AWES TGT Maths Mock Test - 2 - AWES TGT/PGT MCQ

Mohan Yadav has been officially announced as the chief minister-elect for Madhya Pradesh by the Bharatiya Janata Party (BJP).

Space One, a Tokyo-based startup, recently experienced a setback as their first privately developed rocket exploded after takeoff. Despite this setback, Space One aims to increase its launch frequency significantly in the coming years, showcasing its ambitions in the aerospace industry.

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NEP 2020 suggests a flexible higher education system with multiple entry and exit points, allowing students to choose their courses based on their interests and career goals.

School principal fulfils many roles and dealing with students' disruptive behaviour is among the least preferred by them. So, the teacher must try to discipline the students using various means like assigning responsibility to the undisciplined, finding out the underlying cause of his behaviour, and so on. Only after she has done everything without any effect on the student should she send the student to the principal.

If l, m and n are the direction cosines of a line, Direction ratios of the line are the numbers which are Proportional to the direction cosines of the line.

C₁, O, C₂ are collinear

Here, 0 ≤ x- 3 ≤ 7 - x  
⇒0 ≤ x - 3 and x - 3 ≤ 7 - x
By solvation, we will get 3 ≤ x ≤ 5
So x = 3,4,5 find the values of ^7-x P_{x - 3} by substituting the values of x
at x = 3 ⁴P₀ = 1
at x = 4 ³P₁ = 3 
at x = 5 ²P₂ = 2

No of word formed taking E at first place = 3! 
Taking F at first place = 3! 
Taking I in the first place = 3!
W in first and E in second = 2!
W in first F in second and E in third = 1! 
W in first I in second and E in third = 1 
W in first I in second and F in third = 1 
W in first I in second and F in third and E in fourth = 1 
Total =24

By the property of transpose of a matrix ,(AB)’ = B’A’.

Let x and y be two positive numbers. Since a is the single A.M. between x and y
∴ 
It is given that p and q are two geometric means between x and y common ratio r given by 
r = (y/x)^1/3
∴ p = xr = x^2/3 y^1/3 and q = xr² = x^1/3y^2/3
⇒ p³ +q³ = x²y + xy² = xy(x+y) = 2axy = 2a pq

Selecting 3 consonants out of 7,
No. of ways = ⁷C₃ 
Selecting 2 vowels out of 4,
No. of ways = ⁴C₂ 
No. of ways of forming the words
= ⁷C₃* ⁴C₂* 5! (for arrangement of the letters)
= 35 * 6 * 120
= 25200 

Therefore, tanθ =

= x+10 = 3x+4
= x = 3

The parabolas are y² = 4sin² α(x + sin²α) and y² = 4cos² α(x + cos²α), hence the locus is x + cos²α + sin²α = 0 ⇒ x + 1 = 0
Assume the point   as origin and line joining it to the centre as x-axis, the equation to the circle becomes x² + y² - 2x = 0, center is A₁ (1, 0) and the second circle has the equation x² + y² - 2√2 = 0 center A₀ (0, √2)
Similarly A₃(-2, 0), A₄ (0, -2√2) etc.  

The number of onto functions that can be defined from a finite set A containing n elements onto a finite set B containing 2 elements = 2ⁿ − 2.

f(0) = lim(x→0) x sin (1/x)
​We know ∀ x ∈ R,sin (1/x) ∈ [−1,1]
Hence, f(0) = lim(x→0) xsin(1/x) 
= 0

The numbers in the questions are not very clear.
z₁ = 2 + i
z₂ = 1+3i
z₁ – z₂ = (2 – 1) + i (1 – 3)
= 1 – 2i

In vector form Distance between two parallel lines  given by :

n(A) = 3
n(A × A × A) = n(A) * n(A) * n(A)
n(A × A × A) = 3 * 3 * 3 = 27

Since the exterior angle 140 degrees, The sum of the interior angles = (2n - 4)* right angles. So 140n = (2n - 4)* right angles, or
140n = (2n - 4)*90, or
140n = 180n - 360o, or
40n = 360°, or
n = 9 sides.

tan^-1(1-cosx/1+cosx)^½
= tan^-1{(2sin² x/2) / (2cos² x/2)}^½
= tan^-1{(2sin² x/2) / (2cos² x/2)}
= tan^-1(tan x/2)
= x/2

cos35^o cos45^o
Multiply and divide numerator and denominator by 2
1/2{2cos35^o cos45^o}
= 1/2{cos(35^o+45^o) + cos(35^o-45^o)}
= 1/2{cos80^o + cos(-10^o)}    { cos(-x) = cosx 
= {cos80^o + cos10^o}/2