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Frequency of ultrasound,  $\nu$ = 1000 kHz = ${10}^6$ Hz

Speed of sound in air,  $v_a$ = 340 m/s

Speed of sound in water,  $v_w$ = 1486 m/s

The wavelength of the reflected sound is given by the relation

${\lambda }_r=\frac{v_a}{\nu }$ = $\frac{340}{{10}^6}$ = 3.4 $\times {10}^{-4}$ m

The wavelength of the transmitted sound wave is given by

${\lambda }_t=\frac{v_w}{\nu }$ = $\frac{1486}{{10}^6}$ = 1.486 $\times {10}^{-3}$ m

(a) For x =0 and t=0, the function (x – vt )² becomes 0

Hence for x=0 and t=0, the function represents a point and not a wave.

(b) For x =0 and t=0, the function $\log ?\frac{x+vt}{x_0}$ = log 0 = $\propto$

Since the function does not converge to a finite value for x =0 and t = 0, it represents a travelling wave.

(c) For x = 0 and t = 0, the function $\frac{1}{x+vt}$ = $\frac{1}{0}$ = $\propto$

Since the function does not converge to a finite value for x = 0 and t = 0, it does not represent a travelling wave.

Length of the steel wire, l = 12 m

Mass of the steel wire, m = 2.1 kg

Velocity of the transverse wave, v = 343 m/s

Mass per unit length,  $\mu$ = $\frac{m}{l}$ = $\frac{2.1}{12}$ = 0.175 kg/m

The velocity (v) of the transverse wave in the string is given by the relation:

$v=\sqrt{\frac{T}{\mu }}$ , where T is the tension

T = $v^2\times \mu$ = ${343}^2\times 0.175$ = 20588.575 N = 2.06 $\times {10}^4$ N

Height of the tower, h = 300 m

Initial velocity of the stone, u = 0

Acceleration, a = g = 9.8 m/ $s^2$

Speed of sound in air, V = 340 m/s

The time taken by the stone (t), to strike the water can be calculated from the relation

s =us + $\frac{1}{2}$ a $t^2$ as

300 = 0 + $\frac{1}{2}*9.8*t^2$ or t = 7.82 s

Time taken by the sound to reach the top of the tower,  $t_1$ = $\frac{h}{V}$ = $\frac{300}{340}$ = 0.88 s

Therefore, the time when the splash can be heard = 7.82 + 0.88 = 8.7 s

There are nearly eight colleges/ universities in Shahdol that offers a BA programme. These institutes provides the UG course in different specialisations. The mode of study may vary from one specialisation to another. Mentioned below are some of the colleges that offers BA and are located in Shahdol:

• Indira Gandhi Computer Technology
• BSSS College
• Devi Ahilya Vishwavidyalya
• Vikram University
• SAGE University, etc.

Yes, Kirit P. Mehta School of Law offers national scholarships to BA LLB students. The students of NMIMS can avail national scholarships under the below-mentioned schemes.

• Central Sector Scheme of Scholarships for College and University students - Department Of Higher Education. 
• Merit-Cum-Means Scholarship For Professional And Technical Courses Cs - Ministry Of Minority Affairs. 
• Post Matric Scholarship Schemes Minorities CS - Ministry Of Minority Affairs. 
• Prime Minister's Scholarship Scheme For Central Armed Police Forces And Assam Rifles. 

Mass of the string, M = 2.5 kg

Tension in the string, T = 200 N

Length of the string, l = 20 m

Mass per unit length,  $\mu$ = $\frac{M}{l}$ = $\frac{2.5}{20}$ = 0.125 kg/m

The velocity (v) of the transverse wave in the string is given by the relation:

$v=\sqrt{\frac{T}{\mu }}$ = $\sqrt{\frac{200}{0.125}}$ = 40 m/s

Therefore, time taken by the disturbance to reach the other end, t = $\frac{l}{v}$ = $\frac{20}{40}$ = 0.5 s

The GPAT 2026 students' reactions will be out after the exam concludes. The GPAT student reactions comprised details like difficulty level of the exam, topics from which maximum questions were asked in the exam. The GPAT cutoff prediction from the previous year exam basis. 

There is no updated information on seat reservations for BA at PTSNS University. However, the university may follow the rules of the state or central government for seat reservations. There are over 200 seats for BA programmes at the university. The seat allotment procedure is done based on sanctioned intake and merit in the last qualifying exam.

Some entrance exams that are commonly accepted at the top MBA colleges in Hyderabad are given in the table below along with some details about their dates, schedules, and syllabi.

Disclaimer: This information is sourced from the official website and may vary.

As per the SK University official website, the selection of candidates for the BTech programmes is based on the score obtained in the last qualifying exam. Those who have completed their Higher Senior Secondary (Class 12) in the Science stream from a recognised board are eligible to apply. Moreover, according to the general information, many universities accept admission for BTech with a 60% aggregate in Class 12. Interested candidates can visit the official website or contact the admission office directly for more accurate information.

KL University Guntur offers UG and PG course in various specilisations, such as Engineering, Science, Arts, Management, and others. The fee ranges between INR 1.6 lakh - INR 18 lakh. The fee structure is inclusive of multiple components including caution deposit, exam fee, tuition fee, and more. 

Some of the top MBA colleges in Hyderabad, based on the list published by Times 2025, are given in the table below:

Disclaimer: This information is sourced from the official website of the ranking body listed and may vary.

Yes, the Kirit P. Mehta School of Law does offer scholarships to BA LLB students. The institute primarily offers the scholarships to the students on the basis of their merit. Additionally, the scholarships are offered to the students in the form of fee concessions, freeships, and other financial benefits. To apply for the offered scholarships, candidates are required to complete the eligibility criteria according to the applied scholarships. 

After completing a BTech from SK University, candidates have a wide range of career opportunities in the field of engineering. Candidates can seek careers in Computer Science Engineering, Mechanical Engineering, Electrical Engineering, Biotechnology Engineering, Civil Engineering, etc. A list of some of the popular careers after BTech for SK University graduates is as follows:

Students must submit Northwestern University application fees via Debit or a Credit card only. Networks including Visa, Mastercard, Discover and American Express must be prefered to make the payments. Application fees for undergraduate fees is USD 75 and USD 95 for postgraduate programs.

When applying to North Western University a payment of $75 application fee is typically required untill and unless you are fee waiver.

Payment methods for students already enrolled:

1. QuickPay (via CAESAR)
2. FLY WIRE 
3. Cheque