HPSC PGT Mathematics Mock Test - 5 - HPSC TGT/PGT MCQ

Explanation:

• Evolutionary biology: It is a field of science that deals with the study of evolutionary processes like natural selection, speciation & common descent that has led to the diversification of life on earth.
• Charles Darwin is known as the father of ''Evolutionary Biology''.
• Darwin proposed a theory of evolution called natural selection in the year 1859. According to it those populations which are a better fit (reproductively fit) in an environment will be selected by nature and will survive more.
• Charles Darwin wrote a book named ''The origin of species'' which is considered to be the foundation of evolutionary biology.

Additional Information 

• Herbert Spencer- He Was best known for the introduction and application of evolutionary theory to philosophy, psychology, and social sciences
• The famous phrase 'Survival of the fittest' to mean Natural Selection was coined by Herbert Spencer. He originated this phrase after the publication of famous biologist Charles Darwin’s book ‘Origin of Species’ which talked about ‘Natural Selection’.
• Julian Huxley was an English biologist, philosopher, educator, and author who greatly influenced the modern development of embryology, systematics, and studies of behaviour and evolution.
• Stanley Miller along with H.C. Urey provided experimental evidence of ''chemical evolution''

The correct answer is ​Sirajudaula.

Key Points

Battle of Plassey -

• It is a battle fought between the East India Company force headed by Robert Clive and Siraj-Ud-Daulah (Nawab of Bengal).
• The rampant misuse by EIC officials of trade privileges annoyed Siraj.
• The continuing misconduct by EIC against Siraj-Ud-Daulah led to the battle of Plassey in 1757.
• In 1757, when Sirajudaula was defeated in the Battle of Plassey, East India Company decided to build a new fort, one that could not be easily attacked.
• Hence the correct answer is option 3.
• Calcutta had grown from three villages called Sutanati, Kolkata and Govindapur.
• The Company cleared a site in the southernmost village of Govindapur and the traders and weavers living there were asked to move out.
• Around the new Fort William, they left a vast open space which came to be locally known as the Maidan or garer-math.

Additional Information

•  
• Mir Qasim Nawab of Bengal was defeated in the Battle of Buxar.
• Mir Jafar became the Nawab of Bengal after the Battle of Plassey, he gave the British to become the Nawab.

The correct answer is Neeraj Chopra.

Key Points

• Haryana Chief Minister Manohar Lal Khattar announced that a stadium will be built in Olympic gold-medallist Neeraj Chopra's native village in Panipat.
  • Neeraj Chopra is a Javelin throw player.
  • Javelin thrower Neeraj Chopra's native village Khandra is in Panipat.
  • A stadium would be built in Neeraj Chopra's village for ₹10 crores.

Additional Information

The correct answer is golf.

Key Points

• Tvesa Malik is an Indian golf player.
• She is from Gurugram, Haryana.
• She has won the 4th leg of the Hero Women’s Golf Tour.
• Gursimar Badwal is also an Indian golf player. 

Additional Information

Logic: The alphabet that comes first alphabetically, comes first in the dictionary.

So, the correct arrangement should be:

2. Subtle.

4. Sucres.

3. Sudoku.

1. Sugary.

5. Sullen.

Hence, the correct answer is "2, 4, 3, 1, 5".

NEP 2020 proposes mandatory school attendance for all students until the age of 16 to reduce early dropouts.

z₁ = |z₁(cosθ₁ + i sinθ₁)
z₂ = |z₂(cosθ₂ + i sinθ₂)|
Given that |z₁| = |z₂|
And arg(z₁) + arg(z₂) = pi
θ₁ + θ₂ = pi
⇒ θ₁ = pi - θ²
Now, z₁ = |z2|[cosθ(pi - θ₂) + i sin(pi - θ₂)]
= z₁ = z₂(-cosθ₂ + i sinθ₂)
= z₁ = - |z₂|(cosθ₂ - i sinθ₂)|
= z₁ = - |z₂|(cosθ₂ - i sinθ₂)
⇒ z₁ = - z₂(bar)

Let E₁ = P₁ win the tournament, E² = P₂ reaches the semifinal since all players are equally skilled and there are 4 persons in the semifinal 
 both are in semifinal and P₁ wins in semifinal and final 

Hence (C) is the correct answer.

If l, m, n are the direction cosines and a, b, c are the direction ratios of a line then , the directions cosines of the line are given by :

(fof) (x) = f[f(x)] = f(x² - 3x + 2)² - 3(x² – 3x + 2)
= y² – 3y + 2 = (x² – 3x + 2)² – 3(x² – 3x + 2) + 2 =  (x⁴ – 6x³ + 10x² – 3x)

 Let P(x₁ , y₁) be point of contact of two parabola. tangents at P of the two parabolas are

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)


 

We have :

In cartesian co – ordinate system : Equation of a plane passing through three non collinear points (x₁, y₁, z₁),(x₂, y₂, z₂) and (x₃, y₃, z₃) is given  

As we know that, cosA = (b² + c² - a²)/2bc
a = 6, b=4, c=8
cosA = (16+64-36)/2(4)(8)
44/64 
= 0.687
A = cos-1(0.687)
which is approx equals to 46°36’2″

since n is appositive integer

2001 = 3 x 23 x 29 and (3+23+29)
= 55 ⇒ a = 3, b = 23, c = 29

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.

 is a constant function ⇒ bc ad 0 ⇒ ad bc.

R × ( P' ∪ Q' )'=R × [( P' )' ∩ ( Q' )' ] =R × (P ∩ Q) = (R × P) ∩ (R × Q)

For a discrete probability function, the variance is given by

Where µ is the mean, substitute P(x)=ⁿC_x p^x q^(n-x) in the above equation and put µ = np to obtain
V = npq

Required area :

When x > 0 & y < 0, the quadrant contains positive X-axis and negative Y-axis
Therefore, the point lies in the fourth quadrant. 

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