OAVS TGT Math Mock Test - 10 - OTET MCQ

Let the probability of losing the game be x
We know that sum of the the sum of probabilities is equal to 1
So
0.3+x=1
x=0.7

Area of the sector
⇒ Area of the sector
⇒ Area of the shaded region = 462 sq. cm

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

Answer: (a) 3x²-3√2x+1

Explanation: Sum of zeroes = α + β =√2

Product of zeroes = α β = 1/3

∴ If α and β are zeroes of any quadratic polynomial, then the polynomial is;

x²–(α+β)x +αβ

= x² –(√2)x + (1/3)

= 3x²-3√2x+1

We have 2 find (1/α + 1/β)

now 1/α + 1/β = (α + β)/ α β (taking LCM)

now by the given poly. we get

(α + β) = -b/a = 7/5

α β = c/a = 2/5

so, (α + β)/ α β = (7/5) / (2/5)

= 7/2

So, 1/α + 1/β = (α + β)/ α β = 7/2

Hence, 1/α + 1/β = 7/2

The possible outcomes when a dice is thrown = {1, 2, 3, 4, 5, 6}

Number of possible outcomes of a dice = 6

(i) Prime numbers on a dice are 2, 3, and 5.

Total prime numbers on a dice = 3

Probability of getting a prime number = 3/6 = 1/2

So it s an equation of a parabola.

The graph will be that of a parabola.

Both the assertion and the reason are true, but the reason provided is related to the sum of the zeroes, not their product. The correct explanation involves the formula for the product of the zeroes of a quadratic polynomial, c/a, which would lead to 5k/−10, hence determining the value of k.

 According to the definition of parallel lines “lines are parallel if they do not intersect”. They are not intersecting. Definition: a statement that gives the exact meaning of the given word. Hence, 'lines are parallel if they do not intersect' is stated in the form of definition.

Number of outcomes where sum is greater than 8

= 4 + 3 + 2 + 1

= 10

Probability that sum of two numbers is greater than 8

= 10/36

= 5/18

 The correct answer is a.

Distance between two points (x1,y1) and (x2,y2) can be calculated using the formula −

Distance between the points (p,−5) and (2,7)=

(2−p)2  +(7−(−5)) 2 =13 

(2-p)2 + 144 = 13

(2-p)2 + 144 = 169

(2-p)2  = 25

2-p = 5  or 2-p = -5

p = -3 or p = 7

We know S1is the sum of 1st term which is a
S₁ = 3 + 5 = 8 = a
S₂ is sum of first two terms
S₂=3 * 4 + 5 * 2 = 12 + 10 = 22  
And We have a₂= S₂ - S₁ = 22 - 8 = 14
d = a₂ -a₁ = 14 - 8 = 6 

The LCM of two consecutive numbers is their product always.

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

Probability =  1/4

Let radius of the protractor be r 
∴ Perimeter of protractor = Perimeter of semicircle + Diameter of semicircle ⇒ Perimeter of protractor = πr+2r

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

If The graph of the polynomial f(x) = 2x – 5 intersects the x – axis then y = 0 
2x−5 = 0 ⇒ x = 5/2

let us verify the reason on the equation

2x² + ax – a² = 0

That means a are not the zeroes.

Therefore, A is false but R is true.