OAVS TGT Math Mock Test - 4 - OTET MCQ

According to question, Diameter (BD) = 2 x radius = 2 x 12 = 24 cm
∴ Area of square

d = 2^nd term – 1^st term = – 1 – (– 5) = –1 + 5 = 4 Therefore, Both A and R are true and R is the correct explanation for A.

Since if a circle inscribed a square. then the radius of the circle is half of to side of square.
∴  Radius = 10/2 = 5 cm
∴ Area of the circle = πr² = π(5)² = 25π sq. cm 

Assume that √7 be a rational number.
i.e. √7 = p/q, where p and q are co prime.
⇒ 7 = p²/q² 
⇒ 7q² = p²    ...(1)
⇒ p² is divisible by 7, i.e. p is divisible by 7
⇒ For any positive integer c, it can be said that p = 7c, p² = 49c²

Equation (1) can be written as: 7q² = 49c²
⇒ q² = 7c²
This gives that q is divisible by 7.

Since p and q have a common factor 7 which is a contradiction to the assumption that they are co-prime.
Therefore, √7 is an irrational number.

The least number of acute angles that a triangle can have is 2.

As we cannot have more than one right angle or obtuse angle, we have only two or three acute angles in a triangle.

Further, if one angle is acute, sum of other two angles is more than 90⁰ and we cannot have two right angles or obtuse angles.

a₂₁ -a₇ = {a + (21 - 1)d}

- {a + (7 - 1)d} = 84

a + 20d- a - 6d = 84

14d = 84

d = 18/14 = 6

d = 6

So, A is incorrect but R is correct

A linear equation is an equation of a straight line, written in one variable. The only power of the variable is 1. Linear equations in one variable may take the form a x + b = 0, ax+b=0, ax+b=0 and are solved using basic algebraic operations

Concentric circles are circles with a common center. The region between two concentric circles of different radii is called an annulus.
Any two circles can be made concentric by inversion by picking the inversion center as one of the limiting points.

θ = 30°, AB = 200 m

Then, sin 30° = Perpendicular / Hypotenuse

= AB / AC

⇒ 1 / 2 = 200 / AC

⇒ AC = 400 m.

The probability of a sure event is always 1.

Let the breath of the river be h meters.

= 100√2 meters Therefore, the breadth of river is 

sin x + cosec x = 2

Number of tigers in 2007 = 1,411

Decrease in number of tigers = 18,000 – 1,411 = 16,589

The expansion of (2a - 3b + 5c)² -: (2a)² + (- 3b)² + (5c)² + 2× 2a × (-3b) + 2× (-3b)× 5c + 2× 5c + 2a. = 4a² + 9b² + 25c² - 12ab - 30bc + 20ac

Let the radius of the circle be r and side of the square be a.
Then, according to question,
2πr = 4a

Now, ratio of their areas,

Therefore, Area of the circle > Area of the square 

Let the middle term be a, then first term is a−d and next term is a+d

The correct answer is d

A quadratic equation (from the Latin quadratus for "square") is any equation that can be rearranged in standard form as. where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no. term.

Therefore, x3 - x2 = ( x -1)3 is a quadratic equation.

3x² - 2x - 5 = 0
3x² + 3x - 5x - 5 = 0
3x(x+1) - 5(x+1) = 0
(x+1)(3x-5) = 0
x = -1 and 5/3.

Hence roots of given polynomial are -1 and 5/3.

= 2p r (h + r)

= 3872 cm²

If possible let a√b be rational. Then a√b = p/q, 
where p and q are non-zero integers, having no common factor other than 1.
Now, a√b = p/q ⇒ √b = p/aq……….(i)
But, p and aq are both rational and aq ≠ 0. 
∵ p/aq is rational.
Therefore, from eq. (i), it follows that √b is rational.
The contradiction arises by assuming that a√b is rational.
Hence, a√b is irrational.

in triangle ABC

AB = 2.5 cm

BC = 6 cm

AC =  ?

in any triangle sum of two sides >  third side

=> AB +  BC > AC

=> 2.5 + 6 > AC

=> AC < 8.5

AB + AC > BC

=> 2.5 + AC > 6

=> AC > 3.5

BC + AC > AB

=> 6 + AC > 2.5

=> AC > -3.5

Taking all together

 3.5 < AC  < 8.5

3.6 ,  3.8 & 4  lies betwenn them

but not 3.4

Hence Length of AC can not be 3.4 cm

Step-by-step explanation:

p(x) = 2x³ + 6x² – 4x + 9 

Define α,β and γ

Let α,β and γ be the 3 roots

αβ = 3 (Given)

Find the products of all the zeros:

αβγ = - d/a

αβγ = - 9/2

Find the third zeros:

Given αβ = 3

3γ = -9/2

γ = -9/2 ÷ 3

γ = -3/2

The third zero is -3/2