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Leiden University expects minimum GPA of 3.2 on 4 point scale from international students. Along with GPA score, students must take care of various factors while deciding to enter the university. They must have completed 2 years of university studies and have relevant experience in course they are applying for. Students must show their English language requirements by submitting the scores of IELTS and TOEFL.

For Indian Students, Leiden University annual tuition fee ranges between INR 2 L - INR 16 L for UG programs, and INR 7 L - INR 20 L for PG programs. The annual tuition fee for some of the courses of Leiden Uni are given below: 

This is a Objective Type Questions as classified in NCERT Exemplar
Sol:

$\begin{array}{l}GiventhatP\left(n\right):2n<n!\forall n\in N\\ Forn=12<1\left(NotTrue\right)\\ Forn=22\times 2<2!\Rightarrow 4<2\left(NotTrue\right)\\ Forn=32\times 3<3!\Rightarrow 6<3.2.1\Rightarrow 6<6\left(NotTrue\right)\\ Forn=42\times 4<4!\Rightarrow 8<4.3.2.1\Rightarrow 8<24\left(True\right)\\ Forn=52\times 5<5!\Rightarrow 10<5.4.3.2.1\Rightarrow 10<120\left(True\right)\\ So,P\left(n\right)istrueforn\ge 4.\\ Hence,thevalueofthefilleris4.\end{array}$

According to unofficial source, Leiden University acceptance rate is 30%. Low percentage shows that the university is bit competitive but follows simple approach during admission. The university prioritises following factors which includes- strong academic record, relevant work experience, motivation letter, English language proficiency, etc. Students who fulfill the basic eligibility and submit the required documents have a high chance of getting selected.

Leiden University expects a minimum score of 6.5 or above in IELTS. Along with this, international applicants whose first language is not English must demonstrate their English language proficiency. The university recommends students to achieve the following minimum scores in any one of the English exams:

This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

         $\begin{array}{l}Giventhat:cos{1}^0.cos{2}^0.cos{3}^0\dots cos179^0\\ =cos{1}^0.cos{2}^0.cos{3}^0\dots cos90^0.cos91^0\dots cos179^0\\ =0\left[?cos90^0=0\right]\\ Hence,thecorrectoptionis\left(b\right).\end{array}$

This is a Objective Type Questions as classified in NCERT Exemplar
Sol:

$\begin{array}{l}LetP\left(n\right)=x^n-1isdivisiblebyx-k.\\ P\left(1\right)=x-1isdivisiblebyx-k.\\ Sincek=1isthepossibleleastintegralvalueofk.\\ Hence,thecorrectoptionis\left(a\right).\end{array}$

Leiden University accepts applications from over 100 countries. According to an official source, more than 6,000 international students choose Leiden. The reason for their choice is the university's commitment to academic excellence, student satisfaction, high graduation rate, employment rate, and more. Students can check the table below for the Leiden University statistics:

Leiden University offers 48 bachelor's programs and more than 100 postgraduate programs. Some popular courses are Biomedical Science, Clinical Neuropsychology, Chemistry, Industrial Ecology, Astronomy and Data Science, Drug Discovery and Safety, Sustainability, Business and Pubic sector,  and more. Students can check the table below for Leiden University specializations along with the US News rankings:

This is a Objective Type Questions as classified in NCERT Exemplar
Sol:

$\begin{array}{l}LetP\left(n\right)=3.5^{2n+1}+2^{3n+1}\\ P\left(1\right)=3.5^{2.1+1}+2^{3.1+1}=3.5^3+2^4=3\left(125\right)+16=375+16\\ =391=23\times 17\\ So,itisdivisibleby17and23both.\\ Hence,thecorrectoptionis\left(b\right)and\left(c\right).\end{array}$

Yes, to get into National Institute of Foundry and Forge Technology, 50000 is satisfactory rank. With this rank, candidates can fetch any course including BTech in Computer Engineering. Moreover, considering the NIFFT cutoff 2025 the General AI category cutoffs for BTech for the same institute stood between 52112 and 79054. Similary, for the OBC AI category candidates, the needed rank ranged between 18159 and 31249. The rank is more than sufficient to get admission with General AI quota, However, not for OBC AI quota, as the rank is bit too low to get you any course under OBC quota.

With 30% acceptance rate, Leiden University can be considered one of toughest universities in Netherlands to enter. Low percentage shows that the university follows positive approach where it considers several factors such as a strong academic profile, motivation letter, LOR and English language requirements. Students must perform exceptionally well in academics and submit all the mandatory documents to improve their chances.

Vikrant University course admissions are based on entrance exam score or merit-based, as per the course requirement. Vikrant University course admission is subject to fulfilment of the admission criteria. The university provides a wide range of programmes across multiple specialisations. Admissions to the programmes offered at the university are primarily entrance-based. Students can check course-wise selection criteria below:

This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Giventhat:\frac{1-ta{n}^{2}15^0}{1+ta{n}^{2}15^0}\\ Let\theta =15^0\therefore 2\theta =30^0\\ cos2\theta =\frac{1-ta{n}^2\theta }{1+ta{n}^2\theta }\\ \Rightarrow cos30^0=\frac{1-ta{n}^{2}15^0}{1+ta{n}^{2}15^0}\\ \Rightarrow \frac{\sqrt[]{3}}{2}=\frac{1-ta{n}^{2}15^0}{1+ta{n}^{2}15^0}\\ Hence,thecorrectoptionis\left(c\right).\end{array}$

Vikrant University admissions are primarily entrance-based. Candidates can register online for admission to their preferred course. Students can check the detailed Vikrant University course eligibility below:

This is a Objective Type Questions as classified in NCERT Exemplar
Sol:

$\begin{array}{l}LetP\left(n\right)=10^n+3.4^{n+2}+kisdivisibleby9,\forall n\in N\\ P\left(1\right)=10^1+3.4^{1+2}+k=10+3.64+k\\ =10+192+k=202+kmustbedivisibleby9.\\ If\left(202+k\right)isdivisibleby9thenkmustbeequalto5\\ 202+5=207whichisdivisibleby9\\ =\frac{207}{9}=23\\ So,theleastpositiveintegralvalueofk=5.\\ Hence,thecorrectoptionis\left(a\right).\end{array}$

Atal Bihari Vajpayee Medical University (ABVMU), Lucknow, will release the UP CPET 2026 seat allotment results on the site. It is tentative to be out July 12, 2026. Students whose names are mentioned in the list will be eligible to further appear for the admission process.