Given: _ b a a _ a a _ a a b _​

Now, we check each options.

Option (a): a b b a (Follow)

a b a / a b a / a b a / a b a​

Option (b): a a b b (Not Follow)​

a b a / a a a / a b a / a b b​

Option (c): a b a b (Not Follow)​

a b a / a b a / a a a / a b b​

Option (d): b b a a (Not Follow)​

b b a / a b a / a a a / a b a​

So, the correct pattern follows is: a b a

Thus, correct option is (a).

Given: A, B, C, D and E are sitting in a straight line facing North.

(I) Exactly three people sit between B and C.

B _ _ _ C or C _ _ _ B

Who sits on the extreme right end cannot conclude it from (I).

(II) A sits immediately to the left of B.​​

A B _ _ _ or _ A B _ _ or _ _ A B _

or _ _ _ A B

Who sits on the extreme right end cannot conclude it from (II).

• Now combine the both statements we still cannot conclude who sits on the extreme right end.​

Both Statements I and II put together (and not independently) are sufficient to answer the question.

Thus, correct option is (b).

Given:

Should private schools be banned in India?

Arguments:

1. Yes, they are the reason for commercialisation of education.

2. No, because the rich people cannot send their child to government schools.

Explain all the given Arguments:

1. Yes, they are the reason for commercialisation of education (Strong)

Argument 1 highlights the commercialization of education, which is a valid concern in India. Private schools often charge high fees, making education unaffordable for many, and can sometimes prioritize profit over the quality of education.

2. No, because the rich people cannot send their child to government schools (Not strong)

Argument 2, while it may seem logical, is not as strong because it doesn't address the core issue raised by the question, which is whether private schools should be banned. The existence of private schools doesn't directly relate to the rich people's need for quality education; the issue of commercialization is a stronger argument against private schools.

Thus, the correct option is (b) Only Argument 1 is strong

The Correct Answer Is: (d) calcium sulphate hemihydrate

Explanation:

Plaster of Paris (POP) is chemically calcium sulphate hemihydrate (CaSO₄·½H₂O).

It is obtained by heating gypsum (CaSO₄·2H₂O) at about 373K (100°C).

During this heating, three-fourths of the water of crystallization is removed, forming Plaster of Paris.

Information Booster:

• Plaster of Paris is widely used in making sculptures, molds, and casts.
• It is used in orthopedic applications for making fracture casts and surgical molds.
• POP is fire-resistant and a good insulator, making it useful for wall coatings.
• POP should be stored in airtight containers as exposure to moisture causes it to harden prematurely.
• It is also used in dentistry for making dental molds.

Given:

Ashutosh starts from his house (initial position).

Moves 90 m towards North.

Turns left (West) and walks 110 m.

Turns left (South) and walks 150 m.

Turns left (East) and walks 130 m.

All turns are 90° turns only.

According to the given information, Path diagram will be:

As per the path diagram, Ashutosh now in South-East direction, with respect to the starting point.

Thus the Correct option is (a)

Given:

1344, 2196, and 3687

Solution:

2196 - 1344 = 852

3687 - 2196 = 1491

3687 - 1344 = 2343

HCF of the differences
852, 1491

1491 = 1 × 852 + 639

852 = 1 × 639 + 213

639 = 3 × 213 + 0.

(852, 1491) = 213 )

2343 = 11 × 213 + 0.

(213, 2343) = 213

213 = 3 × 71

divisors of 213 are 71 and 3 (but 3 is not two-digit).

x = 71

Remainder ( y )

Dividing any of the original numbers by ( 71) to find ( y )

1344 ÷ 71 = 18 with remainder 1344 - (71 × 18) = 1344 - 1278 = 66.

y = 66

Now,

x - y = 71 - 66 = 5

The correct answer is option (b ) Armenia in 2022.

Explanation:

In a major milestone for India’s defence exports, Armenia became the first foreign country to purchase the Akash Air Defence Missile System from India. The historic deal was signed in 2022, marking a significant step in India's ambition to become a major global defence exporter under the "Make in

India" and "Atmanirbhar Bharat" (self-reliant India) initiatives.

The agreement involved the sale of 15 Akash missile systems and was valued at approximately ₹6,000 crore (Indian Rupees). The Akash system, developed by the Defence Research and Development Organisation (DRDO) and produced by Bharat Dynamics Limited (BDL), is a Short to Medium Range Surface-to-Air Missile (SAM) system capable of engaging multiple aerial targets such as aircraft, drones, and missiles simultaneously.

This export deal not only enhanced India’s stature in the international defence market but also strengthened its strategic ties with Armenia, a country facing increasing regional security challenges. The first delivery of the Akash systems to Armenia began in 2024, demonstrating India's growing capability to meet global defence demands efficiently and on time.

Armenia’s decision to procure the Akash system reflects international trust in Indian defence technology and serves as a model for future exports to other nations. The deal is seen as a landmark in boosting India's defence manufacturing sector and showcasing the effectiveness and reliability of indigenous missile systems like Akash on a global platform.

Given:

The average of 10 observations is 46.

One observation was misread as 42 instead of 142.

Formula Used:

Sum of observations = Average × Number of observations​​

Corrected sum = Sum of observations − Incorrect value + Correct value

Solution:

The incorrect average is 46, so the total sum with the incorrect observation is:

Sum of observations = 46 × 10 = 460

The incorrect observation was 42, and the correct observation should have been 142. So, the corrected sum is:

Corrected sum = 460 – 42 + 142 = 460 + 100 = 560

The correct answer is option (c) Assam.

Explanation:

Manas National Park, located in the foothills of the Himalayas in Assam, is a UNESCO World Heritage Site recognized for its biological diversity and natural beauty. Spanning over an area of 950 square kilometers, it is a significant wildlife reserve that forms part of the Manas River Basin.

The park is not only known for its stunning landscapes but also for its rich ecosystem. It shares a border with Bhutan’s Royal Manas National Park, contributing to a transboundary conservation area that supports the preservation of various species and ecological processes.

Manas is home to numerous endangered species, including the Bengal tiger, one-horned rhinoceros, and wild buffalo. Its diverse habitats range from grasslands to tropical rainforests, providing a haven for both flora and fauna.

This national park plays an essential role in maintaining ecological balance and serves as a key area for conservation efforts in northeastern India. The Manas River, flowing through the park, adds to the park's beauty and is crucial for sustaining its diverse wildlife and plant species.

​The correct answer is (b) R = 2f

Explanation:

• The radius of curvature (R) of a spherical mirror is the radius of the sphere from which the mirror is a part.
• The focal length (f) is the distance between the focus (F) and the pole (P) of the mirror.
• The relationship between radius of curvature (R) and focal length (f) is given by:

R = 2f

• This formula is valid for both concave and convex mirrors.

Information Booster:

Key Terms:

• The radius of Curvature (R): The radius of the sphere from which the mirror is derived.
• Focal Length (f): The distance between the focal point (F) and the mirror's pole (P).
• Pole (P): The midpoint of the mirror’s surface.
• Focus (F): The point where parallel rays converge (concave) or appear to diverge (convex).

Mirror Formula:

• f = focal length
• u = object distance
• v = image distance

Concave Mirror:

• If an object is placed beyond the center of curvature (C), the image is real, inverted, and diminished.
• Used in telescopes, headlights, and shaving mirrors.

Convex Mirror:

• Always forms a virtual, erect, and diminished image.
• Used in rear-view mirrors of vehicles.