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OTET Exam  >  OTET Tests  >  OAVS TGT Math Mock Test - 10 - OTET MCQ

OAVS TGT Math Mock Test - 10 - OTET MCQ


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30 Questions MCQ Test - OAVS TGT Math Mock Test - 10

OAVS TGT Math Mock Test - 10 for OTET 2025 is part of OTET preparation. The OAVS TGT Math Mock Test - 10 questions and answers have been prepared according to the OTET exam syllabus.The OAVS TGT Math Mock Test - 10 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 - 10 below.
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OAVS TGT Math Mock Test - 10 - Question 1
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The 21st term of the AP whose first two terms are -3 and 4, is

Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 1

a1=-3,
a2=4,
d=4-(-3)=7,
a21=?,
a21=a+(n-1)d
=-3+(21-1)7
= -3+(20)(7)
= -3+140
=137

OAVS TGT Math Mock Test - 10 - Question 2
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If (x-1) is a factor of ax – a, then find the value of a​

Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 2

ANSWER :- d

Solution :- f(x) = ax - a……………………..(1)

x - 1 = 0

x = 1

Putting in eq(1)

(1)x - 1 => x - 1

 

For eg :- if we put x = 100

Putting in eq(1)

(100)x - 100 => x - 100

So, all the values of a

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OAVS TGT Math Mock Test - 10 - Question 3
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The value of the expression  is

Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 3

We know that sin 60 =√3/2 and cos 30 = √3/2.
Therefore , Sin 60/cos 30= (√3/2)/(√3/2) = 1

OAVS TGT Math Mock Test - 10 - Question 4
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(x2 + 1)2 - x2 = 0 has
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 4

Given equation is (x2 + 1)2 - x2 = 0
⇒ x4 + 1 + 2x2 - x2 = 0 [∵ (a + b)2 = a2 + b2 + 2ab]
⇒ x4 + x2 + 1 = 0
Let x2 = y
∴ (x2)2 + x2 + 1 = 0
y2 + y + 1 = 0
On comparing with ay2 + by + c = 0, we get
a = 1, b = 1 and c = 1
Discriminant, D = b2 - 4ac
= (1)2 - 4(1)(1)
= 1 - 4 = -3
Since, D < 0
∴ y2 + y + 1 = 0 i.e., x4 + x2 + 1 = 0 or (x2 + 1)2 - x2 = 0 has no real roots.

OAVS TGT Math Mock Test - 10 - Question 5
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If sec 4A = cosec (A-20°),where 4A is an acute angle, find the value of A
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 5

 

OAVS TGT Math Mock Test - 10 - Question 6
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Customers are asked to stand in the lines. If one customer is extra in a line, then there would be two less lines. If one customer is less in line, there would be three more lines. Find the total number of customers.
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 6

Step-by-step explanation:

Customers are asked to stand in the lines. If one customer is extra in a line, then there would be two less lines. If one customer is less in line, there would be three more lines.

 

Let say There are  C customers in a Line  and total L number of lines

 

Total number of customers = ( customers in a line) * (number of Lines)

=>Total number of customers =  CL

 

If one customer is extra in a line, then there would be two less lines

=> Total number of customers = (C + 1)(L -2)

(C + 1)(L -2)  = CL

=> CL + L - 2C - 2 = CL

=> L - 2C  = 2   - eq 1

 

If one customer is less in line, there would be three more lines.

=> Total number of customers = (C - 1)(L +3)

(C - 1)(L +3) = CL

=> CL - L + 3C - 3 = CL

=> - L + 3C = 3    - eq 2

Adding eq 1 & eq 2

=> C = 5

L - 2(5) = 2

=> L = 12

5 customers in a Line

Total Number of customers =  CL = 5*12  = 60

OAVS TGT Math Mock Test - 10 - Question 7
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If ‘p’ is a prime number, then √p is
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 7

√p is an irrational number because square root of every prime number is an irrational number.

OAVS TGT Math Mock Test - 10 - Question 8
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The radius of a cylindrical tank is 28m. If its capacity is equal to that of a rectangular tank of size 28mx16mx11m, then its depth is​
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 8

Let d be the depth of the cylindrical tank. According to the given information, π(28)2 xd=28x16x11
⇒ d=2
Thus, the depth of the cylindrical tank is 2 m.

OAVS TGT Math Mock Test - 10 - Question 9
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The mean of five observations is 15. If the mean of first three observations is 14 and that of last three is 17, then the third observation is
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 9

⇒  It is given that Mean of 5 observations is 15.

∴  The sum of observations =15×5=75.

∴  It is given that mean of the first 3 observations is 14.

∴  The sum of first three observations =14×3=42.

⇒  Given that mean of the last 3 observations is 17.

∴  The sum of the last three observations =17×3=51

∴  The third observation =(42+51)−75
 =93−75

=18

OAVS TGT Math Mock Test - 10 - Question 10
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In ΔABC, D, E and F are respectively mid points of BC, CA and AB. If the lengths of side AB, BC and CA are 7 cm, 8 cm and 9 cm respectively, the perimeter of DEF will be
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 10

Since, D,E,F are the midpoints of BC,CA and AB,Thus

OAVS TGT Math Mock Test - 10 - Question 11
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(p + q)th and (p – q)th terms of an A.P. are respectively m and n. The pth term is :
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 11

l=a+(n-1)d
(p+q)th term is m
m=a+(p+q-1)d
m=a+pd+qd-d  ….1
(p-q)th term is n
n=a+(p-q-1)d
n=a+pd-qd-d   ….2
Adding 1 and 2
m+n=2a+2pd-2d
m+n=2(a+pd-d)
½(m+n=a+(p-1)d
So pth term is ½(m+n)

OAVS TGT Math Mock Test - 10 - Question 12
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If a hemi-spherical dome has an inner diameter of 28 m, then its volume (in m3) is :
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 12

OAVS TGT Math Mock Test - 10 - Question 13
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The LCM of two consecutive numbers is
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 13

The LCM of two consecutive numbers is their product always.

OAVS TGT Math Mock Test - 10 - Question 14
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Two coins are tossed together. The probability of getting head on both the coins is​
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 14

The sample space for the event is :    (H,H)  (T,H)  (H,T)  (T,T)
Therefore total outcomes= 4

Probability =  1/4

OAVS TGT Math Mock Test - 10 - Question 15
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If “1” is a zero of the polynomial P(a) = x2a2 – 2xa + 3x – 2, then x = ______
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 15

The correct solution of this question is given below:

Here, P(a) = x2a2 - 2xa + 3x - 2

1 is a zero of P(a), so P(1) = 0

Therefore, x212 - 2x.1 + 3x - 2 = 0

x2 + x - 2 = 0

(x + 2)(x - 1) = 0

x = -2, 1

OAVS TGT Math Mock Test - 10 - Question 16
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The value of tan 1∘ tan 2∘ tan 3∘………… tan 89∘ is
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 16

tan 1° tan2° tan3° ..............tan 89°
= tan(90° -  89°) tan(90° - 88°) tan(90° -  87°) .........  tan 87° tan 88° tan 89°
= cot 89° cot 88° cot 87° .............tan 87° tan 88° tan 89°
= (cot 89° tan 89°) (cot 88° tan 88°) (cot 87° tan 87°) .............(cot 44° tan 44°) tan 45°
= 1x1x1x1x1.........1 = 1 

OAVS TGT Math Mock Test - 10 - Question 17
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ABCD is a Parallelogram in which AB = 9.5cm and its perimeter is 30cm. Find the length of each side of the Parallelogram?
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 17

We know that the perimeter of parallelogram ABCD can be written as

Perimeter = AB + BC + CD + DA

We know that opposite sides of parallelogram are equal

AB = CD and BC = DA

By substituting the values

Perimeter = 9.5 + BC + 9.5 + BC

It is given that perimeter = 30 cm

So we get

30 = 19 + 2BC

It can be written as

2BC = 30 – 19

By subtraction

2BC = 11

By division we get

BC = 5.5 cm

Therefore, AB = 9.5 cm, BC = 5.5 cm, CD = 9.5 cm and DA = 5.5 cm.

OAVS TGT Math Mock Test - 10 - Question 18
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In the given figure, O is the centre of the circle, and AC is its diameter. Another circle with AB as diameter is drawn. If AC = 54 cm and BC = 10 cm, the area of shaded portion will be 

​
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 18

AC=54cm, Radius=AO=54/2=27cm
Area of the bigger circle= πR2= 22/7 * 27 * 27=2291 (approx)
Diameter of the smaller circle=54-10=44
Radius=44/2=22
Area of the smaller circle= πr2=22/7 * 22 * 22=1521 (approx)
Area of the shaded region=Area of the bigger circle-Area of the smaller circle
= 2291-1521=770 cm2

OAVS TGT Math Mock Test - 10 - Question 19
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The bisectors of the base angles of an isosceles triangle ABC, with AB = AC, meet at O. If ∠B = ∠C = 50°. What is the measure of angle O?
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 19



OAVS TGT Math Mock Test - 10 - Question 20
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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. Represent the above equation in quadratic equation.
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 20
The Correct equation Formed

3x2 + 2x – 85

OAVS TGT Math Mock Test - 10 - Question 21
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The graph of a cubic polynomial x3 – 4x meets the x – axis at (– 2, 0), (0, 0) and (2, 0), then the zeroes of the polynomial are
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 21

To find the zeroes of the polynomial y=x3−4x, we can follow these steps:

Step 1: Set the polynomial equal to zero
To find the zeroes of the polynomial, we need to solve the equation:
x3−4x=0

Step 2: Factor the polynomial
We can factor out x from the equation:
x(x2−4)=0

Step 3: Further factor the quadratic
The expression x2−4 is a difference of squares, which can be factored as:
x(x−2)(x+2)=0

Step 4: Solve for the zeroes
Now, we can set each factor equal to zero:
1. x=0
2. x−2=0 → x=2
3. x+2=0 → x=−2

Conclusion
The zeroes of the polynomial x3−4x are:
x=−2,x=0,x=2

OAVS TGT Math Mock Test - 10 - Question 22
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In the given figure, ABCD is a quadrilateral inscribed in circle with centre O. CD is produced to E. If ∠ADE = 95o and ∠OBA = 30o, then ∠OAC is equal to
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 22

OAVS TGT Math Mock Test - 10 - Question 23
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Zero of a zero polynomial is:
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 23

Zero of the zero polynomial is any real number.
e.g., Let us consider zero polynomial be 0(x-k), where k is a real number For determining the zero, put x-k = 0 ⇒ x = k Hence, zero of the zero polynomial be any real number. 

OAVS TGT Math Mock Test - 10 - Question 24
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If two parallel lines are cut by a transversal, then the pairs of ___________ angles are congruent.
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 24

If two parallel lines are cut by a transversal, the corresponding angles are congruent. If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel.

OAVS TGT Math Mock Test - 10 - Question 25
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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 red face card.
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 25

No. of red face card = 6

Total no of cards = 52

Probability of getting a face card

= No. of red face cards/Total no. of cards

= 6/52 = 3/26

OAVS TGT Math Mock Test - 10 - Question 26
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The largest number which divides 615 and 963 leaving remainder 6 in each case is
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 26

we have to  find the largest number which divide 615 and 963 leaving remainder 6 in each case.

so let us subtract 6 from 615 and 963

⇒ 615−6=609

⇒ 963−6=957

now lets find the HCF

⇒ prime factorisation of 609=29×3×7

prime factorisation of 957=29×3×11

now lets take out the common factors from both the cases

⇒ 29 and 3

x = 29×3 = 87

∴ 87 is the number which will divide 615 and 963 leaving remainder 6 in each case.

OAVS TGT Math Mock Test - 10 - Question 27
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The solution of 5z2 = 3z is​
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 27

We have 5z2=3z
5z2-3z=0
z(5z-3)=0
So either z=0
Or 5z-3 =0  = z=⅗. So there are two solutions

OAVS TGT Math Mock Test - 10 - Question 28
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The number of three digit numbers divisible by 7 is
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 28

Three digits numbers divisible by 7 are 105, 112, 119,.........., 994
Here, a= 105, d = 112 - 105 = 7, an = 994 

OAVS TGT Math Mock Test - 10 - Question 29
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If A1 and A2 be the two A.M.s between two numbers a and b, then (2A1 – A2) (2A2 – A1) is equal to :
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 29

OAVS TGT Math Mock Test - 10 - Question 30
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(x+1)2 − x2 = 0 has
Detailed Solution for OAVS TGT Math Mock Test - 10 - Question 30

Given: (x+1)2 − x2 = 0
⇒ x2 + 1  + 2x − x2 = 0
⇒ 2x + 1 = 0
⇒ x = −1/2
Therefore, (x+1)2 − x2 = 0 has one real root.

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