AWES PGT Math Mock Test - 5 - AWES TGT/PGT MCQ

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• The easterly jet stream sets in along 15°N latitude only after the western jet stream has withdrawn itself from the region.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.

Russia's nuclear energy corporation Rosatom has set a record by installing a research reactor pressure vessel in Mountain Meteor at an altitude of about 4,000 meters above sea level in El Alto, Bolivia.

The naval forces of China, Iran, and Russia recently launched a joint exercise called the “Maritime Security Belt-2024” near the Gulf of Oman. The exercise, which began on March 11 and lasted until 15, is the fifth common military exercise between the three countries in recent years. The exercise aims to safeguard regional maritime security and strengthen maritime cooperation. The exercise is organized in three phases: harbor, sea, and summarize. The exercise focuses on anti-piracy and search and rescue training courses, and includes the participation of Russian warships and aviation.

International Mountain Day is celebrated annually on December 11 to emphasize the vital importance of mountains in our lives. Designated by the United Nations, this day encourages reflection on the protection of these natural wonders for a better future for our planet.

The executive board of the International Monetary Fund (IMF) approved a proposal to make a 50 per cent increase in the quota allocated to members in proportion to their current quotas. The proposal will now be considered and made effective by the board of governors as part of concluding the 16th general review of quotas.
Currently, India has a quota of special drawing rights (SDR) 13,114.4 million which denotes a share of 2.75 per cent, making it the eighth-largest quota-holding country in the IMF.

Psychologist Albert Bandura is the researcher most often associated with learning through observation. He and others have demonstrated that we are naturally inclined to engage in observational learning.

Primary level students learn more by observing pictures and specimens. Thus, they are most effective in teaching primary level students. Pictures and specimens are important visual tools which facilitate learning.

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

Lesson planning should be based on both, the needs of the learners and the process for evaluation to be followed. The content should be presented in such a way that it fulfils the student's academic needs. The process of the evaluation must be decided beforehand, so that the teacher understands how much learning has taken place. Different kinds of evaluation processes could be used, depending upon the learning objectives.

a = 62  d = 57 - 62 = -5
tn = a + (n-1)d
= 62 + (n-1)(-5)
= 62 - 5n + 5
= 67 - 5n
From the options, we take '14'
= 67 - 5(14)
= 67 - 70
= -3 (The first negative term will be at the 14th term)

y²+3=2(2x+y) represents parabola.
y²+3=4x+2y
y²−2y+3=4x
y²−2y+1+3=4x+1
(y−1)²=4x−2
(y−1)²=4(x−1/2)
So, the vertex of parabola=(1/2,1) and axis is parallel to x axis.
a=1
Focus=(1/2+1,1)
=(3/2,1)

Given,  x²/5 + y²/3= 1
We know S₁F₁ × S₂F₂ = b²
∴ S₁F₁ × S₂F₂ = 3

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 

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

We have, α + β = -p,αβ = q
Now (ωα + ω²β)(ω²α + ωβ) = ω³α² +ω⁴αβ+ω²αβ + ω³β²
= α² +β² +(ω+ω²)αβ = α²+β² -αβ = (α + β)² -3αβ = p² -3q

6, a bare in H.P 
 are in A.P.

Because , the determinant of a skew symmetric matrix of odd order is always zero and of even order is a non zero perfect square.

The given curves are : (i) y = x – 1 , x > 1 . (ii) y = - (x – 1) , x < 1. (iii) y = 1 these three lines enclose a triangle whose area is : 1/2 .base.height = 1/2 .2 .1 = 1 sq. unit.

focus lies on x axis
So, the equation  of ellipse is x²/a² + y²/b² = 1
Co-ordinate of focus(+-ae, 0)
ae = 4
e = ⅘
a = 4/e  => 4/(⅘)
a = 5
(a)² = 25
b² = a²(1-e²)
= 25(1-16/25)
b² = 9
Required equation : x²/(5)² + y²/(3)² = 1

The number of elements for a matrix with the order m×n is equal to mn, where m is the number of rows and n is the number of columns in the matrix.

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)]

D. R’s of line are 2 : 1 : 2
D.R’s of Normal to plane is :3 : -2 : 6
Angle between line and plane

A = {(a,1) (0,a)}
A² = {(a,1) (0,a)} * {(a,1) (0,a)}
= {(a²+0, a+a) (0+0, a²)}
A² = {(a2, 2a) (0, a²)}
A * A² = A³
A³ = {(a^2, 2a) (0, a²)} * {(a,1) (0,a)}
= {(a³+0, a²+2a²) (0+0, 0+a³)}
= {(a³, 3a²) (0, a³)}
Therefore Aⁿ => {(aⁿ, 3a^(n-1)) (0, aⁿ)}