OAVS TGT Math Mock Test - 2 - OTET MCQ

Total no. of outcomes=52
No. of ace cards=4
No. of non-ace cards=48
Probability of getting a non-ace card = No. of favourable outcomes / total no. of outcomes
=48/52=12/13

Let the radius of the circle be rr and the side of the square be a.a. Then according to the question, 

  Now, Ratio of their perimeters

Given, A dice is thrown once. So,

Total number of outcomes (n) = 6

Number of prime numbers = {2, 3,5}

So, Favorable number of outcomes (m) = 3

Thus, probability of getting a prime number = m/n = 3/6 = 1/2

To factorise the quadratic polynomial x² + 14x + 45, follow these steps:

• Identify two numbers that multiply to 45 and add up to 14.
• The numbers are 9 and 5.
• Rewrite the middle term: x² + 9x + 5x + 45.
• Factor by grouping:
  Group the first two and last two terms: (x² + 9x) + (5x + 45).
  Factor out the common terms: x(x + 9) + 5(x + 9).
  Combine to get: (x + 9)(x + 5).

Thus, the factorised form is (x + 9)(x + 5).

Draw a line l and a point P not lying on l.

Now, we can draw a straight line parallel to l which passes through P.

Clearly from the figure, only one line can be drawn which is parallel to l and passes through P.

We know Probability law which is law of  complement
Which is P(not A)=1-P(A)
Where P(A)=⅖
P(not A)=1-⅖=3/5

As the case is of 2 consecutive integers, one will be odd and the other one even,
⇒ Their product will always be even i.e. it will always be divisible by an even no., i.e. 2, here.

The HCF of two consecutive even numbers is 2.

The point will lie on the line if L.H.S of the equation is equal to R.H.S

Given equation is 2x - y = 5

Put the point ( 2 , -1) in the above equation

2 . 2 - (-1) = 4 + 1 = 5 = R.H.S

So this proves that the given points lie on the line. 

So option D is correct answer.  

We have first ten multiples of 6 as follows:
6,12,18,24,30,36,42,48,54,60

So, both A and R are correct and R explains A.

The general form of a linear equation in one variable is: ax+b=c where a and b are constants and x is a variable.

So, in a linear equation the degree is 1 i.e., highest power in the variable is 1.
But in ax⁴+bx²+c=0 highest power for x is 4. Hence, it is not linear.

It is the definition of parallel lines.

Let α,β,γ are the zeroes of the given polynomial. Given: α+β+γ = (-3/4)

Sample space - {HH, HT, TH, TT}
Number of total possible outcomes = 4
Number of favourable outcome (both heads) = 1
∴  Probability of getting both head = 1/4

Let one zero of the equation be x
Then, other would be 2x
As we know,
x × 2x = 18
x² = 9
x = 3, -3
Case 1:
If x = 3, 2x = 6
Therefore, -k = sum of roots = 9
⇒ k = -9
Case 2:
If x = -3, 2x = -6
Therefore, -k = -9
⇒ k = 9
So, k can be 9,-9. Therefore, option 'b' is correct.

(100+2)×(100-2). [(a+b)(a-b)=a^2-b^2
100^2 - 2^2
10000 - 4
9996

Clearly, there are 52 cards, out of which there are 12 face cards.

P (getting a face card) = 12/52 = 3/13.

Sample Space=1,2,3,4,5,6,7,8,9
Total number of outcomes=9
No of favourable outcomes(odd)=1,3,5,7,9=5
Probability of odd number=No.of favourable outcomes/total number of outcomes=5/9

Correct Answer :- a

Explanation : Let number of girls in class = x

Boys = 2y - 5

Equation will be : x + 5 = 2y

AP is:  a,a+d,a+2d,a+3d,a+4d
Middle term is a+2d=5
d=4
a+2d=5
a+2*4=5
a=5-8= -3
a+d= -3+4=1
a+3d= -3+3*4=-3+12=9
a+4d= -3+4*4= -3+16=13
So the terms are : -3,1,5,9,13

Trigonometric ratio  is correct.

Let one multiple of 5 be x then the next consecutive multiple of will be (x+5) According to question,

x = −35 is not possible therefore x = 30
Then the other multiple of 5 is x+5 = 30+5 = 35
Then the number are 30 and 35.

ABCD is a rectangle.
∴ AB = CD
⇒ 30 = x + y
or x + y = 30 ..... (i)
Similarly, AD = BC
⇒ 14 = x - y
or x - y = 14 .......(ii)
On adding eq. (i) and (ii), we get
2x = 44
⇒ x = 22
Putting the value of x in eq. (i), we get
22 + y = 30
⇒ y = 30 -22
⇒ y = 8
So, x = 22, y = 8.

Given that the equation 3x + ay = 8 passes through the point (2,2) it means that (2,2) is a solution of the equation 

Putting X= 2 and Y = 2 in the equation we have  
3(2) + a (2) = 8
6 + 2a = 8
2a = 8-6
2a = 2
a = 2/2 = 1
Therefore value of
a = 1

So option D is correct answer. 

The correct formula is l =

Therefore, A is true but R is false.