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This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l}Giventhat:{\left(\frac{1+i}{1-i}\right)}^x=1\\ \Rightarrow {\left(\frac{\left(1+i\right)\left(1+i\right)}{\left(1-i\right)\left(1+i\right)}\right)}^x=1\Rightarrow {\left(\frac{1+i^2+2i}{1-i^2}\right)}^x=1\\ \Rightarrow {\left(\frac{1-1+2i}{1+1}\right)}^x=1\Rightarrow {\left(\frac{2i}{2}\right)}^x=1\\ \Rightarrow {\left(i\right)}^x={\left(i\right)}^{4n}\Rightarrow x=4n,n\in N\\ Hence,thecorrectoptionis\left(b\right).\end{array}$

Bhartiya Skill Development University offers spacious infrastructure with all possible amenities at the disposal of students. The university offers well-equipped infrastructure with smart classrooms, an auditorium, a library, a multipurpose hall, laboratories, seminar halls, recreational activity rooms, a sports facility, and others.

Bhartiya Skill Development University awards various scholarships to UG, PG, and various other course students as financial assistance. To promote equitable and also inclusive skill education in line with the NEP 2020, the following scholarships and various fee concession schemes are offered to students:

• Tuition Fee Concession for:
  • Girls and Transgender
  • Defense Personnel
  • Economically weaker Identities
  • Differently-abled students
  • Socio-cultural identities
• Academic Scholarships and others

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l}Giventhat:\left(z+3\right)\left(\overline{z}+3\right)\\ Letz=x+yi\\ So\left(z+3\right)\left(\overline{z}+3\right)=\left(x+yi+3\right)\left(x-yi+3\right)\\ =\left[\left(x+3\right)+yi\right]\left[\left(x+3\right)-yi\right]\\ ={\left(x+3\right)}^2-y^2{i}^2={\left(x+3\right)}^2+y^2\\ ={\left|x+3+iy\right|}^2={\left|z+3\right|}^2\\ Hence,thecorrectoptionis\left(a\right).\end{array}$

Bhartiya Skill Development University has collaborated with various organisations and companies. The university has signed MoUs with several colleges/ universities. The below-mentioned are the Bhartiya Skill Development University collaborations:

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Candidates must know their Bhartiya Skill Development University eligibility criteria and apply accordingly. Follow the Bhartiya Skill Development University application process mentioned below:

Step 1: Visit the official website of Bhartiya Skill Development University.

Step 2: Select the required course.

Step 3: Pay the application fee.

Step 4: Fill out and submit the application form with the required information.

Candidates who pursued a 5-year Integrated course after 12^th and are applying for XAT exam, can mention their undergraduate and postgraduate scores in the columns specified for the same in the XAT application form. For such candidates too, the minimum academic qualification remains the same.

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l}Giventhat:z=x+iy\\ Ifzliesinthirdquadrant.\\ Sox<0andy<0.\\ \overline{z}=x-iy\\ \frac{\overline{z}}{z}=\frac{x-iy}{x+iy}=\frac{x-iy}{x+iy}\times \frac{x-iy}{x-iy}\\ =\frac{x^2+i^2{y}^2-2xyi}{x^2-i^2{y}^2}=\frac{x^2-y^2-2xyi}{x^2+y^2}=\frac{x^2-y^2}{x^2+y^2}-\frac{2xy}{x^2+y^2}i\\ Whenzliesinthirdquadrantthen\frac{\overline{z}}{z}willalsobelieinthirdquadrant\\ \therefore \frac{x^2-y^2}{x^2+y^2}<0and\frac{2xy}{x^2+y^2}<0\\ \Rightarrow x^2-y^2<0and2xy>0\\ \Rightarrow x^2<y^{2}andxy>0\\ So,x<y<0.\\ Hence,thecorrectoptionis\left(b\right).\end{array}$

Candidates looking for course admission at Indian School of Business Management and Administration, Kolkata must meet the eligibility criteria set by the college. For UG courses candidates must pass Class 12 for UG and graduation for PG programmes. The institute offers more than 10 courses in various streams, such as Accounting & Commerce, Business & Management Studies, etc. The selection criteria for all courses are merit-based.

BSDU has a record of hosting over 100 companies during the placement drives. It has more than 80 industrial partners and faculty visits from Switzerland. Bhartiya Skill Development University is the first Indian university dedicated exclusively to skill-based programmes. The university was established in 2017 and is ranked 3rd by NIRF 2024 under the Skill University category. The university placements are good and the university is visited by top companies for placements such as TATA Motors,  TOYOTA,  Volkswagen, and others

The mode of BSDU course admissions is online. Admission to various courses is based on merit, an entrance test, and a personal interview round. Candidates willing to get admission must first visit the official website. Then, click on the Apply Now tab. Then, select the required course. Then, pay the application fee. Then, fill out and submit the application form with the required information. 

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l}Letz=\frac{1-isin\alpha }{1+2isin\alpha }=\frac{\left(1-isin\alpha \right)\left(1-2isin\alpha \right)}{\left(1+2isin\alpha \right)\left(1-2isin\alpha \right)}\\ =\frac{1-2isin\alpha -isin\alpha +2i^{2}si{n}^2\alpha }{{\left(1\right)}^2-{\left(2isin\alpha \right)}^2}\\ =\frac{1-3isin\alpha -2si{n}^2\alpha }{1-4i^{2}si{n}^2\alpha }=\frac{\left(1-2si{n}^2\alpha \right)-3isin\alpha }{1+4si{n}^2\alpha }\\ =\frac{1-2si{n}^2\alpha }{1+4si{n}^2\alpha }-\frac{3sin\alpha }{1+4si{n}^2\alpha }.i\\ Since,zispurelyreal,then\\ \frac{3sin\alpha }{1+4si{n}^2\alpha }=0\Rightarrow sin\alpha =0\\ So,\alpha =n\pi ,n\in N.\\ Hence,thecorrectoptionis\left(c\right).\end{array}$

ISBMA, Kolkata offers more than 10 courses in various streams, such as Accounting & Commerce, Business & Management Studies, etc. Students can check the table below to know course-wise eligibility and selection criteria:

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l}Letz=sinx+icos2x\\ \overline{z}=sinx-icos2x\\ Butwearegiventhat\overline{z}=cosx-isin2x\\ \therefore sinx-icos2x=cosx-isin2x\\ Comparingtherealandimaginaryparts,weget\\ sinx=cosxandcos2x=sin2x\\ \Rightarrow tanx=1andtan2x=1\\ \Rightarrow tanx=tan\frac{\pi }{4}andtan2x=tan\frac{\pi }{4}\\ \therefore x=n\pi +\frac{\pi }{4},n\in Iand2x=n\pi +\frac{\pi }{4}\\ \Rightarrow x=2x\Rightarrow 2x-x=0\Rightarrow x=0\\ Hence,thecorrectoptionis\left(c\right).\end{array}$

Indian students who want admissions to Arizona State University need to show expertise in certain subjects in accordance with the US admissions coursework. The choice of subjects depends highly on what a student is going to pursue at Arizona State University. Below are common subject requirements for international students: 

Yes, Caltech provides all-round support to all its international students, as part of its International Student Program (ISP). 

The Caltech ISP program provides guidance on visa acquirement, employment authorization, travel guidance, visa delay assistance, community building & support with taxes in the US among other things.

International students can contact university officials via its official website for the same.

The first-year fees for Takshashila University BA courses is to be paid at the last stage of the admission process. At this stage, students who are offered admission are required to pay a one-time fee and some part of the tuition fees. To know more, students can visit the official website of the university.