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Since AM of two positive quantities ≥ their G.M.
(2^sinx + 2^cosx)/2 ≥ √ (2^sinx * 2^cosx)
= √ (2^ (sinx+cosx)
= √2^ (√2cos (x-π/4)
≥ √2^ (-√2) ⇒ 2^sinx + 2^cosx ≥ 2 · 2^ (-1/√2) = 2^ (1-1/√2)

The refractive index is an optical property of the material that describes how much does the light bend or refract while passing from one medium to another. It is the ratio of spee of light in vacuum (c) to speed of light in a material (v)$n=\frac{c}{v}$ Refractive index is the reason which causes refraction. When light travels from a rarer medium (low refractive index) to denser medium (higher refractive index), it will slow down and bend toward the normal. Refractive index also changes according to the wavelength of light. Air has 1.003 refractive index, water has 1.33 refractive index and glass has a refractive index of 1.5 to 1.9.

dy/dx = (y-3x)/ln (y-3x) - 3
dy/dx + 3 = (y+3x)/ln (y+3x)
d/dx (y+3x) = (y+3x)/ln (y+3x)
∫ (ln (y+3x)/ (y+3x) d (y+3x) = ∫ dx
Let ln (y+3x) = t
1/ (y+3x) d (y+3x) = dt
∫ tdt = ∫ dx
t²/2 = x+c
(ln (y+3x)²/2 = x+c

Let A =
| a? |
| b? |
| c? |

Ax? = B?
a? + a? + a? = 1
b? + b? + b? = 0
c? + c? + c? = 0
Similar 2a? + a? = 0 and a? = 0
2b? + b? = 2, b? = 0
2c? + c? = 0, c? = 2
∴ a? = 0, b? = 1, c? = -1,
a? = 1, b? = -1, c? = -1
A =
| 1 0 |
| -1 0 |
| -1 -1 2 |
∴ |A| = 2

The pros and cons of choosing BSc Physiotherapy are:

Pros:

• High demand in healthcare and rehabilitation

• Opportunity to work independently or in hospitals

• Diverse career options (sports, neuro, ortho, cardio rehab)

• Fulfilling and people-oriented profession

Cons:

• Physically demanding job

• Initial salary can be low compared to BPT

• Requires continuous learning and certifications

• Limited awareness about the scope in smaller cities

The skills required to succeed in Physiotherapy are:

• Strong communication skills

• Patience and empathy

• Manual therapy techniques

• Knowledge of anatomy and physiology

• Critical thinking and problem-solving

NDC Institute of Aircraft Maintenance Engineering is one of the first in Gujarat to have received the DGCA, Ministry of Civil Aviation approval. The students receive high-tech audiovisual classes, an engine airframe system workshop, and an electrical Navigation workshop. The college's alumni are currently working in top companies such as Air India, GoAir, and others. The college placements and infrastructure is very good. That is the why students must take part in this college's admission. 

Institute of Event Management application forms are also available online. Candidates meeting the eligibility criteria can apply for the preferred course. Below are the steps to apply for admission:

Step 1: Visit the official IEM website.

Step 2: Fill out the form

Step 3: Complete and submit it.

The highest-paying job roles after BSc Physiotherapy are:

• Sports Physiotherapist – INR 6 – 9 LPA

• Consultant Physiotherapist in Private Hospitals – INR 5 – 7 LPA

• Physiotherapist in International Healthcare Centers – INR 7 – 12 LPA

A (α, 0), B (-α, 0)
⇒ D (α, α² − 1)
Area (ABCD) = (AB) (AD)
⇒ S = (2α) (1 − α²) = 2α – 2α³
dS/dα = 2 - 6α²
= 0 ⇒ α² = 1/3

⇒ α = 1/√3
Area = 2α – 2α³ = 2/√3 - 2/ (3√3)
= 4/ (3√3)

The government jobs available after BSc Physiotherapy are:

Yes, BSc Physiotherapy is often categorized under paramedical courses, as it is part of allied health sciences. It trains professionals who support medical doctors in diagnosing, treating, and rehabilitating patients.

However, physiotherapists hold a distinct professional identity and are not just assistants. They play an independent role in patient care, rehabilitation, and recovery, making it both paramedical and an essential healthcare field on its own.

Yes, NDC Institute of Aircraft Maintenance Engineering is a good college. The NDC Institute of Aircraft Maintenance Engineering popular programmes are Aircraft Maintenance Engineering (B1.1, B1.2, B1.3 & B2) AME (B1.1/B1.2/B1.3/B2) with BTech Aeronautical. The college students are taught Electrical Fundamentals, Materials & Hardware, Basic Aerodynamics, Turbine Aeroplane Aerodynamics, Structures and Systems, and various other subjects. The placements are good. 

Physiotherapy focuses on improving movement, strength, and physical function after injuries, surgeries, or illnesses. It deals with the rehabilitation of muscles, bones, and nerves through exercises and manual therapy.

Occupational Therapy, on the other hand, emphasizes helping patients perform daily activities like dressing, eating, or working, especially after trauma, disability, or developmental issues. While both overlap, physiotherapy is body-function oriented, and occupational therapy is life-function oriented.

No, Biology is typically a mandatory subject for admission into BSc Physiotherapy, as the course heavily involves anatomy, physiology, and medical sciences. Most universities require PCB (Physics, Chemistry, Biology) as the core subjects in Class 12.

However, a few colleges may accept students with PCMB or allied Science backgrounds. It's important to review the specific eligibility criteria of the chosen college before applying.

∫ [π/6 to π/3] (d/dx (tan? x) * sin³3x + tan? x * d/dx (sin³3x) dx
= 1/2 ∫ [π/6 to π/3] d/dx (tan? x * sin?3x) dx
= 1/2 [tan? x · sin?3x] from π/6 to π/3
= 1/2 [ (√3)? · 0 - 1/ (√3)? )]
= -1/18

BPT is generally considered better for students who want a pure clinical career with maximum recognition. It provides extensive practical training, internships, and broader global acceptance.

BSc Physiotherapy is a great choice for those who want to enter healthcare but may also consider teaching, research, or alternative healthcare fields later. The choice depends on career goals — clinical independence vs. academic flexibility.

In order to get admission to the Institute of Event Management candidates must keep certain documents ready. Students can check the list of documents below:

• Scanned Class 10, Class 12 and graduation marksheet
• Leaving Certificate
• Aadhaar Card
• Passport-size photograph
• Signature

Note: The list of documents mentioned above is the general documents. For more details, visit the official website.

Yes, BSc Physiotherapy graduates can open their own clinic, but the scope may be slightly limited compared to BPT graduates, depending on state regulations. You must also register with your local physiotherapy council, where applicable.

Many BSc Physiotherapy graduates gain a few years of experience under senior physiotherapists before starting a private setup. Pursuing higher studies like MPT further boosts credibility and career growth in private practice.

BPT (Bachelor of Physiotherapy) is a 4.5-year professional degree with more in-depth clinical exposure and is recognised for independent practice in many countries. BSc Physiotherapy, on the other hand, is a 3–4-year undergraduate course, often considered more academic.

BPT is generally preferred for those aiming for clinical practice, while BSc Physiotherapy suits students interested in research, teaching, or combining physiotherapy with other healthcare roles.