OAVS TGT Math Mock Test - 6 - OTET MCQ

Diameter is the longest chord of a circle and is always twice the radius.
[∵ Diameter = 2 × Radius]

Given: x = a sec θ cos φ, y = b sec θ sin φ and z = c tan θ

Number of possible outcomes = {2, 3, 5} = 3
Number of Total outcomes = 6
∴ Probability of getting a prime number = 3/6 = 1/2

Let Sharma’s present age be x years then his age 3 years ago is (x−3) years and 5 years from now is (x+5) years. According to question,

But x = 3 does not satisfy the given condition.
Therefore, Sharma's present age is 7 years. 

Smallest prime number = 2 and smallest composite number = 4 
∴ HCF (2, 4) = 2

The number 576 can be factorised as,
576 = 2×2×2×2×2×2×3×3
The number 448 can be factorised as,
448=2×2×2×2×2×2×7
Write the common factors of the given numbers.
2×2×2×2×2×22×2×2×2×2×2
Multiply the common factors to determine the highest common factor (HCF) of the given numbers.
2×2×2×2×2×2 = 642×2×2×2×2×2 = 64
Since the highest common factor (HCF) of the given numbers is 64, this implies that each section will have 64 number of students.
Now, we need to find the number of sections formed.
Let us first find the number of sections formed by the total number of boys by dividing 576 by 64.
576/64 = 9
Now, find the number of sections formed by the total number of girls by dividing 448 by 64.
448/64=7
Thus, the total number of sections formed will be 9+7=16
Hence, option B is the correct answer.

Let AC be the ladder of lenth 14 m and BC = 7 m

Let angle of elevation ∠ACB = θ ∴ cos θ = BC/AC

Step-by-step explanation:mean=2+3+5+7+11+13+17+19+23+29/10

Mean=129/10

Mean=12.9

clearly first term is 4/3
for common difference 1/3-4/3=-1

The volume of a cube with a surface area of 384 sq. cm is 512 cm3, which corresponds to option D.

d=60
so r=30
l=√r²+h²
l= √30²+40²
l=50

(100+1)×(100 - 1) it is the formula of a²-b² so, (100)² -(1)² = 10000-1 = 9999.

(Angle at the centre is double the angle at the circumference subtended by the same chord)

tan 1.tan 2.tan 3...tan (90 - 3 ).tan ( 90 - 2 ).tan ( 90 - 1) 
=tan 1.tan 2 .tan 3...cot 3.cot 2.cot 1 
=tan 1.cot 1.tan 2.cot 2.tan 3.cot 3 ... tan 89.cot 89 
1 x 1 x 1 x 1 x ... x 1 =1

Solution :- sin^2 30° − cos^2 30°

= (1/2)² −((3)^1/2/2)²

= 1/4 - 3/4

= -1/2

The side BC is congruent to side EF.

Given, x³ + 3x² + 3x + a = 0

and its factor is x + 1 = 0 

⇒ x = -1

Put the value in equation i.e. x³ + 3x² + 3x + a = 0

it becomes = (-1) + 3 (1) + 3(-1) + a = 0

⇒ -1 + 3 - 3 + a = 0

⇒ a = 1

Angle of elevation for Guddi is same for the tree and the mall.

So, the ratio of object height to its shadow will be same for the both subjects.

Therefore by proportionality rule,

We have 
Taking LCM,

Multiplying LHS and RHS by x
x²+1=4x
x²-4x+1=0
Which is the required equation.

If α  and β are the zeros of the polynomial then
(x−α)(x−β) are the factors of the polynomial
Thus, (x−α)(x−β) is the polynomial.
So, the polynomial =x² − αx − βx + αβ
=x² − (α + β)x + αβ....(i) 
Now,the quadratic polynomial is  
2 − 3x − x² = x² + 3x − 2....(ii)

Now, comparing equation (i) and (ii),we get,
−(α + β) = 3 
α + β = −3

In a quadratic equation with rational coefficients has an irrational root  α + √β, then it has a conjugate root α - √β.
So if the root is m+ √n the other root will be m- √n

As given in the question, the production increases uniformly , and the company produced 600 sets in the third year and 700 sets in 7th year
So, production increase in 4 years = 100
Production increase per year = 25 sets
Now the question says, initially if the company has produced 600 sets and we have to calculate when the company will produce 1000 sets.
We can use AP in this concept in which we just have to calculate n .

• a_n = a + (n – 1)d
• 1000 = 600 +(n – 1) 25
• 400 = (n – 1) 25
• 16 = (n – 1)
• 17 = n
• Therefore , in 17 years the production will be 1000 units.

 Given, ratio of angles of quadrilateral ABCD is 3 : 7 : 6 : 4.
Let angles of quadrilateral ABCD be 3x, 7x, 6x and 4x, respectively. We know that, sum of all angles of a quadrilateral is 360°.
3x + 7x + 6x + 4x = 360°
=> 20x = 360°
=> x=360°/20° = 18°

Let the length of the shadow BC be 10 meters.
Then the height of the tower AB be 10 meter