Bihar PGT Mathematics Mock Test - 1 - Bihar PGT/TGT/PRT MCQ

'Working against the clock' means to do it as fast as possible and try to finish it before a certain time.
Option 4 is hence the correct option.
Example- The students worked against the clock to get their final presentation ready before the committee.

The correct answer is Option 4. The correct spelling is ‘embarrassment’. 

Atheist' is a person who strongly disbelieves in the existence of God. Option 3 is thus the correct answer.
All other alternatives have no relation to the given phrase. Stubborn stands for a person who is adamant, bogus is something that is not to be taken seriously and devout is a person who believes in God strongly.

Slander is to work on lines so as to defame the character and image of a person. Thus, defame is the nearest synonym to slander.   
Example- During elections, there is a fest of defamation between politicians.

उपर्युक्त विकल्पों में से 'शुद्ध वर्तनी वाला शब्द 'नीरस' है। 

नीरस के पर्यायवाची शब्द हैं - फीका, बेरस, बेजायका, अस्वाद।

A man walks 30 meters towards South, then turning to his right, he walks 30 meters, then turning to his left, he walks 20 meters, again turning to his left, he walks 30 meters. The figure are given below -

50 meters far is he from his starting point.

Hence, "50 meters" is the correct answer.

The logic is :

1) BEH

2) KNR

3) GJM

4) TWZ

Hence, 'KNR' is the odd letter.

Hence. the person will be allowed to appear in the interview.

The logic follows here is:

In fig 1:

12 = 6 ÷ 2 × 4

12 = 3 × 4 

12 = 12

In fig 2:

80 = 20 ÷ 2 × 8

80 = 10 × 8

80 = 80

Similarly,

63 = ? ÷ 2 × 21

63 / 21 = ? ÷ 2

3 = ? ÷ 2

? = 3 × 2

? = 6

Hence, the correct answer is "6".

The correct answer is Odisha.

Key Points

• The Tropic of Cancer is an imaginary line north from the Equator at an angle of 23.50 degrees.
• Tropic of Cancer passes through 16 countries, 3 continents, and 6 water bodies.
• It passes through 8 Indian states.
  

Additional Information

Given:

Five years ago, father's age was 5 times that of his son

After 3 years father will be 3 times as old as his son

Calculation:

Let the present age of son be x years 

Present age of father be y years 

According to the question,

Five years ago, father's age was 5 times that of his son

(y - 5) = 5 (x - 5)

⇒ y - 5 = 5x - 25 

⇒ y - 5x + 20 = 0     ---- (i)

After 3 years father will be 3 times as old as his son

(y + 3) = 3(x + 3)

⇒ y + 3 = 3x + 9

⇒ y - 3x - 6 = 0      ---- (ii)

Solving equation (i) and (ii) we get,

x = 13

∴ Present age of son is 13 years

The correct answer is The Supreme Court.

Key Points 

• The Supreme Court of India is called the custodian of the Constitution in India.
• The highest court in India, the Supreme Court is considered as the guardian of the Constitution.
• The conflicts or quarrels of jurisdiction between the central government and the state governments or between the legislature and the executive are decided by the court.
• It upholds and uplifts the rule of law and also ensures and protects citizens’ rights and liberties as given in the Constitution.
• Therefore, the Supreme Court is also known as the Guardian of the Constitution.​

Additional Information 

• The Indian constitution provides for a provision of the Supreme Court under Part V (The Union) and Chapter 6 (The Union Judiciary).
• The Supreme Court of India is the highest judicial court and the final court of appeal under the Constitution of India, the highest constitutional court, with the power of judicial review.
• India is a federal state and has a single and unified judicial system with a three-tier structure, i.e. Supreme Court, High Courts, and Subordinate Courts.

The correct answer is Liver.

Key Points

• Excessive consumption of alcoholic drinks causes damage to the Liver.
  • Alcohol is readily absorbed from the digestive tract, and up to 98% is metabolised in the liver.
  • Each liver cell contains three pathways for alcohol metabolism.
  • All of these result in the production of a highly toxic metabolite which can contribute to liver cell damage.
  • With regular alcohol use, the regenerative ability of liver cells may be inhibited and lead to sustained liver damage.
  • Long term heavy alcohol use may lead to fat accumulation in the liver, which may progress to alcoholic hepatitis, or liver cirrhosis.
  • Over time, excessive alcohol use can lead to the development of chronic diseases and other serious problems including -
    • High blood pressure, heart disease, stroke, liver disease, and digestive problems. 

Additional Information

• Kidney:
  • Healthy kidneys remove wastes and extra fluid from your blood.
  • But when your kidneys fail, wastes and extra fluid can build up in your blood and make you feel sick. 
  • Kidneys can become damaged from a physical injury or a disease like diabetes, high blood pressure, or other disorders.
  • High blood pressure and diabetes are the two most common causes of kidney failure.
  • Kidney failure does not happen overnight.
• Lungs:
  • Chronic alcohol abuse and heavy drinking can greatly increase the risk of several pulmonary conditions.
    • including lung disease, alcoholic pneumonia, acute lung injury, and acute respiratory distress syndrome.
  • Smokers are more likely than nonsmokers to develop heart disease, stroke, and lung cancer.
    • Smoking can cause lung disease by damaging your airways and the small air sacs (alveoli) found in your lungs.
    • Lung diseases caused by smoking include COPD, which includes emphysema and chronic bronchitis.
• Heart:
  • Smokers are at greater risk for diseases that affect the heart and blood vessels.
  • Increases in your blood pressure can also be caused by weight gain from excessive drinking.
  • Heavy drinking weakens the heart muscle, which means the heart can't pump blood as efficiently.
    • It's is known as cardiomyopathy and can cause death, usually through heart failure.

Given:

No of possible outcomes when two dice are thrown simultaneously: 6 × 6 = 36 

(1,1), (1, 2), (1, 3),  (1, 4), (1, 5), (1, 6) 

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6) 

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6) 

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

Formula used:

Probability = No of favorable outcome ÷ No of total outcomes 

Calculation:

No of outcome with sum 12 (6, 6) = 1

∴ Required probability = 1/36 

The correct answer is Mawsynram.

Key Points

• The highest rainfall in India and the world is recorded at Mawsynram village of Meghalaya.
• It is also known as the land of clouds.
• Mawsynram is a village located in the East Khasi Hills in the district of Meghalaya state in northeastern India, which is 65 kilometres from Shillong.
• Mawsynram receives approximately 11,872 millimetres of rain in an average year.
• The main majority of rains is during the monsoon season.
• Basically, due to the high altitude, it rarely gets truly hot in Mawsynram.
• 14,234 mm is the recorded rainfall in the year 2010.
• According to the Guinness Book of World Records, Mawsynram received 26,000 millimetres (1,000 in) of rainfall in 1985.

Additional Information 

• The second rainiest place is Cherrapunji, which is also located in Meghalaya.
• Here the average annual rainfall is around 11,430 mm (450 in) per year.
• India is a vast country in geographical terms, with various regions experiences very different climatic conditions.
• This is also reflected in the distribution of rainfall in India. Some regions experience very high rainfall and others receive very scanty rainfall.
• The difference between the recorded highest and lowest rainfall in India is approximately 1178 cm.

In a ΔABC, we know that
tanA + tanB + tanC = tanA tanB tanC
∴ tanB + tanC = tanA(tanBtanC – 1) 


⇒ tan² B - (K - 1) tan B + K = 0
For real values of tan B, Disc.
(K – 1)² – 4K > 0 
K² – 6K + 1 > 0 

sin(n+1)x cos(n+2)x - cos(n+1)x sin(n+2)x
⇒ sin[(n+1)x - (n+2)x] 
As we know that sin(A-B) = sinA cosB - cosA sinB
⇒ sin(n+1-n-2)
sin(-x) 
= -sinx

f(x) = x
g(x) = cosx 
D(f) = R
D(g) = R
D(f+g) = D(f) ⋂ D(g)
So , D(f+g) = R
Therefore, given function is defined for real numbers.

And y has a relative minimum at x = 0 if f ‘(0)+a = 0 . a =0.

Solution we know that if f(t) is an odd function the  dt is given integral since   is odd, the given integral is even

We have:
limx→0 ln(1+ax)]/x=a
lim x→0 ln(1+ax)/ax=a
and then:
lim x→0 [ln(1+ax)-ln(1+bx)]/x
= a-b

The lady can select one cotton saree out of 15 cotton varieties in 15 ways since
any of 15 varieties can be selected. Corresponding to each selection of a cotton saree, she can
choose a polyester saree in 13 ways. Hence the two sarees (one cotton and one polyester), by
multiplication principle of counting, can be selected in 15 x 13= 195 ways

All the elements in set-A are presented in set-B. So "A" is a subset of "B".

f (x + 2y) = f (x) + f (2 y) + 4xy for x, y ∈ R putting x = y = 0, we get f (0) = 0

• (A - B) is A but not B which means A excluding the intersection of A and B.
• Similarly, in the figure, the shaded region is A but not C and B which means A excluding B and C. But if B and C both are excluded from A then the intersection of A, B and C get excluded two times.
• So, we take B ∪ C to be excluded from A. Therefore the answer is A - (B ∪ C).

(1/1² + 1/2² + 1/3² + ........∞) = π²/6
⇒ (1/1² + 1/3² + 1/5² + ........∞) + (1/2² + 1/4² + 1/6² + ........∞) = π²/6
=> (1/1² + 1/3² + 1/5² + ........∞) + 1/2²(1/1² + 1/2² + 1/3² + ........∞) = π²/6
=> (1/1² + 1/3² + 1/5² + ........∞) + 1/2²(π²/6) = π2/6
=> (1/1² + 1/3² + 1/5² + ........∞) + π²/24 = π²/6
= π²/8

Let the required circle is x² + y² - 6x - 4y + k = 0 and it is passing through (-2, 14)

If 2 tan^-1 (cos x) = tan ^-1(2 cosec x),

2tan^-1(cos x) = tan^-1 (2 cosec x)

= tan^-1(2 cosec x) 

= cot x cosec x = cosec x = x = π/4