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AWES PGT Math Mock Test - 6 - AWES TGT/PGT MCQ


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30 Questions MCQ Test - AWES PGT Math Mock Test - 6

AWES PGT Math Mock Test - 6 for AWES TGT/PGT 2024 is part of AWES TGT/PGT preparation. The AWES PGT Math Mock Test - 6 questions and answers have been prepared according to the AWES TGT/PGT exam syllabus.The AWES PGT Math Mock Test - 6 MCQs are made for AWES TGT/PGT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for AWES PGT Math Mock Test - 6 below.
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AWES PGT Math Mock Test - 6 - Question 1

_______ gave a slogan 'Freedom is our birth right and we must have it'.

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 1

The correct answer is Bal Gangadhar Tilak.

Key Points

  • Bal Gangadhar Tilak gave a slogan 'Freedom is our birthright and we must have it.
  • Lokmanya Bal Gangadhar Tilak roused the Indian people and injected fresh life into our liberation cause with his electrifying phrase, "Swaraj is my birth-right and I shall have it."
  • Lokmanya Tilak was born in 1856, barely one year before the First War of Indian Independence, into a disappointed and sullen India, and following the defeat of the 1857 insurrection, into a swirl of sorrow and hopelessness.

Important Points

  • Bal Gangadhar Tilak worked valiantly to aid the country's independence from British domination.
  • Bal Gangadhar Tilak, a member of the Lal-Bal-Pal troika, was dubbed the "Father of Indian Unrest" by British colonial rulers.
  • Lokmanya Tilak founded and published two newspapers: the Marathi Kesari and the English The Mahratta. To criticize the colonial overlords, he used his pen as a weapon.
AWES PGT Math Mock Test - 6 - Question 2

Who has been appointed as the chairperson and independent director of PayU Payments Private Ltd?

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 2

Renu Sud Karnad has been appointed as the chairperson and independent director of PayU Payments Private Ltd. Her extensive experience, including her tenure at HDFC Bank, highlights PayU's strategy of leveraging seasoned leadership to navigate the evolving fintech landscape.

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AWES PGT Math Mock Test - 6 - Question 3

Who became the first-ever Indian to win a men's singles trophy at a World Table Tennis (WTT) Feeder Series event in Beirut, Lebanon?

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 3

G. Sathiyan made history by winning the men's singles trophy at the WTT Feeder Beirut 2024 event, becoming the first Indian to achieve this feat in a World Table Tennis Feeder Series tournament. This victory showcased his exceptional skills and talent in table tennis on the international stage.

AWES PGT Math Mock Test - 6 - Question 4

Which institution releases the ‘Production Gap report’?

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 4

The United Nations Environment Programme’s (UNEP) Production Gap report has been released in anticipation of the COP28 climate conference.
It warns that global fossil fuel production over the next seven years is projected to exceed more than double the levels required to stay within the climate goals outlined in the 2015 Paris climate agreement, including the crucial target of limiting global warming to 1.5 degrees Celsius.

AWES PGT Math Mock Test - 6 - Question 5

What is the name of the bi-annual exercise conducted by the Indian Navy off the Mumbai coast?

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 5

The Indian Navy concluded the bi-annual 'Prasthan' exercise off the Mumbai coast, working with defence, state, and civil agencies to enhance preparedness and coordination in addressing contingencies related to oil production platforms.

AWES PGT Math Mock Test - 6 - Question 6
What are the changes required to be made in RTE 2009 as per NEP 2020?
Detailed Solution for AWES PGT Math Mock Test - 6 - Question 6

The National Education Policy (NEP) was approved by the Union Cabinet in July 2020 and aims to implement various improvements to the Indian educational system from the school level to the college level.

Key Points

  • According to NEP 2020, Children from 3 to 18 years old will have access to a free and compulsory high-quality education.
  • This implies that all children between the ages of 3 and 18 will be entitled to receive a quality education from the government, regardless of their socioeconomic status.
  • Everyone has access to get-quality education for all children from the age of 3-18 years instead of 6-14 years as per the RTE 2009.

 Therefore, the Arrangement of free and compulsory education for 3-18-year-old students are the changes required to be made in RTE 2009 as per NEP 2020.

Additional Information

  • Right to Education Act (RTE) provided free and compulsory education to children between the age group of 6-14 years in 2009 and enforced it as a fundamental right under Article 21-A.
  • India became one of 135 countries to make education a fundamental right of every child when the Act came into force on 1 April 2010.
AWES PGT Math Mock Test - 6 - Question 7

In a city, 20 per cent of the population travels by car, 50 per cent travels by bus and 10 per cent travels by both car and bus. Then persons travelling by car or bus is:

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 7

► n(Persons travelling by car) = 20 = n(C)
► n(Persons travelling by bus) = 50 = n(B)
► n(Persons travelling by both car and bus) = 10 = n(C ∩ B)
∴ n(C ∪ B) = n(C) + n(B) - n(C ∩ B)
= 20 + 50 - 10
= 60 

AWES PGT Math Mock Test - 6 - Question 8

In a certain town, 25% families own a cell phone,15% families own a scooter and 65% families own neither a cell phone nor a scooter. If 1500 families own both a cell phone and a scooter, then the total number of families in the town is:

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 8

Step-by-step Explanation:
Since we have given that,
Percentage of families own a cell phone = 25%
Percentage of families own a scooter = 15%
Percentage of families neither own = 65%
So, it becomes,
P(C ∪ S)= 1 - P(C ∪ S)
0.65 = 1 - P(C ∪ S)
1 - 0.65 = P(C ∪ S)
P(C ∪ S) = 0.35
So, it becomes, 
P(C ∪ S) = P(C) + P(S) - P(C ∩ S)
0.35 = 0.25 + 0.15 - x
0.35 = 0.40 - x
x = 0.05
Thus, 0.05 x Total number of families in town = 1500
Total number of families in the town =
1500 / 0.05 = 30,000
Hence, the total number of families in the town is 30,000.

AWES PGT Math Mock Test - 6 - Question 9

U = Set of all teachers in a school and B = Set of all Mathematics teachers in a school, So B’ =?

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 9

U = Set of all teachers in a school
B = Set of all Mathematics teachers in a school
B’ = U – B = Set of all Non-Mathematics teachers in a school

AWES PGT Math Mock Test - 6 - Question 10

Let S = {1, 2, 3}. The function f : S → S defined as below have inverse for 

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 10

Since f(2) = f(3) = 1, then inverse does not exists
Inverse exist for (C) f-1 = {(3, 1), (2, 3), (1, 2)}.

AWES PGT Math Mock Test - 6 - Question 11

The smallest positive integer n, for which 

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 11

n! < [(n+1)/2]n
For(n=1) 1! < [(1+1)/2]1
= 1 < (2/2)1
1 < 1 (False)
 
For(n=2) 2! < [(2+1)/2]2
= 2 < (3/2)2
1 < 6/4 
1 < 3/2
1 < 1.5 (True)
Therefore smallest number will be 2.

AWES PGT Math Mock Test - 6 - Question 12

The number of all odd divisors of 3600 is

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 12

 Number 1 is odd. As any number is divisible by 1: 1
Do prime factorisation of 3600: 2*2*2*2*3*3*5*5
Select all odd numbers from above: 3,3,5,5
Try every possible products of these:
Single number: 3, 5
Two numbers: 3*3, 3*5, 5*5: 9,15,25
Three numbers: 3*3*5, 3*5*5: 45, 75
All four: 3*3*5*5: 225
The odd divisors are: 1,3,5,9,15,25,45,75,225
There are 9 odd divisors of 3600.

AWES PGT Math Mock Test - 6 - Question 13

How many words beginning with ‘T’ and ending with ‘E’ can be formed using the letters of the word”TRIANGLE” ?

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 13

There are 8 letters in the word TRIANGLE.
2 alphabets are fixed, remaining are 6 alphabets
So, number of arrangements = 6P6
= 6!
= 720

AWES PGT Math Mock Test - 6 - Question 14

The values of k, for which the equation x2 + 2(k – 1) x + k + 5 = 0 possess atleast one positive root, are

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 14

AWES PGT Math Mock Test - 6 - Question 15

If a is the nth root of unity, then 1 + 2a + 3a2 + ...... to n terms equal to   

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 15


⇒ αS = α + 2α2 + 3α3 + ...+(n -1)αn-1 +nαn

On subtracting, we get


Since, α is nth root of unity, therfore
αn = 1 

AWES PGT Math Mock Test - 6 - Question 16

If |z| =  z + 3 - 2i, then z equals 

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 16

z =| z | -3+ 2i ⇒ | z |2= (| z | -3)2 + 4 = | z |2 -6 | z | +9 + 4Þ | z | 13/6
=
Thus,  z = - 5/6 + 2i

AWES PGT Math Mock Test - 6 - Question 17

Square root of 5 + 12i is

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 17

(a + ib)2 = 5 + 12i
use (a + b)2 = a2 + b2 + 2*a*b
=> a2 + b2*i2 + 2*a*b*i = 5 + 12i
i2 = -1
⇒ a2 - b2 + 2*a*b*i = 5 + 12i
equate the real and complex coefficients
⇒ a2 - b2 = 5 and ab = 6
a = 6/b
substitute in a2 - b2 = 5
⇒ 36/b2 - b2 = 5
⇒ 36 - b4 = 5b2
⇒ b4 + 5b2 - 36 = 0
⇒ b4 + 9b2 - 4b2 - 36 = 0
⇒ b2(b2 + 9) - 4(b2 + 9) = 0
⇒ (b2 - 4)(b2 + 9) = 0
⇒ b2 = 4 and b2 = -9
b is a real number, so we eliminate b2 = -9
b2 = 4
⇒ b = 2 and b = -2
a = 3 and a = -3
The required number can be 3 + 2i and -3 -2i

AWES PGT Math Mock Test - 6 - Question 18

The coefficients of xp and xq (p, q are + ve integers) in the binomial expansion of (1+x)p+q are

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 18

The ratio of the coefficients of xp and xq in the expansion of (1+x)p+q is

AWES PGT Math Mock Test - 6 - Question 19

Coefficient of a2b5 in the expansion of (a+b)3(a−2b)4 is

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 19

AWES PGT Math Mock Test - 6 - Question 20

Let R = (5√5 + 11)2n+1, f = R - [R], then Rf =

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 20

Given, G = (5√5 + 11)2n + 1 , 0 < G < 1 and R = (5√5 + 11)2n + 1

AWES PGT Math Mock Test - 6 - Question 21

A man saved Rs 21700 in 14 years. In each year after the first he saved Rs 100 more than he did in the preceding year. How much did he save in the first year?

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 21

d = 100
Sn = 21700
n = 14
Sn = n/2[2a + (n-1)d]
21700 = 14/2[2a + (14-1)100]
= 21700 = 7[2a + 1300]
= 3100 = 2a + 1300
⇒ 3100 - 1300 = 2a
⇒ 1800 = 2a
⇒ a = 900

AWES PGT Math Mock Test - 6 - Question 22

The third term of a G.P. is 3, the product of first five terms of this progression is:

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 22


AWES PGT Math Mock Test - 6 - Question 23

The natural numbers are divided into groups 1, (2, 3), (4, 5, 6), (7, 8, 9, 10)....; then the sum of the numbers in the 50th group is

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 23

1
2 3
4 5 6
7 8 9 10
..........
Series for starting number:
1, 2, 4, 7, ...
Let  Tn = an2 + bn + c
a+b+c=1                         ......(1)
4a+2b+c=2                   ......(2)
9a+3b+c=4                   .......(3)
From eq (1), (2), (3), we get:
a= 1/2, b= −1/2, c=1
∴ Tn = n2/2 − n/2 + 1
∴ T50 = (50)2/2 − 50/2 + 1 = 1226
Now, elements in 50th group:
1226, 1227, 1228,.....(50 terms)
∴ Sn = 50/2[2×1226+(50−1)×1]
= 62525

AWES PGT Math Mock Test - 6 - Question 24

If ax2 + bx + c = 0 and bx2 + cx + a = 0 have a common a ≠ 0 

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 24

2 + bα + c = 0 and bα2 + cα + a = 0 ⇒ α = 1 ∴ a + b + c = 0

AWES PGT Math Mock Test - 6 - Question 25

The minor Mij of an element aij of a determinant is defined as the value of the determinant obtained after deleting the​

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 25

A minor, Mij, of the element aij is the determinant of the matrix obtained by deleting the ith row and jth column.

AWES PGT Math Mock Test - 6 - Question 26

The equation of the hyperbola whose foci are (6, 5), (–4, 5) and eccentricity 5/4 is

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 26

Let the centre of hyperbola be (α,β)
As y=5 line has the foci, it also has the major axis.
∴ [(x−α)2]/a2 − [(y−β)2]/b2 = 1
Midpoint of foci = centre of hyperbola
∴ α=1,β=5
Given, e= 5/4
We know that foci is given by (α±ae,β)
∴ α+ae=6
⇒1+(5/4a)=6
⇒ a=4
Using b2 = a2(e2 − 1)
⇒ b2=16((25/16)−1)=9
∴ Equation of hyperbola ⇒ [(x−1)2]/16−[(y−5)2]/9=1

AWES PGT Math Mock Test - 6 - Question 27

The equation of a line passing through the centre of a rectangular hyperbola is x – y –1 = 0. if one of its asymptote is 3x-4y-6 = 0, then equation of its other asymptote is

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 27

Pt of intersection of x-y-1=0 and 3x-4y-6=0 is (-2,-3) other asymptote will be in the form of 4x + 3y + λ =0 and it should pass through (-2,-3). Thus λ = -17

AWES PGT Math Mock Test - 6 - Question 28

The  value of sin310o + sin350o - sin370o is equal to 

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 28

sin310° + sin350° - sin370° 
= 1/4 [(3 sin 10° - sin 30°) + (3 sin 50° - sin 150°) - (3 sin 70° - sin 210°)]

AWES PGT Math Mock Test - 6 - Question 29

Find the direction cosines of the vector joining the points A(1, 2, –3) and B(–1, –2, 1), directed from A to B.

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 29









Therefore, the D.C.’s of vector AB are given by: 

AWES PGT Math Mock Test - 6 - Question 30

If a line has the direction ratios – 18, 12, – 4, then what are its direction cosines ?

Detailed Solution for AWES PGT Math Mock Test - 6 - Question 30

If a line has the direction ratios – 18, 12, – 4, then its direction cosines are given by:








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