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OTET Exam  >  OTET Tests  >  OAVS TGT Math Mock Test - 7 - OTET MCQ

OAVS TGT Math Mock Test - 7 - OTET MCQ


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30 Questions MCQ Test - OAVS TGT Math Mock Test - 7

OAVS TGT Math Mock Test - 7 for OTET 2025 is part of OTET preparation. The OAVS TGT Math Mock Test - 7 questions and answers have been prepared according to the OTET exam syllabus.The OAVS TGT Math Mock Test - 7 MCQs are made for OTET 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for OAVS TGT Math Mock Test - 7 below.
Solutions of OAVS TGT Math Mock Test - 7 questions in English are available as part of our course for OTET & OAVS TGT Math Mock Test - 7 solutions in Hindi for OTET course. Download more important topics, notes, lectures and mock test series for OTET Exam by signing up for free. Attempt OAVS TGT Math Mock Test - 7 | 100 questions in 100 minutes | Mock test for OTET preparation | Free important questions MCQ to study for OTET Exam | Download free PDF with solutions
OAVS TGT Math Mock Test - 7 - Question 1
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If the area and circumference of a circle are numerically equal, then its radius is

Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 1

Let radius of the circle berunits.
∴ Area of the circle = Circumference of the circle 

OAVS TGT Math Mock Test - 7 - Question 2
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Find the probability of getting a number greater than 2 when a die is thrown

Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 2

Probability of getting a number greater than 2 is
number greater than 2 = 4
total outcomes = 6
so, 4/6
=2/3

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OAVS TGT Math Mock Test - 7 - Question 3
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The value of m, if a = 3 and b = 1 is the solution of equation 2a + 3b = m is:

Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 3

In the given question we have  a=3,b=1 the given equation is 2a + 3b=m

By substituting the values of a,b in the given  equation, we get ,

 2 x 3 + 3 x 1 = m 

6 + 3 = m

9 = m 

So option A is the correct answer. 

 

OAVS TGT Math Mock Test - 7 - Question 4
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If a + b = 12 and a2 + b2 = 60, the value of a3 + b3 is:
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 4

The correct option is Option C.

(a + b)² = a² + b² + 2ab

(12)² = 60 + 2ab

ab = (144 - 60)/2

ab = 84/2

ab = 42

Now, 

(a + b)³ = a³ + b³ + 3ab(a+b)

(12)³ = a³ + b³ + (3 × 42 × 12)

a³ + b³ = 1728 - 1512

Therefore, a³ + b³ = 216

OAVS TGT Math Mock Test - 7 - Question 5
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If a square is inscribed in a circle, then the ratio of their areas is​
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 5


Let side of square be x cms inscribed in a circle.

Radius of circle (r) = 1/2(diagonal of square)

OAVS TGT Math Mock Test - 7 - Question 6
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How many points can be common in two distinct straight lines?
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 6
Two distinct lines will always intersect in at most one point. This will be true no matter how many dimensions we're in, as long as we're in a standard Euclidean geometry. One way to see this is to consider what happens if we have two lines which intersect in more than one point.
OAVS TGT Math Mock Test - 7 - Question 7
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In the given figure, BO and CO are the bisectors of ∠B and ∠C respectively. If ∠A = 500, then ∠BOC = ?
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 7

a+b+c = 180
50+b+c= 180
b+c = 130 ............(1)
divide equation (1) by 2 
1/2(b+c) = 65...........(2)
now in triangle obc
o+1/2(b+c) = 180
o+65= 180 ( from (2))
o= 180-65= 115 

OAVS TGT Math Mock Test - 7 - Question 8
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Which of the following has two distinct roots?
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 8

In equation x2+x−5 = 0
a = 1,b = 1,c = −5
∴ b2−4ac = (1)2−4×1×(−5) = 1 + 20 = 21
Since b2−4ac > 0 therefore, x2+x−5 = 0 has two distict roots.

OAVS TGT Math Mock Test - 7 - Question 9
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On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 9

We need to find the L.C.M of 40, 42 and 45 cm to get the required minimum distance.
40 = 2×2×2×5
42 = 2×3×7
45 = 3×3×5
L.C.M. = 2×3×5×2×2×3×7 = 2520

OAVS TGT Math Mock Test - 7 - Question 10
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Solve for y : (√7) y2 – 6y –13 (√7) = 0
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 10


Using mid term splitting

So either y=13/ 
Or y= 

OAVS TGT Math Mock Test - 7 - Question 11
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If the sum of the two zeros of x3 + px2 +qx + r is zero, then pq =
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 11

Sum of two solutions is zero ,so both are inverse of each other. So we have the solutions as a,-a,b.
(x-a)(x+a)(x+b)=(x2-a2)(x+b)=x3+bx2-a2x-a2b
pq=-a2b=r

OAVS TGT Math Mock Test - 7 - Question 12
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In the given figure, what is the measurement of YXZ?
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 12

The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

OAVS TGT Math Mock Test - 7 - Question 13
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The solution of the trigonometric equation 
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 13


cos2θ = 3(cot2θ-cos2θ)
4cos2θ = 3cot2θ
4=3(1/sin2θ)
sin2θ = 3/4
sinθ = √3/2
θ = 60

OAVS TGT Math Mock Test - 7 - Question 14
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Read the following text and answer the following questions on the basis of the same:

Nidhi and Ria are very close friends. Nidhi’s parents own a Maruti Alto and Ria’s parents own a Toyota Liva. Both the families decided to go for picnic to Somnath temple in Gujarat by their own cars. Nidhi car travels x km/h when Ria’s car travels 5 km/h more than Nidhi’s car Nidhi’s car took 4 hours more than Ria’s car in covering 400 km.

Q. What will be the distance covered by Ria’s car in two hours?
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 14
We know that distance = Speed × time

= (x + 5) × 2 = 2(x + 5) km

OAVS TGT Math Mock Test - 7 - Question 15
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The quadratic equation  has
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 15

As, discriminant (b2 - 4ac) of the equation is negative. Therefore, no real roots.

OAVS TGT Math Mock Test - 7 - Question 16
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In the figure, AB || CD and ∠F = 30° the value of ∠ECD is
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 16
In triangle AFE A+F+E=180 (angle sum property of triangle) 90+30+e=180 e=60 fea=bec=60 bec+dec=180. (co interior) dec=120degree.
OAVS TGT Math Mock Test - 7 - Question 17
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Which of the following are the roots of the quadratic equation, x2 - 9x + 20 = 0 by factorisation?
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 17

 ∴ x = 4 and 5 are the roots/solution of the given quadratic equation

OAVS TGT Math Mock Test - 7 - Question 18
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If a letter of English alphabet is chosen at random, then the probability that the letter is a consonant is:
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 18

The probability that the letter is a consonant = (26 - 5)/26 = 21/26.

OAVS TGT Math Mock Test - 7 - Question 19
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A sum of Rs.700 is to be used to award 7 prizes. If each prize is Rs.20 less than its preceding prize, then the value of the first prize is
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 19

Let the first prize be a.
The seven prizes form an AP with first term a and common difference d = −20
Now the sum of all seven prizes = Rs. 700

OAVS TGT Math Mock Test - 7 - Question 20
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In a swimming pool measuring 90 m x 40 m, 150 men take a dip. If the average displacement of water by a man is 8 m3, then rise in water level is
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 20

Volume of water displaced = 150 x 8 = 1200 m3 
⇒ 90 x 40 x h = 1200
⇒ 

OAVS TGT Math Mock Test - 7 - Question 21
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If two supplementary angles are in the4 ratio 2 : 7, then the angles are :
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 21

Let, One angle be 2x and another angle be 7x.
Now, 2x+7x=180
9x =180
x =180/9=20
Therefore, one angle = 2*20 = 40
Another angle = 7*20 = 140.

OAVS TGT Math Mock Test - 7 - Question 22
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Amit starts his exercise regime with 25 push ups on Monday. He plans to increase 5 push ups every following Monday. How many push ups will he be doing on the 3rd Monday since he started?​
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 22

On 1st Monday he did 25
on 2nd next he did 25+5=30 
on 3rd Monday he did 30+5=35

OAVS TGT Math Mock Test - 7 - Question 23
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If A and B are the angles of a right angled triangle ABC, right angled at C, then 1+cot2A =​
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 23
ABC is a Δ, right angle at c.
1 +cot^2 =?........ 
we know that.....
Cosec^2 - cot^2= 1...
So,
=> 1+ cot^2
=> cosec^2 A
=> (AB)^2/( CB)^2 
= sec ^2B.
OAVS TGT Math Mock Test - 7 - Question 24
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): If the nth term of an A.P. is 7 – 4n, then its common differences is – 4.

Reason (R): Common differences of an A.P. is given by d = an + 1 – an
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 24
We are given, an = 7 – 4n

Also, an + 1 = 7 – 4(n + 1) = 7 – 4n – 4 = 3 – 4n

d = a(n + 1)–an

= 3 – 4n – 7 + 4n = – 4

Therefore, Both A and R are true and R is the correct explanation for A.

OAVS TGT Math Mock Test - 7 - Question 25
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The 7th term from the end of the A.P. – 11, – 8, – 5, ……., 49 is
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 25

OAVS TGT Math Mock Test - 7 - Question 26
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The class size of a distribution is 25 and the first class interval is 200-224. Then, the class marks of first two class intervals are
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 26

class mark of 1st interval=212

class mark of 2nd interval=236.5

Step-by-step explanation:

First Class interval=200-224

class mark=upper limit +lower limit divided by 2..

class mark of first interval is =200+224 divided by 2=212

Second class interval=224-249

class mark of second interval =224 +249 divided by 2

answer= 236.5

OAVS TGT Math Mock Test - 7 - Question 27
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): The equation has no root.

Reason (R): x - 1 ≠ 0, then only above equation is defined.
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 27
Both A and R are true and R is the correct explanation of A.

x = 1

However at x = 1 the expression is not defined.

Hence the above equation has no real roots.

OAVS TGT Math Mock Test - 7 - Question 28
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If HCF(a, b) = 12 and a × b = 1800, then LCM(a, b) is
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 28

Using the result, HCF × LCM = Product of two natural numbers
 ⇒ LCM (a, b) = 1800/12 = 150

OAVS TGT Math Mock Test - 7 - Question 29
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Read the following text and answer the following questions on the basis of the same:

A small scale industry produces a certain boxes of candles in a day. Number of boxes prepared by each worked on a particular day was 2 more than thrice the number of workers working in the industry. The number of boxes produced in a particular day was 85.

Q. Nature of roots of the above quadratic equation are:
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 29
We can see, the discriminant of the given quadratic equation is positive but not a perfect square. Hence, the roots of a quadratic equation are real, unequal.
OAVS TGT Math Mock Test - 7 - Question 30
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A die is thrown once. The probability of getting an even number and a multiple of 3 is
Detailed Solution for OAVS TGT Math Mock Test - 7 - Question 30

Number of possible outcomes = {6} = 1
Number of Total outcomes = 6
∴ Required Probability = 1/6

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