Bihar PGT Mathematics Mock Test - 3 - Bihar PGT/TGT/PRT MCQ

Rumble means a heavy sound that reverberates. Roar is the only option that is quite similar in meaning. Thus, option 4 is correct.
Example- The roar of the ocean could be heard before the cyclone struck.

The correct option is Option 3, i.e., 'disdainfully'.
The sentence talks about the contempt that the administration had. As such, the administration can frequently only speak ill of it. The word ‘disdainfully’ means ‘refused with contempt or hate’. Hence, the correct option is Option 3.

सिन्धु नदी का नाम स्त्रीलिंग में प्रयुक्त नहीं होता है।

ऋग्वेद के नदीस्तुति सूक्त में सिंधु नदी का लिंग निर्धारण तो नहीं है, लेकिन बाकी की नदियां स्त्रीलिंग ही हैं. दांडेकर लिखती हैं, पश्तो भाषा में सिंधु, अबासिन या पितृ नदी है जिसे लद्दाखी भाषा में सेंगे छू या शेर नदी भी कहते हैं।

The correct answer is Sulphur Cycle

Key Points

• The sulphur reservoir is in the soil and sediments where it is locked in organic (coal, oil and peat) and inorganic deposits (pyrite rock and sulphur rock) in the form of sulphates, sulphides and organic sulphur.
• It is released by weathering of rocks, erosional runoff and decomposition of organic matter and is carried to terrestrial and aquatic ecosystems in a salt solution.
• The sulphur cycle is mostly sedimentary except two of its compounds, hydrogen sulphide (H₂S) and sulphur dioxide (SO₂), which add a gaseous component.
• Sulphur enters the atmosphere from several sources like volcanic eruptions, combustion of fossil fuels (coal, diesel etc.), from the surface of the ocean and gases released by decomposition.
• Atmospheric sulphur dioxide is carried back to the earth after being dissolved in rainwater as weak sulphuric acid (acid rain).
• Sulphur bound in a living organism is carried back to the soil, to the bottom of ponds and lakes and seas through excretion and decomposition of dead organic material.

Image of Sulphur Cycle

The pattern followed is:

Hence, the correct answer is "PM".

The correct answer is Ethyl mercaptan.

Key Points

• The stench due to leakage from the LPG cylinder because of Ethyl mercaptan.
  • LPG gas is basically propane and butane.
  • It is odourless in its natural state.
  • The smell that you notice when there is a leak is actually the stench of an entirely different agent, called ethyl mercaptan​.
    • This substance is added to the gas when it leaves the main storage terminals.
• Hence, option 4 is correct.

• Methane :
  • Methane is a chemical compound with the chemical formula CH₄.
  • Methane is a one-carbon compound in which the carbon is attached by single bonds to four hydrogen atoms
  • It is a group-14 hydride and the simplest alkane and is the main constituent of natural gas.
  • It is a colourless, odourless, non-toxic but flammable gas.
  • It has a role as a fossil fuel, a member of greenhouse gas, and a bacterial metabolite.
• Butane :
  • Butane or n-butane is an alkane with the formula C₄H₁₀.
  • Butane is a gas at room temperature and atmospheric pressure.
  • Butane is a highly flammable, colourless, easily liquefied gas that quickly vaporizes at room temperature.
  • Butane is a hydrocarbon and a highly flammable, colourless, odourless, easily liquefied gas.
  • It is typically used as fuel for cigarette lighters and portable stoves, a propellant in aerosols, a heating fuel, a refrigerant.
• Propane :
  • Propane is a three-carbon alkane with the molecular formula C₃H₈.
  • It is a gas at standard temperature and pressure, but compressible to a transportable liquid. 
  • Propane is a flammable hydrocarbon gas that is liquefied through pressurization and commonly used for fuel in heating, cooling, hot water, and vehicles.
  • Propane can also be used for refrigerants, aerosol propellants, and petrochemical feedstock.​ 

The logic followed here is:

• In each figure A, B, and C, the image is divided into two equal parts and one of the parts is shaded whereas, in figure D more than half of the figure is shaded. 

Hence, figure D is the odd one out of the given figures. 

The correct answer is January 24.

Key Points

• National girl child day is celebrated every year on the 24th of January as a national observance day for the girl child.
• It is to offer more support and new opportunities for the girls in the country.
• It aims to increase awareness among people about all the inequalities faced by the girl child in society.
• It was initiated in 2008 by the Ministry of Women and Child Development and the Government of India.
• The Government of India has started National Girl Child Day to bring equality in society as a campaign.

Additional Information

• The International Girl Child Day is celebrated every year on 11th October.

nth G.M. between a and b is
G_n = arⁿ
Where common ratio is r = (b/a)^(1/(n+1))
​So, to insert 3 geometric means between 1 and 256
 r = (b/a)^(1/(n+1))
r = (256/(1)^(1/(3+1))
r = (256)^1/4
r  = (4)^(4)1/4
r = 4
G_n = 1 * (4)ⁿ
G₁ = 1 * (4)¹ = 4
G₂ = 1 * (4)² = 16
G₃ = 1 * (4)³ = 64
The terms are  4, 16, 64

0 , because the particular solution is free from arbitrary constants.

The equation of the plane through the line of intersection of the planes

Let z = x + iy
Then z² =  x² + 2ixy - y²
And real(z2) = x² - y²  = 0  …………...(1)
And |z| = √x² + y²
|z| = 2
Hence √x² + y² = 2  ………..(2) 
Or x² +  y² = 4 …….(3)
Solving (1) and (3) , we get x = ± √2 and 
y = ± √2
It has 4 solutions.

No. of proper subsets = 2ⁿ-1

As the value of ‘n’ increases, it becomes difficult and tedious to calculate the value of ⁿC_x.

put x = tan A, y = tan B, z = tan C
tan A tan B + tan B tan C + tan C tan A = 1
tan C [tan A + tan B] = 1– tan A tan B

Co-efficient of x⁵ in (1+x²)⁵ (1+x)⁴
= {⁵C₀ (1)⁰ + ⁵C₁ (1)x² + ⁵C₂ (1)(x2)2 + ⁵C₃ (1)(x²)³ + ⁵C₄ (1)(x²)⁴ + ⁵C₅ (1)(x²)⁵} * {4C0 (1) + 4C1 (x) + 4C2 (x)2 + 4C3 (x)3 + 4C4 (x)4}
= {⁵C₂(x)⁴ * ⁴C₁(x) + ⁵C₁(x)⁴ + ⁵C₁(x)² * ⁴C₃(x)³} 
∴ coefficient of x5
=> (5×4)/(2×1) × 4)x⁵ + (5×4)x⁵
⇒(10×4+20)x⁵
⇒ 60x⁵

Equation of tangents and normal with slope 'm' will be 

A+2B=7------(1)
3A+2B=9------(2)
Subtracting (2) from (1)
we get, 2A=2
A=1
Subsitute A=1 in (1)
1+2B=7
2B=6
B=3
therefore A = 1, B = 3
 

Rank of a non zero matrix is always greater than or equal to 1.

μ = (22 + 26 + 28 + 20 + 24 + 30)/6
= 150/6 
= 25
x(i) = (xi - μ)²
x(22) = (22-25)² = 9
x(26) = (26-25)² = 1
x(28) = (28-25)² = 9
x(20) = (20-25)² = 25
x(24) = (24-25)² = 1
x(30) = (30-25)² = 25
​
(xi - μ)²  = 70
Standard deviation : [(xi - μ)²]/N
= (70/6)^½
= 3.42

In any traingle The sum of 3 sides of a traingle is equal to 180°

Given 

A=72°

B=48°

A+B+C=180°

72°+48°+C=180°

C=180°-120°

C=60°

For No solutions,   for given system of equations we have 

The given quadratic equation 5x²−4x+2+k(4x²−2x−1)=0 can be resolved as: 5x²−4x+2+k(4x²−2x−1)=0
⇒5x²−4x+2+4kx²−2kx−k=0
⇒(5+4k)x²−(4+2k)x+(2−k)=0
We know that the sum of the roots of a quadratic equation ax^2+bx+c is − b/a​
 and the product of the roots is c/a
Now, in the equation (5+4k)x²−(4+2k)x+(2−k)=0, we have:
Product of the roots is: c/a = 2−k/(5+4k)
​
Also, it is given that the product of the roots is 2, therefore,
=2−k/(5+4k)=2
⇒2−k=2(5+4k)
⇒2−k=10+8k
⇒−k−8k=10−2
⇒−9k=8
⇒k=−8/9
Hence, k=−8/9

Step-by-step explanation: