Bihar STET Paper 1 Mathematics Mock Test - 5 - Bihar PGT/TGT/PRT MCQ

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.

8a³ + b³+ 12a²b + 6ab²
8a³ + b³+ 12a²b + 6ab²
= (2a)³ + (b)³ + 3(2a)(b) (2a + b)
= (2a + b)³ | Using Identity VI
= (2a + b)(2a + b)(2a + b)

Because the circles are congruent, therefore their radius are same

Length of arc AXB = [θ/(360°)] × 2πr = [(75°)/(360°)] × 2πr

Length of arc A’YB’ = [θ/(360°)] × 2πr = [(25°)/(360°)] × 2πr

Required Ratio = ([(75°)/(360°)] × 2πr) : ([(25°)/(360°)] × 2πr) = 3 : 1

If the graph of a polynomial intersects the x-axis at three points, then the number of zeroes are 3 because number of zeroes of the polynomial are the number of the coordinates of the points where its graph intersects the x-axis.

In the figure, two circle with centers O and O' intersect each other at B and C.

ACD is a line, ∠AOB=130^∘

Arc AB subtends ∠AOB at the centre O and ∠ACB at the remaining part of the circle.

Let x and (16 - x) are two parts of 16 where (16 - x) is longer and x is smaller .
A/C to question,
2 × square of longer = square of smaller + 164
⇒ 2 × (16 - x)² = x² + 164
⇒ 2 × (256 + x² - 32x ) = x² + 164
⇒ 512 + 2x² - 64x = x² + 164
⇒ x² - 64x + 512 - 164 = 0
⇒ x² - 64x + 348 = 0
⇒x² - 58x - 6x + 348 = 0
⇒ x(x - 58) - 6(x - 58) = 0
⇒(x - 6)(x - 58) = 0
⇒ x = 6 and 58

But x ≠ 58 because x < 16
so, x = 6 and 16 - x = 10

Hence, answer is 6 and 10.

The shaded region denotes the sector of a circle. The unshaded part is also a sector.

Notice that it is enclosed by two radii and an arc.

To show: ∠PSR + ∠PQR = 180°
∠SPQ + ∠SRQ = 180°

In △DSA,

∠DAS + ∠ADS + ∠DSA = 180° (angle sum property)

+ ∠ SA = 180° (since RD and AP are bisectors of ∠D and ∠A)

∠DSA = 180°
∠PSR = 180°−

(∵ ∠DSA = ∠PSR are vertically opposite angles)

Similarly,

∠PQR = 180°− 

Adding (i) and (ii), we get, ∠PSR + ∠PQR = 180°
=360° − 1/2 ​× (∠A + ∠B + ∠C + ∠D)
 

=360°− 1/2​ × 360° = 180° ∴ ∠PSR + ∠PQR = 180°

In quadrilateral PQRS,

∠SPQ + ∠SRQ + ∠PSR + ∠PQR = 360°
=> ∠SPQ + ∠SRQ + 180° = 360°
=> ∠SPQ + ∠SRQ = 180°

Hence, showed that opposite angles of PQRS are supplementary.

We have,

∠B = 30° and AC = 4 m

sinθ=p/h or perpendicular/hypotenuse [perpendicular = side directly in front of θ ]

Then, sin 30° = AC / AB

⇒ 1 / 2 = 4 / AB

⇒ AB = 8 m.

Given equation is x²-5x+7=0
We have discriminant as b²-4ac=(-5)²-4*1*7= -3
And x = , Since we do not have any real number which is a root of a negative number, the roots are not real.

AP is:  a,a+d,a+2d,a+3d,a+4d
Middle term is a+2d=5
d=4
a+2d=5
a+2*4=5
a=5-8= -3
a+d= -3+4=1
a+3d= -3+3*4=-3+12=9
a+4d= -3+4*4= -3+16=13
So the terms are : -3,1,5,9,13

In triangle ABD and FEC:
► AB = FE ( given )
► ∠FEC = ∠ABD ( 90degree)
► BC = DE
CD is common part coming in both triangles.
► BC + CD = CD + DE
► BD = CE
Therefore, triangle ABD is congruent to triangle FEC by SAS rule of congruence.

 Since, 5 and 8 are the remainders of 70 and 125, respectively. Thus, after subtracting these remainders from the numbers, we have the numbers 65 = (70-5),
117 = (125 – 8), which is divisible by the required number.
Now, required number = HCF of 65,117                                     [for the largest number]
For this, 117 = 65 × 1 + 52 [∵ dividend = divisior × quotient + remainder]
⇒ 65 = 52 × 1 + 13
⇒ 52 = 13 × 4 + 0
∴ HCF = 13 
Hence, 13 is the largest number which divides 70 and 125, leaving remainders 5 and 8.

A polynomial of degree 3 is called a cubic polynomial. 

For example, x³−1, 4a³ − 100a² + a − 6, and m²n + mn² are all cubic polynomials with atmost 3 zeroes (having degree 3).

Hence, the polynomial having atmost 3 zero is a cubic polynomial.

Teaching aptitude refers to have a deep interest in transferring knowledge and making students learn specific skills by giving primacy to their needs and experiences.

Key Points

Generally speaking, teaching implies:

• keen desire to teach.
• dedication towards teaching.
• possessing an ability to teach.
• interest in the teaching work orientation.
• specific ability and potentiality in teaching profession.
• intrinsic motivation towards the teaching-learning process.

Hence, it could be concluded that all options are true in the context of teaching aptitude.

A teacher needs to ensure that all the learners in her class feel accepted and valued. To do this, the teacher should get to know the social and cultural backgrounds of her students, and encourage diverse opinions in the class. The teachers must encourage students to research and share information about their ethnic background as a means of fostering a trusting relationship with fellow classmates. She should analyze and celebrate differences in traditions, beliefs, and social behaviors. This makes students realize that their beliefs and traditions constitute a culture as well, which is a necessary breakthrough in the development of a truly culturally responsive classroom.

Lesson planning should be based on both, the needs of the learners and the process for evaluation to be followed. The content should be presented in such a way that it fulfils the student's academic needs. The process of the evaluation must be decided beforehand, so that the teacher understands how much learning has taken place. Different kinds of evaluation processes could be used, depending upon the learning objectives.

NEP 2020 proposes mandatory school attendance for all students until the age of 16 to reduce early dropouts.

NEP 2020 recognizes the role of school counselors in providing mental health support to students.

The correct answer is Odisha.

Key Points

• India is the world's fifth-largest producer of manganese after China, Gabon, South Africa, and Australia.
• Manganese is not found as a free element in nature. It is usually found in combination with iron.
• The most important manganese ore is pyrolusite.
• Manganese is primarily used in the iron and steel industry.
• It is the essential raw material for manufacturing steel alloys.
• 6 kilograms of manganese ore is required for manufacturing one tonne of steel.
• State-wise reserves of Manganese:
  • Odisha (44%),
  • Karnataka (22%),
  • Madhya Pradesh (13%), etc.

The ‘Asia-Pacific Leaders’ Conclave on Malaria Elimination’ will be organized in New Delhi by the Union Ministry of Health and Family Welfare in partnership with the Asia Pacific Leaders Malaria Alliance (APLMA) as a precursor to World Malaria Day.
Its goal is to reaffirm political commitment to achieve malaria elimination by 2030.

The naval forces of China, Iran, and Russia recently launched a joint exercise called the “Maritime Security Belt-2024” near the Gulf of Oman. The exercise, which began on March 11 and lasted until 15, is the fifth common military exercise between the three countries in recent years. The exercise aims to safeguard regional maritime security and strengthen maritime cooperation. The exercise is organized in three phases: harbor, sea, and summarize. The exercise focuses on anti-piracy and search and rescue training courses, and includes the participation of Russian warships and aviation.

In 1994, Supreme Court of India ordered Ministry of Environment and Forest to establish a special division to develop a green belt around Taj Mahal.

The above information can be summarized below diagram,

Therefore, the code for “was” will be “3”. 

Hence, option 4 is the correct answer.

Given:

x + y + 1 = 0

Concept Used:

(a + b )³ = a³ + b³ + 3ab (a + b)

Calculations:

x + y + 1 = 0

⇒ x + y = -1

Cubing on both sides we get

(x + y)³ = ( -1 )³

⇒ x³ + y³ + 3xy( x + y ) = -1

⇒ x³ + y³ + 3xy ( -1) = -1

∵ x + y = -1

⇒ x³ + y³ - 3xy = -1

∴ required value = -1