OAVS TGT Math Mock Test - 8 - OTET MCQ

The graph of the polynomial
f (x) = 2x - 5

Method.

Let us consider, y = f (x) = 2x - 5

Now, when x = 0, y = - 5

and when y = 0, x = 5/2

So, we get two points (0, - 5) and (5/2, 0).

We plot the two points on a graph paper considering two rectangular axes XOX' and YOY'. Then, we find a straight line as shown in the graph.

We see that the line intersects x-axis at the point (5/2, 0).

as there are 11 students  so 6 th student would be middle one
a=45
a+(6-1)d=55
a+5d=55
45+5d=55
5d=10
d=2

x - 2 is a factor of x³ - 3x² + 4x - 4
∵ remainder is zero
Similarly x + 1 is a factor of 2x³ + 4x + 6
but x - 1 is not a factor of x⁵ + x⁴ - x³ + x² - x + 1
∵ remainder is not zero
∴ Statements 1 and 2 are correct.

1, ∵ It is a sure event.

Number of possible outcomes = 2
Number of Total outcomes = 52
∴ Required Probability = 2/52 = 1/26

The correct answer is:

2. a = bq + r, 0 ≤ r < b.

Explanation:

This is the division algorithm, a fundamental concept in number theory.

The division algorithm states that for any two positive integers aaa (the dividend) and b (the divisor), there exist unique whole numbers q (the quotient) and r (the remainder) such that:

a=bq+r

Where:

• q is the quotient (how many times b fits into a),
• r is the remainder (what is left over after dividing),
• 0≤r<b, meaning the remainder is always less than the divisor b but greater than or equal to zero.

Example:

Suppose a=23 and b=5. When you divide 23 by 5:

• The quotient q=4 (because 5 fits into 23 four times),
• The remainder r=3 (because 23−(5×4)=3).

So, the equation becomes:

23=5×4+3

Where a=23, b=5, q=4, and r=3, which fits the form of the division algorithm.

Thus, option 2 is the correct answer because it accurately represents the division algorithm.

The sector is the region between an arc and two radii joining the center to the endpoints of the arc.
Example: In the given figure, OAB is the sector of the circle.

A linear polynomial has 1 zero.

A quadratic polynomial has 2 zeroes.

A cubic polynomial has 3 zeroes.

In general, any polynomial has as many zeroes as its degree.

Four circles of radius 5 cm are cut out.
Area cut = 4*(π5²) = 100π
Total area of circular sheet = π(20)² = 400π
Area uncut = 300 π
The ratio of uncut to cut portion is 3 : 1

A fair dice has number 1,2,3,4,5,6 only . So there are no number greater than 6
No. of favourable outcomes=0
Total no. of outcomes=6
Probability of getting no. higher than 6=No. of favourable outcomes/Total no. of outcomes=0/6=0
 

Number of outcomes where sum is 7 = 6

Probability that sum of two numbers is 7

= 6/36

= 1/6

Here, in the denominator of the given fraction the highest power of prime factor 5 is 3, therefore, the decimal expansion of the rational number  will terminate after 3 decimal places.

Use pythagoras theorem in right triangle,

10² -[16/2]² = 100 -64 = 36 = [6]² ; hence the other diagonal = 6x2 = 12cm

We have, 
Dividing by cosθ

Substituting the value of tan θ
we receive the answer.

A quadratic equation in variable x is of the form ax²+ bx + c = 0, where a, b, c are real numbers a ≠ o, because if a=0 then the equation becomes a linear equation.
If we can factorise ax² + bx + c, a ≠ 0 into product of two linear factors then roots can be found by equating each factor to zero because if two factors are in multiplication and equal to zero then either of the factor is zero.
A real number R is said to be a root of the quadratic equation ax² + bx + c = 0 if a(R)² + bR + c = 0. , root means that the value gives answer equal to zero.
So all are correct.

Draw a line AB parallel to MN and PQ
 

X = = 

Use the distance formula to determine the distance between two points.

√{1-(-4)}² +{(-5)-7}²

=√25+144

=√169

=13

Three face cards from spades have been removed.
Total cards=52-3=49
Total No of black face cards=3+3(3 in each spades and clubs)
Remaining black face cards=6-3=3
Probability of getting black face card=  no. of favourable outcomes/ total no. of outcomes=3/49

∠DBA = ∠DCA = 58° …(1)

[Angles in same segment]  ABCD is a cyclic quadrilateral : 

Sum of opposite angles = 180 degrees 

∠A +∠C = 180° 

75° + ∠C = 180° 

∠C = 105° 

Again, 

∠ACB + ∠ACD = 105° 

∠ACB + 58° = 105° 

or ∠ACB = 47° …(2) 

Now,  ∠ACB = ∠ADB = 47° [Angles in same segment] 

Also, ∠D = 77° (Given) 

Again From figure, ∠BDC + ∠ADB = 77° 

∠BDC + 47° = 77° 

∠BDC = 30° 

In triangle DPC 

∠PDC + ∠DCP + ∠DPC = 180° 

30° + 58° + ∠DPC = 180° 

or ∠DPC = 92° 

Zero of the polynomial is x -2 =0 =>x = 2 put the value of x = 2 (2²)² + a(2)³ + 2(2)² - 3(2) = 16 + 8a + 8 - 6 = 18 + 8a = 0 = 8a = -18 = a = -18/8 = a = -9/4

Here
2x + 3x + 5x = 50 = ⇒ 10x = 50 ⇒ x = 5
Number of red balls = 2 x 5 = 10
Number of white balls = 3 x 5 = 15
Number of blue balls = 5 x 5 = 25
Now, Number of possible outcomes = 25 + 10 = 35
And Number of total outcomes = 50
∴ Required Probability = 35/50 = 7/10 

Given, a marble of radius 2.1 cm is put into a cylindrical cup full of water of radius 5 cm and height 6 cm.

We have to find the quantity of water that flows out of the cylindrical cup.

We know that when the marble is put inside the cylindrical cup full of water the volume of water displaced is equal to the volume of the marble.

So, volume of water that flows out = volume of the marble

Volume of sphere = (4/3)πr³

Given, radius = 2.1 cm

So, volume of marble = (4/3)(22/7)(2.1)³

= 38.808 cm³

Therefore, the volume of the water that flows out is 38.8 cm³

p (x)= x^2-8x+k
p (x)=Ax^2+Bx+C(The equation is in this form)

Let the zeroes be 'a' and 'b'

It is given that 
=> a^2+b^2=40
=> (a+b)^2 - 2ab = 40 ----1

sum of zeroes
=> a+b = -B/A = -(-8)/1 = 8

Product of zeroes 
=> a*b = C/A  = k

Substitute these values in the equation1 we get
=> 8^2 - 2k = 40
=> 64 - 2k = 40
=> 2k = 24
=> k = 12

Therefore the value of k is 12

Taking n = 1,

a₁ = 9 – 5(1) = 9 – 5 = 4

Taking n = 2,

a₂ = 9 – 5(2) = 9 – 10 = -1

Taking n = 3,

a₃ = 9 – 5(3) = 9 – 15 = -6

Therefore the series is 4, -1, -6, …

So, a = 4, d = a₂ – a₁ = -1 – 4 = -5

Now, we have to find the sum of the first 15 terms of the AP

⇒ S₁₅ = 15 × (-31)

⇒ S₁₅ = -465

Hence, the sum of 15 terms is -465.