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AWES TGT/PGT Exam  >  AWES TGT/PGT Tests  >  AWES TGT Mock Test Series 2025  >  AWES TGT Maths Mock Test - 10 - AWES TGT/PGT MCQ

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


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30 Questions MCQ Test AWES TGT Mock Test Series 2025 - AWES TGT Maths Mock Test - 10

AWES TGT Maths Mock Test - 10 for AWES TGT/PGT 2025 is part of AWES TGT Mock Test Series 2025 preparation. The AWES TGT Maths Mock Test - 10 questions and answers have been prepared according to the AWES TGT/PGT exam syllabus.The AWES TGT Maths Mock Test - 10 MCQs are made for AWES TGT/PGT 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for AWES TGT Maths Mock Test - 10 below.
Solutions of AWES TGT Maths Mock Test - 10 questions in English are available as part of our AWES TGT Mock Test Series 2025 for AWES TGT/PGT & AWES TGT Maths Mock Test - 10 solutions in Hindi for AWES TGT Mock Test Series 2025 course. Download more important topics, notes, lectures and mock test series for AWES TGT/PGT Exam by signing up for free. Attempt AWES TGT Maths Mock Test - 10 | 200 questions in 180 minutes | Mock test for AWES TGT/PGT preparation | Free important questions MCQ to study AWES TGT Mock Test Series 2025 for AWES TGT/PGT Exam | Download free PDF with solutions
AWES TGT Maths Mock Test - 10 - Question 1
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Which organization collaborated with MeitY to unveil the BhashaNet portal for promoting digital inclusivity in India?

Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 1

The National Internet Exchange of India (NIXI), the National Internet Exchange of India, partnered with the Ministry of Electronics and Information Technology (MeitY) to introduce the BhashaNet portal, aimed at enhancing digital inclusivity and linguistic diversity in the country, showcasing their joint commitment to digital inclusion efforts.

AWES TGT Maths Mock Test - 10 - Question 2
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here will the National Para Badminton Championship be hosted?

Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 2

The National Para Badminton Championship will be held in Jamshedpur at Mohan Ahuja Stadium. Organized jointly by the Badminton Association of India and Tata Steel, the event will witness over 300 para-athletes from across India competing.

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AWES TGT Maths Mock Test - 10 - Question 3
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When is World Oral Health Day celebrated?

Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 3

World Oral Health Day is celebrated annually on March 20 to raise awareness about oral health and its connection to overall well-being. It was first observed on September 12, 2007, which marked the birthday of Dr. Charles Godon, the founder of FDI World Dental Federation. The day aims to highlight the importance of oral hygiene and preventive measures against common oral diseases like cavities, which affect a significant portion of the global population.

AWES TGT Maths Mock Test - 10 - Question 4
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Find the value of x which satisfies 5x – 3 < 7, where x is a natural number.
Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 4

The given inequality is 5x– 3 < 7
=> 5x – 3 + 3 < 7 + 3                             [3 is added both sides]
=> 5x < 10
=> x < 10/5
=> x < 2
When x is a real number, the solutions of the given inequality are given by x < 2, i.e., all real numbers x which are less than 2.

AWES TGT Maths Mock Test - 10 - Question 5
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The sum of the binomial coefficients of the 3rd, 4th terms from the beginning and from the end of (a + x)n is 440 then n =
Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 5

Applying the above conditions, we get
nC2 + nC3+ nCn−2 + nCn−3 = 440
2(nC2 + nC3)=440
nC2 ​ + nC3=220
n(n−1)/2!+ [n(n−2)(n−1)]/3!=220
n(n−1)/2 ​(1+(n−2)/3=220
n(n−1)/2 (n+1)/3=220
n(n2−1)/6 ​= 220
n3−n=1320
n3−n−1320=0
The only real root of the above equation is 11.
Hence n=11

AWES TGT Maths Mock Test - 10 - Question 6
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If z1 and z2 are non real complex numbers such that |z1| = |z2| and Arg(z1)+Arg(z2)= π, then z1 =
Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 6

z1 = |z1(cosθ1 + i sinθ1)
z2 = |z2(cosθ2 + i sinθ2)|
Given that |z1| = |z2|
And arg(z1) + arg(z2) = pi
θ1 + θ2 = pi
⇒ θ1 = pi - θ2
Now, z1 = |z2|[cosθ(pi - θ2) + i sin(pi - θ2)]
= z1 = z2(-cosθ2 + i sinθ2)
= z1 = - |z2|(cosθ2 - i sinθ2)|
= z1 = - |z2|(cosθ2 - i sinθ2)
⇒ z1 = - z2(bar)

AWES TGT Maths Mock Test - 10 - Question 7
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Two parabolas y2 = 4a(x – l1) and x2 = 4a(y – l2) always touch one another, the quantities l1 and l2 are both variable. Locus of their point of contact has the equation
Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 7

 Let P(x1 , y1) be point of contact of two parabola. tangents at P of the two parabolas are

AWES TGT Maths Mock Test - 10 - Question 8
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Equation of a plane passing through three non collinear points (x1, y1, z1),(x2, y2, z2) and (x3, y3, z3) is
Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 8

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  

AWES TGT Maths Mock Test - 10 - Question 9
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Find angle A in the following figure
Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 9

As we know that, cosA = (b2 + c2 - a2)/2bc
a = 6, b=4, c=8
cosA = (16+64-36)/2(4)(8)
44/64 
= 0.687
A = cos-1(0.687)
which is approx equals to 46°36’2″

AWES TGT Maths Mock Test - 10 - Question 10
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Which of the following is an even function?
Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 10

Because, f(- x) = f(x) is the necessary condition for a function to be an even function, which is only satisfied by x2+ sin2x .

AWES TGT Maths Mock Test - 10 - Question 11
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Number of positive integral ordered pairs of (a, b) such that 6, a, b are in H.P is
Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 11

6, a bare in H.P 
 are in A.P.

AWES TGT Maths Mock Test - 10 - Question 12
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If A = {x : x is a muliple of 4} and B = {x : x is a muliple of 6}, then A ∩ B consists of all multiples of:
Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 12

L.C.M of 4 and 6 is 12.

Given, A = {x:x is a multiple of 4}
              = {4,8,12,16,20,…}


and     B = {x:x is a multiple of 6}
              = {6,12,18,24,…}


∴A ∩ B = {12,24,…}
             = {x:x is amultiple of 12}

AWES TGT Maths Mock Test - 10 - Question 13
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If  then domain of fof is
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AWES TGT Maths Mock Test - 10 - Question 14
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F(x) = tan (log x)
F'(x) =
Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 14

∫tan(log x) dx
log x = t
x = et
dx = et dt
f(t) = ∫tan t dt
f’(t)= sec2 t
= sec2(log x)

AWES TGT Maths Mock Test - 10 - Question 15
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The area bounded by the curve y = 4x - x2 and the x- axis is equal to
Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 15

For x - axis, y = 0,

Therefore, 4x - x2 = 0

Therefore, x = 0 or x = 4

Required area :

AWES TGT Maths Mock Test - 10 - Question 16
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If the latus rectum of an hyperbola be 8 and eccentricity be 3/√5 then the equation of the hyperbola is
Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 16

Give eccentricity of the hyperbola is, e= 3/(5)1/2
​⇒ (b2)/(a2) = 4/5..(1)
And latus rectum is =2(b2)/a=8
⇒ b2/a=4…(2)
By (2)/(1) a=5
∴ b2=20
Hence required hyperbola is, (x2)/25−(y2)/20=1
⇒ 4x2−5y2 =100

AWES TGT Maths Mock Test - 10 - Question 17
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If θ is the angle between any two vectors  when θ is equal to
Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 17


AWES TGT Maths Mock Test - 10 - Question 18
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The smallest value of the polynomial x3−18x2+96 in the interval [0, 9] is
Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 18

To find the smallest value of the polynomial

f(x) = x³ - 18x² + 96 on the interval [0, 9], follow these steps:

Step 1: Find the derivative

To locate critical points, we differentiate the function:

f'(x) = 3x² - 36x

Step 2: Set the derivative equal to zero

3x² - 36x = 0

Factor the expression:

3x(x - 12) = 0

This gives two critical points:
x = 0 and x = 12

Step 3: Check which points lie in the interval [0, 9]

Since x = 12 is outside the interval, we only consider:

  • x = 0

  • x = 9 (right endpoint of the interval)

Step 4: Evaluate f(x) at x = 0 and x = 9

  • f(0) = 0³ - 18(0)² + 96 = 96

  • f(9) = 9³ - 18(9)² + 96
    = 729 - 1458 + 96
    = -633

Step 5: Conclusion

The smallest value of the function on [0, 9] is:

-633 at x = 9

AWES TGT Maths Mock Test - 10 - Question 19
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If A is a non singular matrix and A’ denotes the transpose of A , then
Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 19

Because , |A|=|A′|

AWES TGT Maths Mock Test - 10 - Question 20
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If a, b, c, d, x are real and the roots of equation (a2 + b2 + c2)x2 - 2 (ab + bc + cd)x + (b2 + c2 + d2) = 0 real and equal, then a, b, c, d are in
Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 20

Roots are real and equal
⇒ (a2 + b2 + c2) (b2 + c2 + d2)-(ab + bc + cd)2 = 0 
⇒ b2 = ac, c2 = bd, ac = bd
⇒ a, b, c, d are in G.P

AWES TGT Maths Mock Test - 10 - Question 21
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The minimum value of (x) = sin x cos x is 
Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 21

Sinx cosx = 1/2 (sin2x) and minimum value of sin2x is – 1 .

AWES TGT Maths Mock Test - 10 - Question 22
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The function f (x) = a x + b is strict increasing for all x ∈ R iff
Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 22

Since f ‘ (x) = a , therefore , f (x) is strict increasing on R iff a > 0.

AWES TGT Maths Mock Test - 10 - Question 23
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What is the value of tan 25°?
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AWES TGT Maths Mock Test - 10 - Question 24
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Vector equation of a plane that contains three non collinear points having position vectors 
Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 24

Vector equation of a plane that contains three non collinear points having position vectors

AWES TGT Maths Mock Test - 10 - Question 25
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Four alphabets A, M, P, O are purchased from a warehouse. How many ordered pairs of initials can be formed using these?
Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 25

Total number of letters = 4
 Number of ordered pairs of letters that can be formed like (A, M) or (P, O) etc = 4P2 ​= 4!/2!
​= 24/2
​= 12

AWES TGT Maths Mock Test - 10 - Question 26
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The function f(x) = sin x2 is
Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 26

For even function: f(-x) = f(x) , 
therefore, f(− x)
 = sin (− x)2 = sin x2 = f(x).

AWES TGT Maths Mock Test - 10 - Question 27
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Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 27

Using 

AWES TGT Maths Mock Test - 10 - Question 28
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Determine the direction cosines of the normal to the plane and the distance from the origin. Plane z = 2
Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 28

We have z = 2 . , it can be written as : 0x+0y+1z = 2. Compare it with lx+my+nz = d , we get ; l = 0 , m = 0 , n = 1 and d = 2 . therefore , D.C.’s of normal to the plane are 0 , 0 , 1 and distance from the origin = 2.

AWES TGT Maths Mock Test - 10 - Question 29
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The function is not differentiable at
Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 29

By verification f ' (2 -) ≠ f ' (2 +)
∴ f(x) is not differentiable at x = 2

AWES TGT Maths Mock Test - 10 - Question 30
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There are three coplanar parallel lines. If any p points are taken on each of the lines, then find the maximum number of triangles with the vertices of these points.

(2010)
Detailed Solution for AWES TGT Maths Mock Test - 10 - Question 30

The number of triangles with vertices on different lines
= PC1 × PC1 x PC1 = p3
The number of triangles with 2 vertices on one line and the third vertex on any one of the other two lines 

∴ the required number of triangles = P3 + 3P2(P - 1)
= 4p3 – 3p2 = p2 (4p – 3)
(The work “maximum” shows that no selection of points from each of the three lines are collinear).

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