Bihar PGT Mathematics Mock Test - 5 - Bihar PGT/TGT/PRT MCQ

The statement shows that ONGC is claiming to have started a new refinery at Digboi. This shows an activity that has been executed in the past and the sentence has to be in the simple past tense.
Thus only option 3 fulfills this criteria and hence is correct. 

The correct option is Option 2, i.e., ‘get down to’.
The sentence talks about a manager telling his subordinates that enough discussion was done and it was time to work. The phrasal verb ‘get down to’ means ‘to get serious about something’. Hence, the correct option is Option 2.

समास - दो या दो से अधिक शब्दों से मिलकर जो नया और छोटा शब्द बनता है उस शब्द को हिन्दी में समास कहते हैं।

युद्धभूमि शब्द का समास विग्रह - युद्ध के लिए भूमि (सम्प्रदान तत्पुरुष समास)

तत्पुरुष समास - वह समास है जिसमें बाद का अथवा उत्तर पद प्रधान होता है तथा दोनों पदों के बीच का कारक-चिह्न लुप्त हो जाता है। वह समास है जिसमें बाद का अथवा उत्तर पद प्रधान होता है तथा दोनों पदों के बीच का कारक-चिह्न लुप्त हो जाता है। 

विभक्तियों के नामों के अनुसार तत्पुरुष समास के छः भेद हैं-

कर्म तत्पुरुष - को 

करण तत्पुरुष - से और के द्वारा 

सम्प्रदान तत्पुरुष - के लिए और को 

अपादान तत्पुरुष - से 

सम्बन्ध तत्पुरुष - का, के, की

अधिकरण तत्पुरुष - में पर और पर

अत: विकल्प (B) सही है I

वर्ण - हिन्दी भाषा में प्रयुक्त सबसे छोटी इकाई वर्ण कहलाती है।

य वर्ण का उच्चारण स्थान – तालु है।

तालु से उच्चारित वर्ण - इ,च,छ,ज,झ, ञ , य,श

अत: विकल्प (A) सही है I

केशव अलंकार सम्प्रदायवादी आचार्य कवि थे। इसलिये स्वाभाविक था कि वे भामह, उद्भट और दंडी आदि अलंकार सम्प्रदाय के आचार्यों का अनुसरण करते। इन्होंने अलंकारों के दो भेद माने हैं, साधारण और विशिष्ट। साधारण के अन्तर्गत वर्णन, वर्ण्य, भूमिश्री-वर्णन और राज्यश्री-वर्णन आते है जो काव्यकल्पलतावृत्ति और अलंकारशेखर पर आधारित हैं।

अत: विकल्प (C) सही है I

मुहावरा मूलत: अरबी भाषा का शब्द है जिसका अर्थ है बातचीत करना या उत्तर देना। कुछ लोग मुहावरे को 'रोज़मर्रा', 'बोलचाल', 'तर्ज़ेकलाम', या 'इस्तलाह' कहते हैं I

तन पर नहीं लत्ता, पान खाए अलबत्ता मुहावरे का अर्थ - झूठा दिखावा करना I

अत: विकल्प (D) सही है I

समाधान : इसका सही उत्तर विकल्प घर - लोक है। अन्य विकल्प इसके अनुचित हैं। 

भवन का अर्थ - घर

भुवन का अर्थ - लोक

अतः विकल्प (B) सही है।

The logic follows here is:

In a figure:

Middle number = (Top number × bottom number) - (left number × right number) 

In fig 1:

Middle number = (9 × 10) - (7 × 8)

= 90 - 56

= 34

In fig 2:

Middle number = (12 × 8) - (8 × 7)

= 96 - 56

= 40

Similarly,

In fig 3:

Middle number = (11 × 7) - (4 × 9) 

? = 77 - 36

? = 41

Hence, the correct answer is "41".

Key Points

Monsoon in India:

• The southwest monsoon sets in over the Kerala coast by 1st June and moves swiftly to reach Mumbai and Kolkata between 10th and 13th June.
• By mid-July, southwest monsoon engulfs the entire subcontinent
• During April and May when the sun shines vertically over the Tropic of Cancer, the large landmass in the north of the Indian ocean gets intensely heated.
• This causes the formation of intense low pressure in the northwestern part of the subcontinent.
• Since the pressure in the Indian Ocean in the south of the landmass is high as the water gets heated slowly, the low-pressure cell attracts the southeast trades across the Equator.
• These conditions help in the northward shift in the position of the ITCZ.
• The southwest monsoon may thus, be seen as a continuation of the southeast trades deflected towards the Indian subcontinent after crossing the Equator.
• These winds cross the Equator between 40°E and 60°E longitudes.
• The shift in the position of the ITCZ is also related to the phenomenon of the withdrawal of the westerly jet stream from its position over the north Indian plain, south of the Himalayas.
• The easterly jet stream sets in along 15°N latitude only after the western jet stream has withdrawn itself from the region.
• This easterly jet stream is held responsible for the burst of the monsoon in India.

Hence, the Mansoon arrives in India approximately in early June.

The correct answer is the 86^th amendment.

Key Points

• The 86^th amendment to the Constitution of India in 2002, provided the Right to Education as a Fundamental Right in Part-III of the Constitution.
• The amendment inserted Article 21A which made the Right to Education a fundamental right for children between 6-14 years.
• The 86^th amendment provided for follow-up legislation for Right to Education Bill 2008 and finally Right to Education Act, 2009.

The correct answer is Humayun.

Key Points

  Humayun:

• Din Panah was the sixth city of Delhi constructed by the second Gurkani emperor Humayun during his reign stretching from the early to the mid 15th century as a symbol of imperial tolerance of all religions, particularly the different sects of Islam.
• It was among the first cities to be built by the Gurkanis after their entry in Hindustan and at one point of time so popular for its open-arm welcome to the learned and wise, it is believed to have overshadowed towns and cities of Persia, Central Asia, and Turkey as the center of Islamic culture.
• During World War II, its citadel was home to Japanese detainees and later during the partition of former British India, a shelter for thousands of refugees in transit for present-day India and Pakistan. Today, only the citadel survives and is a historical attraction.

Additional Information

• Akbar:
  • ​Hamzanama paintings were produced during the reign of Akbar.
  • ​He was the third Mughal Emperor.
    • He reigned from 1556 to 1605.
    • He introduced the Mansabdari system. 
    • He built the Agra fort.
• Jahangir:
  • He reigned from 1605 to 1627.
  • He established Zanjis-i-Adil (chain of justice) at Agra for the seekers of royal justice.
  • He married Mehr-un-Nisa whom he gave the title of Nur Jahan (light of the world). 
  • He wrote his autobiography Tuzuk-i-Jaha.
• Babur:
  • ​He was the founder of the Mughal Empire in India.
  • Baburnama, also known as Tuzk-e Babri is the biography of Babur written by him.
  • Humayun was the son of Babur.

In the question,

11² = 121

13² = 169

17² = 289

19² = 361

23² = 529

24² = 576

Thus we can say except for (24)² , all the given number is a square of a prime number.

Hence, Option (2) is correct.

The correct answer is Dublin.

• Dublin is the capital and largest city of Ireland.

13.24 + 24.35 + 35.46 – 46.57 = 2 × ?

⇒ 73.05 – 46.57 = 2 × ?

⇒ 26.48 = 2 × ?

⇒ 26.48/2 = ?

∴ 13.24 = ?

The correct answer is Twelfth Five year plan

Key Points

• Planning Commission was replaced by a new institution – NITI AAYYOG on January 1, 2015, with emphasis on ‘Bottom–Up’ approach to envisage the vision of Maximum Governance, Minimum Government, echoing the spirit of ‘Cooperative Federalism.
• 12^th Five-year plan was underway from 2012-2017.
• Administrative Setup
  • Chairperson: Prime Minister
  • Vice-Chairperson: To be appointed by the Prime-Minister
  • Governing Council: Chief Ministers of all states and Lt. Governors of Union Territories.
  • Regional Council: To address specific regional issues, Comprising Chief Ministers and Lt. Governors Chaired by Prime Minister or his nominee.
  • Ad-hoc Membership: 2 members in ex-officio capacity from leading Research institutions on a rotational basis.
  • Ex-Officio membership: Maximum four from the Union council of ministers to be nominated by the Prime minister.
  • Chief Executive Officer: Appointed by Prime-minister for a fixed tenure, in rank of Secretary to Government of India.
  • Special Invitees: Experts, Specialists with domain knowledge nominated by Prime-minister.

Additional Information

The correct answer is the Nationalist Congress Party.

Nationalist Congress Party:

• Founded- 25 May 1999.
• Founder- Sharad Pawar, P.A. Sangma, and Tariq Anwar.
• Party Philosophy- Progressivism, Populism, Secular democracy, Gandhian secularism, Egalitarianism, Social justice, Federalism, Social conservatism, Nationalism.
• Election Symbol- Clock.
• Student wing- Nationalist Student Congress.

All India Trinamool Congress:

• Founded- January 1998
• Founder- Mamata Banerjee
• Party Philosophy- Secularism and populism.
• Election Symbol- Twin flowers in the grass.
• Student wing- Trinamool Chhatra Parishad.

Indian National Congress:

• Founded- 1885.
• Founder- Allan Octavian (A.O) Hume.
• Party Philosophy- Indian Nationalism (Liberal nationalism), Social democracy, Democratic socialism, Gandhian socialism, Progressivism.
• Student wing- National Students Union of India (NSUI).
• Election Symbol- The hand.

Bahujan Samaj Party:

• Founded- April 14, 1984.
• Founder- Kanshi Ram.
• Party Philosophy- Human rights, Social equality, Secularism, Social justice, Self-respect.
• Election Symbol- Elephant.

Concept-

Vestigial organs are the organs that once were useful in an animal's body millions of years ago, but now they are useless or very close to useless.

Key Points Human heart-

• The human heart is not vestigial as at present times it has its own functions in the human body.
• The human heart is an organ that pumps blood throughout the body.
• Heart pumps the blood through the vessels of the circulatory system, supplying oxygen and nutrients to the tissues and removing carbon dioxide and other wastes.
• The tissues of the body need a constant supply of nutrition in order to be active which is performed by blood.

Additional Information Wisdom teeth

• Wisdom teeth are no longer totally necessary. Today, humans cook food to soften it, and we can cut and crush it with utensils.So at this time they are vestigial.
• Early humans needed to chew coarse, hearty foods, they required a broader jaw.
• Wisdom teeth grew in to give them more chewing power for this purpose.

Nictitating membrane of eye

• In humans, the nictitating membrane is the pink lump in the inner corner of the eyes which is known as the caruncula lacrimalis.
• In this structure, the remaining of the nictitating membrane are permanently folded into that corner and no longer functional.So it is vestigial.

Vermiform appendix

• The human appendix may be considered as a vestigial organ as it has been proved that the removal of the organ after infancy does not create any harm.
• Its function is to digest cellulose.

The logic follows here is:-

1st and 3rd letters are interchanged.

4th and 6th letters are interchanged.

And 2nd letter is placed as it is.

Similarly,

Hence, the correct answer is "TNMFED".

cosα - isinα is root of zⁿ + a₁z^n-1 + a₂z^n-2 + ----
a_n (1/z)ⁿ + a_n-1(1/z)^n-1 + -------+ a₁(1/z) + 1 = 0.
-----+a_n-1z+a_n = 0 i.e of
Equating real and imaginary parts on both sides, 

a_n cos nα + a_n-1 cos (n-1)α + -----+a₂ cos 2α + a₁ cos α + 1 = 0

P(n) = 4 + 8 + 12 +……+ 4n = 2n (n + 1)
P(6) = 4 + 8 + 12 +……+ 4(6) 
= 2(6)[(6) + 1)]

x-y-3=0

n(A) = 4 and n(B) = 2

Therefore, n(A x B) = 8

Number of subsets of A x B having atleast 3 elements = 2⁸ – ⁸C₀ – ⁸C₁ – ⁸C₂

= 256 – 1 – 8 – 28

= 219

or a symmetric matrix A’ = A . therefore , 

∫tan(log x) dx
log x = t
x = e^t
dx = e^t dt
f(t) = ∫tan t dt
f’(t)= sec² t
= sec²(log x)

5th term in the expansion of (x²/2 − 2/x²)¹² is
Tr+ 1= nCr x^r* y^(n−r)
T5 = 12C4[(x²/2)⁴ (-2/x²)⁸]
= (12! * x⁸ * 2⁸)/ (4! * 8! *2⁴ * x¹⁶)
= 7920x⁻⁴

Let
X – no. of correct answers by guessing in the set of 5 multiple choice questions. 5 multiple choice questions.
Probability of success = p = 1/3
Probability of failure = q = 1 - p = 2/3
P(r) = ⁿC_r p^rq^n-r  r = 0,1,2,,....n
P (guessing more than 4 correct answers)


 

The greatest integer function ⌊x⌋ returns the largest integer less than or equal to x. For x², this means that ⌊x²⌋ will be the greatest integer less than or equal to x².

The integral becomes:

The function ⌊x²⌋ will be 0 on the interval (0,1)(0,1), 1 on the interval [1,√2​], and 4 on the interval [√2,2].

So, the integral is the sum of the areas of these intervals:

Evaluating these integrals:

So, the value of the integral is 4.