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OAVS TGT Math Mock Test - 4 - OTET MCQ


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30 Questions MCQ Test - OAVS TGT Math Mock Test - 4

OAVS TGT Math Mock Test - 4 for OTET 2024 is part of OTET preparation. The OAVS TGT Math Mock Test - 4 questions and answers have been prepared according to the OTET exam syllabus.The OAVS TGT Math Mock Test - 4 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 - 4 below.
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OAVS TGT Math Mock Test - 4 - Question 1

Factorise:(3x- 5y)3+ (5y – 2z)3 + (2z – 3x)3

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 1

 

 

OAVS TGT Math Mock Test - 4 - Question 2

The area of the square that can be inscribed in a circle of radius 12 cm is

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 2

According to question, Diameter (BD) = 2 x radius = 2 x 12 = 24 cm
∴ Area of square

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OAVS TGT Math Mock Test - 4 - Question 3

The area of the circle that can be inscribed in a square of side 10cm is

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 3

Since if a circle inscribed a square. then the radius of the circle is half of to side of square.
∴  Radius = 10/2 = 5 cm
∴ Area of the circle = πr2 = π(5)2 = 25π sq. cm 

OAVS TGT Math Mock Test - 4 - Question 4

The value of ‘k’ for which the numbers x, 2x + k, 3x + 6 are in A.P. is

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 4

OAVS TGT Math Mock Test - 4 - Question 5

√7 is

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 5

Assume that √7 be a rational number.
i.e. √7 = p/q, where p and q are co prime.
⇒ 7 = p2/q2 
⇒ 7q= p2    ...(1)
⇒ p2 is divisible by 7, i.e. p is divisible by 7
⇒ For any positive integer c, it can be said that p = 7c, p2 = 49c2

Equation (1) can be written as: 7q2 = 49c2
⇒ q2 = 7c2
This gives that q is divisible by 7.

Since p and q have a common factor 7 which is a contradiction to the assumption that they are co-prime.
Therefore, √7 is an irrational number.

OAVS TGT Math Mock Test - 4 - Question 6

In the given data if n = 230, l = 40, cf = 76, h = 10, f = 65, then its median is

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 6

Median=L + 
=40 + 
=40 + 6 = 46

OAVS TGT Math Mock Test - 4 - Question 7

Read the following text and answer the following questions on the basis of the same: In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line (see figures).

A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are dropped in the bucket.

Q. What is the distance run to pick up the 2nd potato?
Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 7
Distance run to pick up the 2nd potato = 2 × (5 + 3) = 16 m
OAVS TGT Math Mock Test - 4 - Question 8

Reduction of a rupee in the price of onion makes the possibility of buying one more kg of onion for Rs.56. Find the original price of the onion per kg?

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 8

OAVS TGT Math Mock Test - 4 - Question 9

A triangle can have______.

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 9

The least number of acute angles that a triangle can have is 2.

As we cannot have more than one right angle or obtuse angle, we have only two or three acute angles in a triangle.

Further, if one angle is acute, sum of other two angles is more than 900 and we cannot have two right angles or obtuse angles.

OAVS TGT Math Mock Test - 4 - Question 10

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : Common difference of an AP in which a21 -a7 = 84 is 14.

Reason : n th term of AP is given by an = a + (n - 1)d

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 10
We have, an = a + (n - 1)d

a21 -a7 = {a + (21 - 1)d}

- {a + (7 - 1)d} = 84

a + 20d- a - 6d = 84

14d = 84

d = 18/14 = 6

d = 6

So, A is incorrect but R is correct

OAVS TGT Math Mock Test - 4 - Question 11

A linear equation in one variable is an equation of the form ………..

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 11

A linear equation is an equation of a straight line, written in one variable. The only power of the variable is 1. Linear equations in one variable may take the form a x + b = 0, ax+b=0, ax+b=0 and are solved using basic algebraic operations

OAVS TGT Math Mock Test - 4 - Question 12

Circles having the same centre and different radii are called______.

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 12


Concentric circles are circles with a common center. The region between two concentric circles of different radii is called an annulus.
Any two circles can be made concentric by inversion by picking the inversion center as one of the limiting points.

OAVS TGT Math Mock Test - 4 - Question 13

Read the following text and answer the following question on the basis of the same:

'Skysails' is that genre of engineering science that uses extensive utilization of wind energy to move a vessel in the sea water. The sky sails technology allows the towing kite to gain a height of anything between 100 m to 300 m. The sailing kite is made in such a way that it can be raised to its proper elevation and then brought back with the help of a telescopic mast that enables the kite to be raised properly and effectively.

Q. What should be the length of the rope of the kite sail in order to pull the ship at the angle θ and be at a vertical height of 200 m?

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 13
In ΔABC, we have

θ = 30°, AB = 200 m

Then, sin 30° = Perpendicular / Hypotenuse

= AB / AC

⇒ 1 / 2 = 200 / AC

⇒ AC = 400 m.

OAVS TGT Math Mock Test - 4 - Question 14

In figure, AB and CD are parallel to each other. The value of x is :

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 14


OAVS TGT Math Mock Test - 4 - Question 15

The probability of a sure event is

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 15

The probability of a sure event is always 1.

OAVS TGT Math Mock Test - 4 - Question 16

A bridge across a river makes an angle of 45° with the river bank. If the length of the bridge across the river is 200m, then the breadth of the river is

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 16

Let the breath of the river be h meters.

= 100√2 meters Therefore, the breadth of river is 

OAVS TGT Math Mock Test - 4 - Question 17

If sin x + cosec x = 2, then sin19x + cosec20 x =

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 17

sin x + cosec x = 2

OAVS TGT Math Mock Test - 4 - Question 18

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. What is the total decline in number of tigers between 1960 to 2007?

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 18
Number of tigers in 1960 = 18,000

Number of tigers in 2007 = 1,411

Decrease in number of tigers = 18,000 – 1,411 = 16,589

OAVS TGT Math Mock Test - 4 - Question 19

A cone of height 8 m has a curved surface area 188.4 2. The radius of the base is : (Take π = 3.14) :

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 19

OAVS TGT Math Mock Test - 4 - Question 20

The expansion of (2a – 3b + 5c)2.

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 20

The expansion of (2a - 3b + 5c)² -: (2a)² + (- 3b)² + (5c)² + 2× 2a × (-3b) + 2× (-3b)× 5c + 2× 5c + 2a. = 4a² + 9b² + 25c² - 12ab - 30bc + 20ac

OAVS TGT Math Mock Test - 4 - Question 21

If the circumference of a circle and the perimeter of a square are equal, then

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 21

Let the radius of the circle be r and side of the square be a.
Then, according to question,
2πr = 4a

Now, ratio of their areas,

Therefore, Area of the circle > Area of the square 

OAVS TGT Math Mock Test - 4 - Question 22

The sum of three terms of an A.P. is 72, then its middle term is

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 22

Let the middle term be a, then first term is a−d and next term is a+d

OAVS TGT Math Mock Test - 4 - Question 23

The 10th term of an A.P. 2, 7, 12, …….. is

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 23

OAVS TGT Math Mock Test - 4 - Question 24

Which of the following is a quadratic equation?

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 24

The correct answer is d

A quadratic equation (from the Latin quadratus for "square") is any equation that can be rearranged in standard form as. where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no. term.

Therefore, x3 - x2 = ( x -1)3 is a quadratic equation.

OAVS TGT Math Mock Test - 4 - Question 25

Which of the following equations has - 1 as a root?

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 25

3x² - 2x - 5 = 0
3x² + 3x - 5x - 5 = 0
3x(x+1) - 5(x+1) = 0
(x+1)(3x-5) = 0
x = -1 and 5/3.

Hence roots of given polynomial are -1 and 5/3.

OAVS TGT Math Mock Test - 4 - Question 26

The length of each side of a rhombus is 10cm and one of its diagonal is of length 16cm. The Length of the other Diagonal is:

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 26
Firstly we know that diagonal of rhombus bisects each other. thus half of diagonal =8cm.
by pythagoras theorem we find another half of diagonal.that is 6 cm
as we diagonals bisect other thus another diagonal
=2×6=12cm
OAVS TGT Math Mock Test - 4 - Question 27

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : Total surface area of the cylinder having radius of the base 14 cm and height 30 cm is 3872 cm2 .

Reason : If r be the radius and h be the height of the cylinder, then total surface area = (2prh +2pr2).

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 27
Total surface area = 2prh +2pr2

= 2p r (h + r)

= 3872 cm2

OAVS TGT Math Mock Test - 4 - Question 28

If a is a non-zero rational and √b is irrational, then a√b is:

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 28

If possible let a√b be rational. Then a√b = p/q, 
where p and q are non-zero integers, having no common factor other than 1.
Now, a√b = p/q ⇒ √b = p/aq……….(i)
But, p and aq are both rational and aq ≠ 0. 
∵ p/aq is rational.
Therefore, from eq. (i), it follows that √b is rational.
The contradiction arises by assuming that a√b is rational.
Hence, a√b is irrational.

OAVS TGT Math Mock Test - 4 - Question 29

In ΔABC, AB = 2.5 cm and BC = 6 cm. Then, the length of AC cannot be

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 29

in triangle ABC

AB = 2.5 cm

BC = 6 cm

AC =  ?

in any triangle sum of two sides >  third side

=> AB +  BC > AC

=> 2.5 + 6 > AC

=> AC < 8.5

AB + AC > BC

=> 2.5 + AC > 6

=> AC > 3.5

BC + AC > AB

=> 6 + AC > 2.5

=> AC > -3.5

Taking all together

 3.5 < AC  < 8.5

3.6 ,  3.8 & 4  lies betwenn them

but not 3.4

Hence Length of AC can not be 3.4 cm

OAVS TGT Math Mock Test - 4 - Question 30

If the product of two zeros of the polynomial f(x) = 2x3 + 6x2 – 4x + 9 is 3, then its third zero is

Detailed Solution for OAVS TGT Math Mock Test - 4 - Question 30

Step-by-step explanation:

p(x) = 2x³ + 6x² – 4x + 9 


Define α,β and γ

Let α,β and γ be the 3 roots

αβ = 3 (Given)


Find the products of all the zeros:

αβγ = - d/a

αβγ = - 9/2


Find the third zeros:

Given αβ = 3

3γ = -9/2

γ = -9/2 ÷ 3

γ = -3/2

The third zero is -3/2

 

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