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OTET Exam  >  OTET Tests  >  OAVS TGT Math Mock Test - 9 - OTET MCQ

OAVS TGT Math Mock Test - 9 - OTET MCQ


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30 Questions MCQ Test - OAVS TGT Math Mock Test - 9

OAVS TGT Math Mock Test - 9 for OTET 2024 is part of OTET preparation. The OAVS TGT Math Mock Test - 9 questions and answers have been prepared according to the OTET exam syllabus.The OAVS TGT Math Mock Test - 9 MCQs are made for OTET 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for OAVS TGT Math Mock Test - 9 below.
Solutions of OAVS TGT Math Mock Test - 9 questions in English are available as part of our course for OTET & OAVS TGT Math Mock Test - 9 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 - 9 | 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 - 9 - Question 1
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(sec2θ - 1) (1 - cosec2θ) =

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OAVS TGT Math Mock Test - 9 - Question 2
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If cos A + cos2 A = 1, then sin2 A + sin4 A is

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OAVS TGT Math Mock Test - 9 - Question 3
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If 3 is a zero of the polynomial f(x) = x4 – x3 – 8x2 + kx + 12, then the value of k is –

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OAVS TGT Math Mock Test - 9 - Question 4
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The angle which, an arc of a circle subtends at the centre is ….. the angle which it subtends at any point on the remaining part of the circumference.
Detailed Solution for OAVS TGT Math Mock Test - 9 - Question 4
Given : An arc ABC of a circle with center O , and a point C on the remaining part of the circumference.
To Prove : Angle AOB =  Twice angle ABC
Construction : Join OC and produce it to a suitable point D
Proof : Let angles 1,2,3,4,5,6 be as shown in figure 
              a) OA=OB=OC [RADII OF THE SAME CIRCLE ARE EQUAL]
              b)1=4,2=3 [ANGLES OPPOSITE TO EQUAL SIDES ARE EQUAL]
              c)5=4+1=Twice angle1 [EXTERIOR ANGLE PROPERTY] 
              d)6=2+3=Twice angle 2 [EXTERIOR ANGLE PROPERTY]
              e)5+6=Twice angle (1+2) [ADD STATEMENT c AND d]
              f)Angle AOB = Twice angle ACB [WHOLE = SUM OF ALL ITS PARTS]

OAVS TGT Math Mock Test - 9 - Question 5
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A data is such that its maximum value is 75 and range is 20, then the minimum value is
Detailed Solution for OAVS TGT Math Mock Test - 9 - Question 5

Let minimum value be x ,
So,
75 - x = 20
x = 75 - 20
x = 55

OAVS TGT Math Mock Test - 9 - Question 6
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The circumference of a circle whose diameter is 4.2cm is
Detailed Solution for OAVS TGT Math Mock Test - 9 - Question 6

Given : Diameter (d) = 4.2 cm
∴ Circumference  

OAVS TGT Math Mock Test - 9 - Question 7
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Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer as

Assertion : The measure of ∠AOC = 60º

Reason : Angle subtended by an arc of a circle at the centre of the circle is double the angle subtended by arc on the circumference.
Detailed Solution for OAVS TGT Math Mock Test - 9 - Question 7

Join BO.

In ΔAOB , we have

OA = OB [radius]

∠OBA = ∠OAB

[Angle opposite to equal sides of a triangle are equal]

∠OBA = 30º ...(1)

Similarly, in ΔBOC , we get OB = OC

∠OCB = ∠OBC

∠OBC = 40º ...(2)

∠ABC = ∠OBA + ∠OBC

= 30º + 40º = 70º

[Using (1) and (2)]

Since angle subtended by an arc of a circle at the centre of the circle is double the angle subtended by the arc on the circumference.

∠AOC = 2 x ∠ABC

= 2 x 70º = 140º
As the Assertion states that ∠AOC=60∘, it is false.

OAVS TGT Math Mock Test - 9 - Question 8
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The probability of an event that is certain to happen is
Detailed Solution for OAVS TGT Math Mock Test - 9 - Question 8

The probability of an event is a number describing the chance that the event will happen. An event that is certain to happen has a probability of 1. An event that cannot possibly happen has a probability of zero. If there is a chance that an event will happen, then its probability is between zero and 1.

Examples of Events:

  • tossing a coin and it landing on heads
  • tossing a coin and it landing on tails
  • rolling a '3' on a die
  • rolling a number > 4 on a die
  • it rains two days in a row
  • drawing a card from the suit of clubs
  • guessing a certain number between 000 and 999 (lottery)
OAVS TGT Math Mock Test - 9 - Question 9
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Direction: India's national animal Tiger (which has also been under the radar of the government as its population declined in the country) has witnessed an increase in its population.

A survey was done by the Ministry of Environment, Forests and Climate change, according to which tiger population is on rise at the rate of 6 per cent every year from 2006 and 2018.

Pranav has found a report on status of tigers in India in last 100 years. He has some queries as follow :

Q. How much decrease in number of tigers was there between 1900 and 1960?
Detailed Solution for OAVS TGT Math Mock Test - 9 - Question 9
Number of tigers in 1900 = 40,000

Number of tigers in 1960 = 18,000

Decrease in number of tigers = 40,000 – 18,000 = = 22,000

OAVS TGT Math Mock Test - 9 - Question 10
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Find the largest number which divides 62,132,237 to leave the same reminder
Detailed Solution for OAVS TGT Math Mock Test - 9 - Question 10

Trick is HCF of (237-132), (132-62), (237-62)
= HCF of (70,105,175) = 35

OAVS TGT Math Mock Test - 9 - Question 11
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If altitude of the sun is 60°, the height of a tower which casts a shadow of length 30m is
Detailed Solution for OAVS TGT Math Mock Test - 9 - Question 11

Given: Angle of elevation θ = 60°
Let the height of the tower AB be hmeters.
And the length of the shadow BC is 30 meters.

Therefore the hieght of the tower is 30√3 meters.

OAVS TGT Math Mock Test - 9 - Question 12
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Read the following text and answer the following questions on the basis of the same:

On a weekend Rani was playing cards with her family. The deck has 52 cards.If her brother drew one card.

Find the probability of getting a jack of hearts.
Detailed Solution for OAVS TGT Math Mock Test - 9 - Question 12
Total number of cards = 52

We have 4 Jack cards

Total number of Jack of hearts = 1

P (getting a face card) = Number of jack of heart cards/Total number of cards

= 1/52

OAVS TGT Math Mock Test - 9 - Question 13
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In the given figure, the value of x which makes POQ a straight line is :
Detailed Solution for OAVS TGT Math Mock Test - 9 - Question 13
2x+ 30+ 4x = 180 6x = 150 x = 25
OAVS TGT Math Mock Test - 9 - Question 14
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If ax2 + bx + c, a ≠ 0 is factorizable into product of two linear factors, then roots of ax2 + bx + c = 0 can be found by equating each factor to
Detailed Solution for OAVS TGT Math Mock Test - 9 - Question 14

Roots of the equation means a value of x such that the equation becomes zero when that value is substituted. If the equation can be represented into product of two linear equations then the roots can be found by keeping each of the equation equal to zero.We know two numbers in multiplication is equal to zero only when either of the number is zero.So we get zeros of the equation putting the two linear equations equal to 0

OAVS TGT Math Mock Test - 9 - Question 15
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The diameter of a wheel is 1.26 m. The distance travelled in 500 revolutions is
Detailed Solution for OAVS TGT Math Mock Test - 9 - Question 15

Radius of the wheel = 1.26/2 = 0.63 m
Distance travelled in one revolution

∴ Distance travelled in 500 revolutions
= 500 x 3.96 = 1980 m

OAVS TGT Math Mock Test - 9 - Question 16
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The common difference of the A.P whose Sn = 3n2+ 2n is
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Thus, initial term of the A.P. is 5 and the common difference is 6.

OAVS TGT Math Mock Test - 9 - Question 17
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​=
Detailed Solution for OAVS TGT Math Mock Test - 9 - Question 17


Taking LCM

OAVS TGT Math Mock Test - 9 - Question 18
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What is the probability of a sure event?​
Detailed Solution for OAVS TGT Math Mock Test - 9 - Question 18

A sure event is an event, which always happens. For example, it's a sure event to obtain a number between “1”“1” and “6”“6” when rolling an ordinary die.

The probability of a sure event has the value of 11.

OAVS TGT Math Mock Test - 9 - Question 19
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Given that one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is zero, the product of the other two zeroes is
Detailed Solution for OAVS TGT Math Mock Test - 9 - Question 19

Let p(x) =ax3 + bx2 + cx + d
Given that, one of the zeroes of the cubic polynomial p(x) is zero.
Let α, β and γ are the zeroes of cubic polynomial p(x), where a = 0.
We know that,

OAVS TGT Math Mock Test - 9 - Question 20
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If 4tan θ = 3, 
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OAVS TGT Math Mock Test - 9 - Question 21
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Perimeter of a parallelogram is 22 cm. If the longer side, measures 6.5 cm, the measure of the shorter side will be:​
Detailed Solution for OAVS TGT Math Mock Test - 9 - Question 21
Let the length of the shorter side be x cm
length of longer side= 6.5 cm
perimeter= 22 cm
>2[sum of adjacent sides]=22
>2[longer side+shorter side]=22
>2[6.5+x] = 22 = 22/2 =11
>6.5 + x =11 = 11 - 6.5 = 4.5
> x= 4.5
OAVS TGT Math Mock Test - 9 - Question 22
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DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : Sum of first 10 terms of the arithmetic progression - 0.5 , - 1.0, - 1.5 , .......... is -27.5

Reason : Sum of n terms of an A.P. is given as where a = first term, d = common difference.
Detailed Solution for OAVS TGT Math Mock Test - 9 - Question 22

Both are correct. Reason is the correct reasoning for Assertion.

Assertion,

= 5 [- 1 - 4.5]

= 5 (- 5.5) = -27.5

OAVS TGT Math Mock Test - 9 - Question 23
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If (x-2) is the factor of x2 + 2x+ a, find the value of ‘a’.
Detailed Solution for OAVS TGT Math Mock Test - 9 - Question 23

If x-2 is a factor then 2 is the zero of the polynomial
by substituting 2 in the given polynomial,we get
2^2+2(2)+a=0
8+a=0
a=-8

OAVS TGT Math Mock Test - 9 - Question 24
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In the given figure, PQ||RS and EF||QS. If ∠PQS = 60°, then the measure of ∠RFE is:
Detailed Solution for OAVS TGT Math Mock Test - 9 - Question 24

60°+ QSR=180°[co interior angles]

QSR=120°

RFE=QSR

So,RFE=120°

OAVS TGT Math Mock Test - 9 - Question 25
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Direction: Ladli Scheme was launched by the Delhi Government in the year 2008. This scheme helps to make women strong and will empower a girl child. This scheme was started in 2008.

Read the above bar graph and answer the following questions :

Q. What was the difference in budget in the year 2008 - 09 and 2009 - 10?
Detailed Solution for OAVS TGT Math Mock Test - 9 - Question 25
2008 - 09 = 9060

2009 - 10 = 9160

= 9160 - 9060 = 100.

OAVS TGT Math Mock Test - 9 - Question 26
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Two planes intersect each other to form a :
Detailed Solution for OAVS TGT Math Mock Test - 9 - Question 26
Two non-parallel planes in space form a line upon intersection, as long as each plane is unique. Three non-parallel planes intersect at a point. The best and simplest example is to fold a piece of paper. Since the folded paper now represents two distinct planes, the crease itself is the intersection point, forming a line.
OAVS TGT Math Mock Test - 9 - Question 27
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Five friends playing a game in which they are standing at different positions, P, S, T, R and

Rohan is watching them playing. Few questions came to Rohan's mind while watching the game. Give answer to his questions by looking at the figure.

Q. Name the point whose y-co-ordinate is zero :
Detailed Solution for OAVS TGT Math Mock Test - 9 - Question 27
As point Q lies on x-axis. Therefore, its y-coordinate is zero.
OAVS TGT Math Mock Test - 9 - Question 28
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In the following figure, PQ = PR and SQ = SR, then
Detailed Solution for OAVS TGT Math Mock Test - 9 - Question 28

In △PQR and △SRQ,

► PQ = SR(Given)
► QR = QR(Common)
► PR = SQ(Given)

By SSS property:
△PQR≅△SRQ
Therefore, ∠PQS =∠PRS

OAVS TGT Math Mock Test - 9 - Question 29
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Progressions with equal common difference are known as
Detailed Solution for OAVS TGT Math Mock Test - 9 - Question 29

Progressions with equal common difference are known as Arithmetic Progression.

OAVS TGT Math Mock Test - 9 - Question 30
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If a chord of a circle of radius14cm subtends a right angle at the centre of the circle, then the area of the sector is
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