 1, then b² = 1,

3 = 35 – 2a²

2a² = 32

a² = 16

a = ± 4

If b = ± 3, then b² = 9 

27 = 35 – 2a²

2a² = 8

a² = 4

a = ± 2

[(4, 1), (4, -1), (-4, 1), (-4, -1), (2, -3), (2, 3), (-2, 3), (-2, -3)]

Therefore there are 8 elements in total.

Upper Triangular matrix is given by  :
.
 Here, a_ij=0 , if i is greater than j.and a_ij ≠ 0, if I is less than j.

Let
X = TATANAGAR
Y = CALCUTTA
P(X) = P(Y) = 1/2
E – Two consecutive letters TA are visible.
Two consecutive letters from X are TA, AT, TA, AN, NA, AG, GA, AR

Two consecutive letters from Y are CA, AL, LC, CU, UT, TT, TA

∴ By Bayes Theorem,

A and B are disjoint set so their is no common element between A and B.
n(AuBuC) = n(A)+n(B)+ n(C)-n(AnB)-n(Anc)-n(BnC)+n(AnBnC)
As we know n(AuB)=n(A)+ n(B)-n(AnB)
Here when we add A and B we are adding (AnB) two times , as it is present in both A and B. So we subtract (AnB) one time from A and B.
Which means we need to take the area of A and B set but no area should repeat.
When we take three sets A,B and C
We take area of A+ Area of B + area of C ————eq
But they are intersecting so the area we are taking is greater than actual area. We have again added (AnB), (AnC) and (BnC) twice. Therefore we subtract the intersecting area from eq one time as done above
A+B+C-(AnB)-(AnC)-(BnC)
 
The intersection of the sets a and b is the set of all the elements which belong to both A and B. It is denoted by A ∩ B (“A intersection B”).
• If A and B do not have any element in common then A ∩ B= a null set = Ø.

On comparing the given equations with: 
, we get: 

^n+r-1C_r-1

12(x) >30

=> x>30/12 

=> x>2.5

=>x=3 

Put,
cos^-1x = θ ⇒ x = cos θ ⇒ cos θ