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

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Girija Subramanian, the current Chairperson and MD of Agriculture Insurance Company (AIC), has been selected as the next CMD of New India Assurance by the Financial Services Institutions Bureau (FSIB). This selection process also included appointments for other executive positions in PSU general insurers.

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The United States announced the provision of an additional $600 million in security assistance to Ukraine, which includes various military equipment, as Ukrainian forces engage in conflict with Russian troops in the eastern Donbas region.

Socialization is an important process for the functioning and continuation of society. It is a process of learning the rules, habits, and values of a group to which a person belongs whether it is family, friends, colleagues, or any other group.

If a student passes a comment, then the teacher must ignore the comment and continue taking class. 

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Let f(x) = x² + 2ax + b = (x + a)² + b – a²
So minimum value of f(x) is b – a²
Since hence b - a² > c
i.e., b - c > a²

The geometric mean of two numbers, say x, and y is the square root of their product x * y.
 Mean = [x * y]^1/2
= [5 * 8]^1/2
= [40]^1/2
= 2(10)^1/2

f(x) = Min {x + 1,∣x∣ + 1}
x = 0 ⇒ ∣x∣ = x
f(x) = min {x + 1,x + 1}
= x + 1
x < 0,∣x∣ = −x
f(x) = min {x + 1,−x + 1}
−x + 1> x + 1
x < 0
⇒x < 0, f(x) = x + 1
x > 0,f (x) = x + 1
⇒ f(x) = x + 1 for all x
∴f(x) is differential everywhere (continuous and constant slope)

z₁ = (1, α) = cosα + isinα = e^iα  ......(i)
⇒ z₂ = (1, β) cosβ+isinβ = e^i/β  ......(ii)
⇒ z₃ =(1, γ). cosγ +isinγ =e^iγ   ......(iii)
Also, Z₁ +Z₂ +Z₃ = 0 

⇒ (cosα+cosβ+cosγ)+i(sinα+sinβ+sinγ) = 0
⇒ ccosα+cosβ+cosγ = 0
and sinα+sinβ+sinγ = 0 ... (iv) 

[(Using (i), (ii), (iii)] 
⇒ E = (cosα+cosβ+cosγ - i (sinα+sinβ+sinγ)
   [(Using (i)]

Angle between skew lines is the angle between two intersecting lines drawn from any point 

If you interchange (switch) two rows (or columns) of a matrix A to get B, then det(B) = –det(A). Hence, the determinant is -(-7)

= 7

e² = (a² / b²) + 1
3 = (a² / b²) + 1
a²/b² = 2
a² = 2b²
Product of perpendicular distance of any point on hyperbola = (a²b²)/a² + b²
= [2(b²).b²]/(2b² + b²)
= [2b²]/3 = 6
= 2b² = 18
=> b² = 9
=> b = 3
Length (2b) = 2(3) 
= 6

Required area :

Let A (a, b) and G (x. y) Now A, G, O are collinear
⇒ x = (2*0 + a)/3
⇒ a = 3x
and similarly b = 3y
Now (a,b) lies on the circle = 9x² + 9y² = 9
=> x² + y² = 1

Given 

Each of the answer choices in the form of the product of two factors on the left and a “≥ 0” or “ ≤ 0” on the right.
The product will be negative when the two factors have opposite signs, and it will be positive when the factors have the same sign. Choice (a), for example, has a “≥0”, so you’ll be looking for other factors to have the same sign.


The graph of x ≤ 0 and y ≤ 2x looks like this.

Together, they make the graph in the figure.

Let us say that the two particular friends are A and B.
If A is invited among six guests and B is not, then:  number of  combinations to select 5 more guests from the remaining 8 friends:
          C(8, 5) =  8 ! / (5! 3!)  = 56
If B is invited among the six guests and A is not , then the number of ways of selecting the remaining 5 guests =  C(8, 5) =  56
Suppose both A and B are not included in the six guests list : then the number of such combinations =  C(8, 6) = 7 * 8 /2 = 28
So the total number of sets of guests that can be selected =  140.

x¹¹ cos x is an odd function.

Given hyperbola is 25x²−16y²=400
If (6, 2) is the midpoint of the chord, then equation of chord is T = S1
​⇒25(6x)−16(2y)=25(36)−16(4)
⇒75x−16y=450−32
⇒75x−16y=418

Multiplying numerator and denominator with 1 + 2isinα/2 then real part = 0

z = x + iy
z = -x + 0i {-x > 0}
Principle arg(x) = π

Let  It is given that left| , then , 

Putting these values in (1) , we get : 

Correct Answer :- b

Explanation : α₁,α₂,........,α₉₉

α₁, 1α₂,........,1α₉₉

α₁α₂, α₂α₃, α₃α₄................α₉₈α₉₉ 

Sum of α₁α₂, α₂α₃, α₃α₄................α₉₈α₉₉ = 0

Therefore, x - 1 = 0

x = 1

y = V^3/3
V = x² - 2x + 3
y = 1/3*v³
dy/dx = d/dx{1/3*(x²-2x+3)³} 
= 1/3*3*(x²-2x+3)²*(2x-2) 
{d/dx(xⁿ)=nx^n-1*dx/dx} 
= 2(x-1)*(x²-2x+3)²

A solid has shape, size, position and can be moved from one place to another. So, solid has three dimensions

 A point is that which has no part i.e., no length, no breadth and no height. So, it has no dimension.

 Boundaries of a solid are called surfaces. A surface (plane) has only length and breadth. So, it has two dimensions.