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

p(x) = ax
p(x) = 0
ax = 0
x = 0/a
x = 0
{0 by something is equals to 0}
Therefore,0 is the zero of the polynomial. 
Checking:-
p(0) = a(0)
= 0

If the coefficient of x² is zero , then the equation is not a quadratic equation , its a linear equation. So its necessary condition for the quadratic equation. 

Angle acb = 75 ( linear pair) Ab= Ac hence angle B= angle c in triangle ABC angle a+B+c= 180. angle B+ c = 150 hence angle c a= 30

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 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

Sn=3n²+5n

S₁=a₁=3(1)²+5(1)=8

S₂=3(2)²+5(2)=22

S₂=22=a₁+a₂

a₂=22-8=14

d=a₂-a₁=14-8=6

n^th term value is 164,then what is n?

n^th term=a+(n-1)d

164=8+(n-1)6

164-8 / 6=n-1

156/6=n-1

26+1=n

n=27

So 27^thterm is 164.

One metre = 100 cm, a = 100 cm

since every year it grows 4 cm less than it did the preceding year, d = -4

Thus, it is an AP, with initial term a = 100 and d = -4

The tree will stop its growth, when nth term of the series is 0.

Nth term = a + (n - 1)d

0 = 100 + (n - 1)(-4)

0 = 100 - 4n + 4

0 = 104 -4n

4n = 104

n = 104/4

n = 26 years

⇒   We have the sequence, 1,2,3.......n
⇒   This is an AP, with the initial term a=1 and the common difference d=1.
∴   The sum of n terms of an AP is given by,


→   Arithmetic mean of n numbers a1​,a2​,a3​,a4​,...an​ is given by the formula

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

A solid has shape, size, position and can be moved from one place to another. So, solid has three dimensions

 A point is that which has no part i.e., no length, no breadth and no height. So, it has no dimension.

 Boundaries of a solid are called surfaces. A surface (plane) has only length and breadth. So, it has two dimensions.

It is the definition of parallel lines.

Non-leap year contains 365 days = 52 weeks + 1 days
52 weeks contain 52 Sundays
We will get 53 Sundays if one Sunday will come in a week. 
Number of Total possible outcomes = 7
Number of possible outcomes = 1
∴ Required Probability = 1/7

We know, surface area of sphere = 4πr²

⇒ 4(π)r² = 221.76

⇒ r² = 7/22​ × 221.76 × 1/4 ​= 7 × (10.08) × 1/4 ​

⇒ r = 4.2cm

Then, diameter equals 2r = 2 × 4.2 = 8.4 cm, which is true and reason is also correct.

Moreover reason is the correct explanation of assertion.

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

(x + x + 2 + x + 4 + x + 6 + x + 8) / 5 = 11

5x + 20 =  55

5x = 35 ⇒ x = 7

Theorem: Angles opposite to equal sides of an isosceles triangle are equal.

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

Common difference=¼-0=½-¼=¼
Next term =¾+¼=1
Next term =1+¼=5/4

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.

HCF of 95 and 152 = 19



 

LCM of 50 and 48 = 1200
∴ 1200 sec = 20 min
Hence at 12.20 pm they will beep again for the first time.

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. 

Given:

BE = CD

Concept Used:

When 2 sides of a triangle are equal, then it is isosceles.

When 2 angles and 1 side of 2 triangles is equal, then both the triangles are similar.

Calculations:

In △ABE and △ACD,

BE = CD (Given)

∠BEA = ∠CDA (90° each)

∠BAE = ∠CAD (Common Angle)

∠ABE = ∠ACE (By Sum angle property)

⇒ △ABE is similar to △ACD

⇒ AB = AC

∴ If the altitudes from two vertices of a triangle to the opposite sides are equal, then the triangle is isosceles.