Bihar STET Paper 1 Mathematics Mock Test - 7 - Bihar PGT/TGT/PRT MCQ

Solution :- sin^2 30° − cos^2 30°

= (1/2)² −((3)^1/2/2)²

= 1/4 - 3/4

= -1/2

Let the breath of the river be h meters.

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

Given: 5x²+8x+4 = 2x²+4x+6
⇒ 5x²−2x²+8x−4x+4−6 = 0
⇒ 3x²+4x−2 = 0
Here, the degree is 2, therefore it is a quadratic equation.

7sin²x+3cos² x=4
7sin²x+3(1-sin²x)=4
7sin²x+3-3sin²x=4
4sin²x=4-3
4sin²x=1
sin²x=¼
sinx=½
Cosec x=1/sinx=2
Cos x= 
Sec x= 1/cos x= 
Cosec x + sec x=2+ 

Let x = the length of a side of the square

So area of square = x² = 50cm²

3 cot θ = 2 ⇒ cot θ = 2/3 ⇒ tan θ = 3/2 

The surface area of a cube of side 27 cm can be found using the formula:Surface area of a cube = 6a^2, where a is the length of the side of the cube.Given:
Length of side of the cube = 27 cmSubstituting the value into the formula:Surface area of the cube = 6 × 27^2
Surface area of the cube = 6 × 729
Surface area of the cube = 4374 cm^2Therefore, the surface area of the cube of side 27 cm is 4374 cm^2, which corresponds to option C

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.

Let BD be the whole height of the tree

The tree breaks at point C and makes ΔABC as given into the figure such that

AC = CD

In rt. ΔABC 

 Let p (x) = ax² + bx + c be the required polynomial whose zeroes are -2 and 5.

∴ Sum of zeroes = -b/a
⇒  - 2 + 5 = 3 = -(-3)/1  ...(i)
and product of zeroes = c/a
⇒  -2 x 5 = -10/1 ...(ii)
From Eqs. (i) and (ii)
a = 1, b = -3 and c = -10
∴ p(x) = ax² + bx + c = 1.x² - 3x - 10
= x² - 3x - 10
But we know that, if we multiply/divide any polynomial by any arbitrary constant. Then, the zeroes of polynomial never change.
∴ p(x) = kx² - 3kx - 10k [where, k is a real number]
⇒ p(x) = x²/k - 3x/k -10/k [where, k is a non-zero real number]

Hence, the required number of polynomials are infinite i.e., more than 3.

a₄ - b₄ = (a₁ + 3d) - (b₁ + 3d)
= a₁ b₁ = - 1 - (-8) = 7

Here a = 11 and d = 2, t_n= 99, n = ?
Sum of the n terms = (n/2)[2a+(n -1)d]
But t_n = a + (n -1)d
⇒ 99 = 11+ (n-1)2
⇒ 99 -11 = (n-1)2
⇒ 88/2 = (n-1)
∴ n = 45.
subsitute n = 45  in sum of the n terms we obtain
⇒ s_{45 =} (45/2)(2×11 + (45 -1)2)
⇒ s_{45 =} (45/2)(110)
⇒ s₄₅ = 45×55.
⇒  s₄₅ = 2475.
∴ sum of all two digit odd positive numbers = 2475.

Observing both the AP’s we see that the common difference of both the AP’s is same ,so difference between their corresponding terms will be same ie,a₁-b₁=2.5-3.72=-1.22
a₂-b₂=2.51-3.73=-1.22
 So , a₁₀₀₀₀₅-b₁₀₀₀₀₅=-1.22

The quadratic equation is of the form  x² - (sum of zeros) x + (product of zeros)
=x² - 5x - 14

A gifted child is one whose IQ is above 130. He/she derives many creative ideas, explores many possible solutions for a single problem, thinks in a divergent way. always have a curiosity to know about new things, always brings something unusual and entertaining beyond the level of thinking at the same age children. All these qualities are found in gifted children. 
Hence, the correct answer is, 'Fighting with others.'

The main aim of CCE is to evaluate every aspect of the child during their presence at the school. This is believed to help reduce the pressure on the child during/before examinations as the student has to sit for multiple tests throughout the year, of which no test or the syllabus covered is repeated at the end of the year, whatsoever. The CCE method is claimed to bring enormous changes from the traditional chalk and talk method of teaching, provided it is implemented accurately. As a part of this new system, student's marks have been replaced by grades which are evaluated through a series of curricular and extra-curricular evaluations along with academics. The aim is to reduce the workload on students and to improve the overall skill and ability of the students by means of evaluation of other activities.

Essay type questions do not provide scope to assess the students objectively. Mrs. Suman is using essay type questions. These questions are subjective in nature and their answers vary from subject to subject; whereas multiple choice questions, true/false type questions, or one word answer type questions are used to assess the students objectively.

Refusing to help children unless they have tried themselves is the characteristic of an effective teacher.
It is better to try and fail than not try at all. A teacher must let the children try to do things and also to handle problems/situations in a controlled environment.

Four characteristic stages of a child's intellectual development were developed by Piaget. These include sensory-motor stage, preoperational stage, concrete operational stage and formal operational stage.

Inclusive Education means education for all children in school as It refers to the inclusion of all children in the education system, regardless of their differences and disabilities.

Key Points

• It values the diversity, each child brings to the classroom and facilitates all with equal opportunities to learn and grow.
• Inclusive education improves the quality and making provisions of education for all.
• It provides a provision to include disabled children along with normal children in a regular classroom environment.
• It refers to an education system that accommodates all children regardless of their physical, intellectual, social, emotional, linguistic, or other conditions.

Additional Information

Basic Principles of Inclusive Education:

• Equity and equal opportunities for all.

• Well constructed educational plan.

• Use of multilingualism as a resource.

• Use of specific pedagogical strategies.

• Sensitization towards individual differences.

Hence, it could be concluded that inclusive education refers to a school education system that includes children regardless of physical, intellectual, social, linguistic or other differently-abled conditions.

Nalin Negi has been appointed as the Chief Executive Officer of BharatPe after serving as the interim CEO and CFO. Under his leadership, the company has seen significant revenue growth and achieved positive Ebitda, showcasing his experience and strategic capabilities in the fintech and banking sectors.

The atmosphere of Earth consists of different layers of gases encompassing the planet Earth that is held by Earth's gravity. The climate ensures life on Earth by retaining bright sun-based radiation, warming the surface through warmth maintenance, and lessening temperature extremes in the middle of day and night.

∠DAC = ∠B + ∠C
(Exterior angle prop. of a Δ ABC)
According to question,
130° = 2A + 3A
5A = 130°
A = 26°
∴ ∠B = 52°; ∠C = 78°

Given: 24$3@8#45*5
After replacing the symbols we get:
24 + 3 x 8 - 45 ÷ 5
= 24 + 3 x 8 - 9
= 24 + 24 - 9
= 48 - 9
= 39
Hence, 39 is the correct answer.