AWES PGT Math Mock Test - 10 - AWES TGT/PGT MCQ

Weighing nearly a trillion metric tonnes and covering an extensive area of 4,000 square km, the colossal iceberg A23a, originating from West Antarctica's Filchner-Ronne Ice Shelf in 1986, has broken its decades-long stillness, marking a noteworthy event in its movement after more than 30 years.

The Union Ministry of road transport and highways is planning to extend its Incident Management Services (IMS) to all national highways.
The purpose of this step is to minimize road fatalities and improve safety for road users. Incident Management Services (IMS) on national roads will be provided, run, and maintained by businesses.

All 6,650 villages in Jammu and Kashmir have achieved Open Defecation Free Plus Model status, making it the first union territory in India to do so. This is a significant achievement, as it means that all villagers now have access to safe and sanitary toilets and that greywater and solid waste are being managed effectively.

Theory of Multiple Intelligence which describes eight different kinds of intelligence is propounded by an American cognitive psychologist 'Howard Gardner'.

The National Education Policy 2020 proposed various reforms in school education as well as higher education including technical education that has to be adopted by all educational institutions.

Key Points The ECCE program needs to be determined by children’s developmental and contextual needs, providing for more need-based inputs and an enabling environment.

• Ensuring quality ECCE - early childhood care and education for all children between 3-6 years.
• It was believed that a common ‘curriculum’ would not be appropriate for all.
• It comprises details of the goals for different domains of development, i.e. physical, language, cognitive, socio-emotional, creative, and aesthetic appreciation, to be fostered to ensure holistic development of children under six years.​

Hence we can say that the full form of ECCE is Early Childhood Care and Education.

Additional Information Other reforms of NEP 2020 include -

• Equitable and inclusive education - Special emphasis is given to Socially and Economically Disadvantaged  Groups (SDGs).
• Ensuring Universal Access at All Levels of schooling from pre-primary school to Grade 12.
• New Curricular and Pedagogical Structure (5+3+3+4).
• Setting up of State School Standards Authority (SSSA).

Number of sides of a cube = 6
Number of colour of a cube = 6
Number of ways of colouring =?
Consider a cube in 3D space 
Each of the sides towards East West North South and remaning two up and down 
Now fixing up positions down is also fixed 
Total number of ways 
= 6!/(4×6)
​= 5×3×2 
= 30 Ways
Hence, the correct answer is 30 Ways

A = {2, 3, 4, 8, 10}
B = {3, 4, 5, 10, 12}
C = {4, 5, 6, 12, 14}
► (A ∩ B) = {3,4,10}
► (A ∩ C) = {4}
► (A ∩ B) U (A ∩ C) = {3,4,10}

The hyperbola is given by
2x² + 5xy + 2y² + 4x + 5y = 0 ............................(i)
Since the equation of hyperbola will differ from equation of asymptote by a constant. So, equation of asymptote is
2x² + 5xy + 2y³ + 4x + 5y + λ = 0 ......................(ii)
If (ii) represents 2 straight lines, we must have 
abc + 2fgh - af²- bg² - ch² = 0
or 22λ + 2.5 / 2.4 / 2.5 / 2 - 2.25 / 4 - 2.4 - λ (25 / 4) = 0
or 9λ = 18 ∴  λ = 2 
2x² + 5xy + 2y³ + 4x + 5y + 2 = 0

tan^-1 (tan 3π/5)
This can be written as:
tan^-1 (tan 3π/5) = tan^-1 (tan[π – 2π/5])
= tan^-1 (- tan 2π/5) {since tan(π – x) = -tan x}
= –tan^-1 (tan 2π/2)
= –2π/5

Option (a) :- for x = nπ
let n=1
so, x= 1 x π =π
therefore , sinx + icos2x
sinπ + icos 2π
0 + i= i
Now,
cosx - isin2x
cosπ - isin2π
or, -1 -0 = -1
hence no conjugate
Option (b) :- x = 0
sin0 + icos0
0+i= i
now ,
cos0 - isin0
= 1
hence no conjugate.
option (c) :- x = (n+1/2)π
if n= 1
x=3π/2
sin3π/2 + icos3π
-1 - i
Now,
cos3π/2 - isin3π
0-0= 0
hence no conjugate
Thus option D is correct

Mean deviation of a data set is the average of the absolute deviations from a central point (Average value).

As (1 – p) is root of the equation: x² + px + (1 – p) = 0

(1 – p)² + p(1 – p) + (1 – p) = 0

(1 – p)[1 – p + p + 1] = 0

(1 – p) = 0

p = 1

Therefore, given equation now becomes

x² + x = 0

x(x + 1) = 0

x = 0, -1

 (1+x)ⁿ= nC0+ nC1x+ nC2x²+...+ nC0xⁿ ....(1)
(1−x)ⁿ= nC0 − nC1x+ nC2x²−...+ nC0 xⁿ....(2)
⇒(1+x)ⁿ−(1−x)ⁿ = nC0+ nC1x+ nC2x²+...+ nC0xⁿ− nC0+ nC1x− nC2x²+...+ nC0xⁿ
 =2(nC1x+nC3x³+....+xⁿ)

Given: n=60 and put x=1
⇒(1+1)⁶⁰−(1−1)⁶⁰
 =2⁶⁰
⇒2⁶⁰=2(nC1x+nC3x³+....+xⁿ)

∴Sum of odd powers of x in the expansion is = nC1x+nC3x³+....+xⁿ =2⁶⁰−1 =2⁵⁹

Matrix C is given in Transpose form. So, Matrix C is 3x1 order.

The unit place can be filled in 2 ways because question asked to find 3 digit odd numbers from 5,6,7,8 and the other two places can be filled in 4 ways as repetition is allowed.
So, Unit's place can be filled in 2 ways. Decimal place can be filled in 4 ways. Hundred's place can be filled in 4 ways.
 => 4*4*2 = 32.

For both lines to be parallel tangent the distance between both lines
should be equal to the diameter of the circle
⇒ 4 = |c₁−c₂|/(1+3)^1/2
⇒∣c₁−c₂∣ = 8

Correct Answer : a

Explanation :  {1 + cotα - sec(π/2 + α)} {1 + cotα + sec(π/2 + α)}

As we know that (a-b)(a+b) = a² - b²

(1 + cotα)² - [sec(π/2 + α)]²

1 + 2cotα + cot²α - (-cosecα)²

2cotα + 1 + cot²α - cosec²α

As we know that 1 + cot²α = cosec²α

= 2cotα + cosec²α - cosec²α

= 2cotα

Let us consider a graph symm. with respect to line x = 2 as shown in the figure.

From the figure

f (x₁) = f (x₂), where x₁ = 2-x and x₂ = 2+x
∴ f (2 - x) = f (2+x)

First of all change the speed into m/s. You will get 4 m/s. It means that the wheel moves 4 metres a second i.e arc subtended by the wheel per second is 4m. Now, as we know that angle= arc÷radius. So, divide 4m by 0.35m ( convert 35 cm into metre or 4m into cm, as you wish). So, angle= (400÷35) radians = 80/7 radians. So, the answer is b).

sin x + sin y = sin (x + y)




The possibilities are x = 0 or, y = 0 or, x + y = 0
When x = 0 , y = ±1
When y = 0 , x = ±1

Clearly, there are 6 pairs.

Equation of ellipse : x²/9 + y²/1= 1
Co−ordinates of point P is : (acosθ , bsinθ)
Equation of normal at point (x1, y1) is :
a²x/x1 − b²y/y1 = (ae)²
Equation of normal at point P is:
ax/cosθ− by/sinθ= (ae)²−−−−−(1)
Equation of diameter at Q is : y = (−b/a)tanθ−−−−−(2)
Point of intersection of equation 1 and 2 is :
ax/cosθ + (b²/acosθ) = (ae)²
Or , x = ae²cosθ − b²/a²
And y = − be²sinθ + b³/a³ (from 2)
∴ Point R(ae²cosθ − b²/a² , − be²sinθ + b³/a³)
Let mid point of PR is (h,k)
h =[acosθ + ae²cosθ − (b²/a²)]/2
Or , 2h + b²/a²= acosθ + ae²cosθ
Or , cosθ= [2h + (b²/a²)/(a + ae²)]
k = [bsinθ − be²sinθ + (b³/a³/2)]/2
Or , sinθ = [2k − (b³/a³)/(b − be²)]
On squaring adding we get :
[2h + (b²/a²)]/(a + ae²)² + [2k − (b³/a³)] / (b − be²)²= 1
Which is an equation of ellipse.

P(-x,-y) lies on the 3rd or 4th quadrant
So, according to the question, points lies in 3rd quadrant
i.e. 3(π/2)

f(x) = (x-3)(x-1)/[(x2 -4)^1/2]
= x2 - 4 = 0
(x-2)(x+2) = 0
x = 2 and -2
(-∞, -2 ) U (2,∞)

A × B = {(x, a), (x, b), (y, a), (y, b)}
A = {x, y}

none of these  : 7/25

A = 1
L = 11
Sn = 36
⇒ n( a +L) /2 = 36
⇒ n(1+11)= 72
⇒ n *12 = 72
⇒ n = 6
No.of terms = 6