Bihar STET Paper 1 Mathematics Mock Test - 6 - Bihar PGT/TGT/PRT MCQ

Option (B) and (D) , both are the correct answers.  We have x(x + 1) + 8 = (x + 2) (x – 2)
=x² + x + 8 = x² - 4
= x = -12, which is not a quadratic equation
Also, in (B) (x + 2)² = x³ – 4
=x² +4x + 4=x³ - 4, which is a cubic equation

Total number of outcomes = 52
Favourable outcomes = four cards are of Jack.
Total number of favourable outcomes = 4

Probability = Number of favourable outcomes/ Total number of outcomes.

Required probability = P(jack) = 4/52= 1/13.

Hence, the probability of getting Jack is 1/13.

Option C is correct answer.

For the given point  (2,1)

x = 2 and y = 1

Putting value in 2x + y = 5
2 (2) +1 = 5
5 = 5

So point (2,1) lies on the line 2x + y = 5

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

Modal class is the interval which has the highest frequency ie, which occur most of the times.Here highest frequency is 13 in the class interval 20-30. So lower limit of the class interval is 20.

Given: Angle of elevation θ = 60°
Let the height of the tower AB be hmeters.
And the length of the shadow BC is 30 meters.

Therefore the hieght of the tower is 30√3 meters.

class mark of 1st interval=212

class mark of 2nd interval=236.5

Step-by-step explanation:

First Class interval=200-224

class mark=upper limit +lower limit divided by 2..

class mark of first interval is =200+224 divided by 2=212

Second class interval=224-249

class mark of second interval =224 +249 divided by 2

answer= 236.5

Let AB be the tree and AP be the shadow.
Let AB = x meters. Then AP = x√3 meters
Also ∠APB = θ
In right angled triangle ABP 

Therfore the angle of elevation of the Sun is 30°.

As the number 2m will always be even, so if we add 1 to it then, the number will always be odd.

⇒ cos A = cos 60°

⇒ A = 60°

Then, 9 cot² A – 1 = 9(cot 60°)² – 1

= 2

Given, p(x) = 2x+5
For zero of the polynomial, put p(x) = 0
⇒ 2x + 5 = 0
⇒ x = -5/2

Thus, zero of the polynomial p(x) is -5/2. 

Mean of 5 nos.= 28

Therefore, sum of the 5 nos. = 28 * 5 = 140 

The the no. exclude by 'x'.

New sum of 4 nos.= 140 - x

New mean = 28- 2 = 26

Therefore, (140 - x ) / 4 = 26

=> 140 - x = 104

=> x = 36

Hence the height of the tower is 10√3 meters.

We know that the midpoint of two points (x1, y1) and (x2, y2) is given by:
((x1 + x2) / 2, (y1 + y2) / 2)

Given midpoint is (2, 2p + 2).

So,
(3p + (-2)) / 2 = 2 --> (3p - 2) / 2 = 2
Multiply both sides by 2:
3p - 2 = 4
3p = 6
p = 2

Now, substitute p = 2 in the second part:
(4 + 2q) / 2 = 2p + 2
(4 + 2q) / 2 = 4 + 2
(4 + 2q) / 2 = 6
Multiply both sides by 2:
4 + 2q = 12
2q = 8
q = 4

So, p = 2 and q = 4.

Answer:
c) 2, 4

a = pq²

b = p³q

LCM (a,b) = p³q²

If x-2 is a factor then 2 is the zero of the polynomial
by substituting 2 in the given polynomial,we get
2^2+2(2)+a=0
8+a=0
a=-8

5³ - 2³ - 3³​​​​​​​
= 125 - 8 - 27
= 90

All children love to play. Play is a natural instinct of children. It is the natural expression of their needs. It develops the physical, cognitive, social, and emotional growth of a child. Friederich Froebel, the pioneer in childhood education, was of the view that the education of young children should be based on play. He believed that creative play had to be designed so that it could be transformed into creative work.

Advantages of the Play-way method of teaching in a classroom are as follows:

• Playing games is a natural instinct with young children. They not only participate in the games spontaneously, but they can also organize the game effectively.
• Children can create a new game; they devise the rules for playing the game and observe strictly the self-created discipline.
• This helps to nurture the creative skills of children along with the development of several life skills like problem-solving, leadership, rational thinking, self-expression, communication skills, cooperative learning, group living, etc.
• Learning becomes a natural, joyful, and energizing experience. As play is a natural activity, instinctive and joyful, children do not feel learning as a burden and stressful but participate in it voluntarily.
• It provides sufficient scope to the children to fulfil their physical, emotional, and cognitive needs.
  • Physical development and acquisition of motor skills depend upon the maturation of the parts of the body and the opportunities available to the child to practice these skills. Play provides the child with opportunities to practice.
  • Play situations provide opportunities to handle and examine objects and explore the surroundings which help children to find answers to the questions in their minds and to understand the reason why things happen the way they do. By allowing children to play as they like, will help them in learning.
  • Play allows children to discover and learn for themselves. To discover means to find out about things and events for oneself
• It helps to build healthy student-teacher and student-student relationships. 
• In a play-way method, learning takes place through activities and learners remain active, not passive.

From the above, it is clear that all the statements mentioned in the question regarding the advantages of the play-way method are true.

The rate of development of an individual child is different from that of another child. This principle is known as the ‘principle of individual differences’. For instance, some children may learn to walk in 8 months, while some may take more than a year to start walking. 

It is important for teachers to know variables such as physical characteristics, intelligence, perception, gender, ability, learning styles, which are individual differences of learners. An effective and productive learning-teaching process can be planned by considering these individual differences of students.

A disorder is a disturbance in physical or mental health or functions. It may be caused by genetic factors, disease, or trauma.

The Assessment process should not be boring, or it should be on the basis of only one aspect. The teacher should be careful about using a variety of ways to collect information, about the students learning across scholastic and co-scholastic boundaries. Only scholastic areas should not be focused on assessment. It should also include co-scholastic areas.
Hence, the correct answer is, 'Using a variety of ways to collect information about the students learning across scholastic and co-scholastic boundaries.'

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HCF is 23. So the other two numbers would be,
(23 * 13) and (23 * 14).
Thus Larger Number = 23 * 14 = 322.

For this question, we will use the given table-

The relation of NZ : MA  is given below-

Similarly,

We will apply the same relation to TV : ? as-

Hence, Option (3) is correct.