AWES PGT Math Mock Test - 8 - AWES TGT/PGT MCQ

The Correct Answer is Option 1 i.e Tomara Rajputs.

• Tomara Rajputs (8th Century -12th Century):
  • Anangapala was considered to be the founder of this dynasty.
  • Delhi became the capital of a kingdom for the first time under the Tomara Rajputs.
  • They were defeated by Chauhans in the middle of the twelfth century.
  • The name of Anangpala is inscribed in the Iron Pillar of Delhi. 
• Chauhans (1165-1192):
  • Prithviraj Chauhan was the most important ruler of this dynasty.
  • In the first battle of Tarain 1191 AD, he defeated Muhammad Ghori.
  • In the second battle of Tarain 1192 AD, he was defeated by Muhammad Ghori.
•  Aurangzeb (1658-1707):
  • He was the sixth Mughal Emperor.
  • He executed the ninth Sikh guru Guru Tegh Bahadur in 1675 AD.
  • He re-imposed Jaziya in 1679 AD.

The US-India Strategic and Partnership Forum (USISPF) has appointed former Revenue Secretary and former Secretary of Economic Affairs Tarun Bajaj as the head of the US-India Tax Forum. A 1988 batch Haryana cadre IAS officer, Tarun Bajaj has served as Revenue Secretary. The US-India Tax Forum was officially launched on February 25, 2020.

Non-discursive communication refers to any form of communication that does not involve the use of words or language.

• Speaking involves the use of words or language to communicate, which is the opposite of non-discursive communication.
• Non-discursive communication includes forms of communication that do not involve the use of words, such as facial expressions, body language, gestures, and silence.
• It is an important aspect of human communication and can play a significant role in how we interact with others and convey meaning and emotion.

Thus, it is concluded that Speaking is NOT a form of non-discursive communication.

Equilibration takes place when a child strikes balance between the two processes while trying to internalise the perceived object.

Equilibration: The process of striking a balance between accommodation and assimilation. On the other hand, When the child strikes a balance between the two processes while trying to internalize the perceived object, adaptation (a relatively stable structure) takes place.

Lawrence Kohlberg, an American psychologist, has propounded the 'Theory of Moral Development'.

• He has made a systematic study of moral development in his theory that is categorized into 3 levels and 6 stages. 

Set S of odd positive an odd integer less than 10 is {1, 3, 5, 7, 9}.
Then, Cardinality of set S = |S| which is 5.

The orthogonal projection on x- axis is given by : 

sin θ is 3/5.
on simplifying:
(secθ + tanθ)/(secθ - tanθ)
We get, (1+sin θ)/(1-sin θ)
=(1+3/5)/(1-3/5)
=(8/2)
=4

Let √(5 – 12i) = x + iy
Squaring both sides, we get
5 – 12i = x² + 2ixy +(iy)² = x² – y² + 2xyi.
Comparing real and imaginary parts , we get
5 = x² – y² ———– (1) and xy = – 6 ———— (2)
Squaring (1), we get
25 = (x² – y²)2 = (x² + y²)² – 4x²y²
⇒ 25 = (x² + y²)² – 4(– 6)²
⇒ (x² + y²)² = 169
⇒ x² + y² = 13 ———- (3)
Adding (1) and (3) we get
2x² = 18
⇒ x = ± 3.
Subtracting (1) from (3) we get
2y² = 8
⇒ y = ± 2.
Hence, square root of √(5 – 12i) is (3 – 2i)
Similarly, √(5 + 12i) is (3 + 2i)
√(5 + 12i) + √(5 – 12i)
⇒ (3 + 2i) + (3 - 2i)
⇒ 6

For the 1st point chords can be drawn with joining 9 other points.
For the 2nd point distinct chords can be drawn with joining 8 other points.
 For the 9th point distinct chords can be drawn with joining 1 other point. 
So, total no. of points = 9 + 8 + 7 + . . . . . . + 1 = 45 

sin(n+1)Asin(n+2)A + cos(n+1)Acos(n+2)A = cos (n+1)Acos(n+2)A + sin(n+1)Asin(n+2)A = cos{A(n+2-n-1)} = cos (A.1) = cos A

(1 + a)²ⁿ = C_o + C₁a + C₂a² + … + C_2n a²n
Differentiate both sides w.r.t. ‘a’.

A21 = {(0, -1) (3,4)}
⇒ (0 - (-3)) = 3
A21 = (-1)⁽²⁺¹⁾ (3)
= -3

|x| is not differentiable at x = 0
|x| is continuous at x = 0

But α + β = p and α + 4β = 2q ⇒ β = (1/3)(2q – p) and α = (2/3)(2p – q)

  

write 1 as in R₁ and take out  common from R₁ , we get : 

because row 1 and row 3 are identical.

Acceleration is a vector quantity , because acceleration is defined as the rate of change of velocity w.r.t. time.

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 by :



Therefore, the equations of the planes that passes through three points (1,1,0), (1,2,1),  (-2,2,-1) is given by :



⇒ (x-1)(-2) - (y-1) (3) + 3z = 0
⇒ 2x+3y - 3z = 5

The given system of equations does not have solution if :


⇒ (-2 + λ) = 0 ⇒ λ = 2

Here , D.R’s of normal to the plane are 1, 1 , 1 ,its D.C ‘s are :

On dividing x + y + z = 1 by √3 , we get :
 It is of the form : lx+my+nz = d , therefore , d = 1/√3 .

is an ellipse, whose focus is (2, -3) , directrix 3x - 4y + 7 = 0 and eccentricity is 1/2.
Length offrom focus to directrix is 



So length of major axis is 20/3

The eccentricity for ellipse is always less than 1. The eccentricity is always 1 for any parabola. The eccentricity is always 0 for a circle. The eccentricity for a hyperbola is always greater than 1.

(2^1/5 +3^1/10)⁵⁵ is
Total term = 55 + 1 = 56

Here r = 0, 10, 20, 30, 40, 50
Number of rational terms = 6;  
Number of irrational terms = 56 - 6 = 50