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As per the latest country-level rankings given by Shiksha, the Bilkent University is deemed the #1 higher educational institute in the country.

Based in Ankara, the institute attains a global university rank #448 as part of the latest Shiksha Popularity Rankings, topping the charts for MS & MA courses in Shiksha's course-specific rankings.

Izmir Institute of Technology & Istanbul University rank #2 & #3 respectively among all colleges & universities in Turkey.

38. (i) Given, 3x + 2y 12 = 0.

3x + 2y = 12

Dividing both sides by 12 we get,

$\Rightarrow \frac{3x}{12}+\frac{2y}{12}=\frac{12}{12}$

$\Rightarrow \frac{x}{4}+\frac{y}{6}=1.$

Comparing the above equation with $\frac{x}{a}+\frac{y}{b}=1$ = we get, x-intercept, a = 4 and y-intercept b = 6.

(ii) Given, 4x - 3y = 6

Dividing the both sides by 6.

$\frac{4x}{6}-\frac{3y}{6}=\frac{6}{6}$

$\Rightarrow \frac{2x}{3}-\frac{y}{2}=1$

$\Rightarrow \frac{x}{3/2}+\frac{y}{(-2)}=1.$

Comparing above equation by $\frac{x}{a}+\frac{y}{b}=1$ we get, x-intercept a = $\frac{3}{2}$ and y-intercept, b = -2

(iii) Given, 3y + 2 = 0.

3y = -2

$y=-\frac{2}{3}$

As the equation of line is of form y = constant, it is parallel to x-axis and has no x-intercept.

y-intercept = -$\frac{2}{3}$

The cost of an Engineering programme at Isik University varies with the level of the course.

All undergraduate Engineering courses have a fixed annual tuition fee of USD 4,800 (INR 4.1 L), while the discounted cost of the same being USD 4,320 (INR 3.7 L).

However, students interested in pursuing a PG course in the Engineering specialisation of their choice must shell out USD 10,200 (INR 8.71 L) for the entire course duration.

Scholarships worth 50% discount on the PG courses are also available to eligible candidates.

For admission to the MBA course, AIMS Institutes accepted various entrance test scores, including MAT scores. Candidates aspiring for admission could appear for the MAT 2025 exam. As per official sources, the 2025 session of the MAT exam was held on 31 May 2025 for the Paper-Based Test (PBT) and 8 June 2025 for the Computer-Based Test (CBT).

The cost of studies at Isik University varies based on the course & the kind of accommodation a student opts to pursue.

Check out the table below for a detailed breakdown of the Isik University cost of attendance:

Source: Isik University

Turkey is not cheap to study, as is the case with other popular European countries.

The estimated annual costs of studies in private universities in Turkey ranges between USD 4,000-USD 9,000 (INR 3.4 L-INR 7.7 L).

Further, students must also take into account the costs associated with living in the country which ranges between USD 400-USD 650 (INR 34.2 K-INR 55.5 K) per month, as per data curated from an unofficial source.

Exercise 9.3

37.  (i) Given, x + 7y = 0.

7y = -x

y = $\frac{-1}{7}$ x + 0.

Comparing the above equation with y = mx + c we get, slope, m = -$\frac{1}{7}$ and c = 0, y-intercept

(ii) Given, 6x + 3y - 5 = 0

3y = -6x + 5

y = -$\frac{6}{3}$ x + $\frac{5}{3}$ = -2x + $\frac{5}{3}$

Comparing the above equation with y = mx + c we get, slope, m = -2 and $c=\frac{5}{3}$ , y-intercept

(iii) Given, y = 0

y = 0xx + 0

Comparing the above equation with y = mx + c we get, Slope, m = 0 and c = 0, y-intercept.

10. Given, n (A × A)=9

n (A) ×n (A) = 9.

n (A)² = 3².

n (A) = 3 .

And (–1,0), (0,1) $\in$ A × A i.e., A × A = { (x, y), x $\in$ A, y $\in$ B}

? A= {–1,0,1}

And A × A= {–1,0,1} × {–1,0,1}

= { (–1, –1), ( –1,0), ( –1,1), (0, –1), (0,0), (0,1), (1, –1), (1,0), (1,1)}

As per data curated from an unofficial source, the Isik University acceptance rate stands at 45%, placing it among fairly selective universities in Turkey.

The institute prioritises students with a solid academic background & therefore interested students are required to maintain the same & submit respective applications on time to have the best possible chance of admission.

9. Given, n (A)=3

n (B)= 2

So, n (Ax B)=n (A).n (B)=3x 2=6

as (x, 1), (y, 2), (z, 1) ∈Ax B= { (x, y), x∈Aand y∈B}.

A= {x, y, z} and B= {1,2}

As n (A) = 3as n (B) = 2

Heriot Watt University organises various career fairs and workshops to prepare students for the workplace. The university also has its own career portal where students get notified about all the job vacancies. Whereas University of Birmingham oganises a career expo two times a year in which various organisations participate and students get the opportunity to present their portfolio. In Amity University Dubai, Student Success Centre prepares the students for interviews and with CVs.

Isik University world rankings are not available as given by a prominent ranking publication, however its European Rankings for the year 2025 are available as given by a popular ranking publication.

The institute ranks #601 in Europe & #61 as part of the European Universities-West region rankings given by the same source.

Isik is a private university based in Istanbul, Turkey that first opened its doors under its current name to the general public in the year 1996 & is funded by the Feyziye School Foundation.

Its history can be dated back to 1885, when it was known as the Feyz-I Sibyan School, having started in Salonica region of the country.

Mustafa Kemal Ataturk then changed its name to Isik which means “light”.

Isik University can be considered a decent option for pursuing higher studies from abroad.

The institute offers courses across a number of industry relevant streams that includes: Software Engineering, Business Administration & Management, Architecture, Accounting & Auditing, & Finance among others.

Apart from offering all essential campus facilities such as libraries, 50+ students clubs & world class sports facilities, it also maintains a dedicated internship listing resource that lists hundreds of internship opportunities in the country.

8. A Given, A= {1,2}

B= {3,4}

So, A× B= { (1,3), (1,4), (2,3), (2, 4)}

i.e., n (A ×B)=4

A ×B will have subset =2⁴=16.They are,

Φ, { (1,3)}, { (1,4)}, { (2, 3)}, { (2,4)}, { (1,3), (1,4)}, { (1,3), (2,3)},

{ (1,3), (2, 4)}, { (1,4), (2, 3)}, { (1,4), (2, 4)}, { (2,3), (2, 4)},

{ (1,3), (1,4), (2, 3)}, { (1,3), (1,4), (2,4)}, { (1,3), (2,3), (2, 4)}, { (1,4), (2,3), (2,4)},

and { (1,3), (1,4), (2,3), (2,4)}

MIT has many MS courses that are highly ranked as per different ranking bodies. Some top courses are Engineering and Technology, Mathematics, Physics and Astronomy, Biological Sciences, etc. The MS course rankings at the university are given as follows:

36. 

Let the given points be A (3, 0), B (–2, –2) and C (8, 2). Then by two point form we can write equation of line passing point A (3, 0) and B (–2, –2) as

$y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

$\Rightarrow y-0=\frac{-2-0}{-2-3}\left(x-3\right)$

$\Rightarrow y=\frac{-2}{-5}\left(x-3\right)$

$\Rightarrow 5y=2\left(x-3\right)$

$\Rightarrow 5y=2x-6$

$\Rightarrow 2x-5y-6=0\left(1\right)$

If the three points A, B and C are co-linear, C will also lieonm the line formed by AB or satisfies equation (1).

Hence, putting x = 8 and y = 2 we have

L.H.S. = 2 × 8 – 5 × 2 – 6

= 16 – 10 – 6

= 0 = R.H.S.

The given three points are collinear.

No, admission to the AIMS Institutes MBA course is purely entrance-based. Candidates seeking admission must have appeared in one of the accepted entrance exams. The list below showcases all the national-level entrance tests conducted by the institute:

• MAT
• XAT
• CMAT
• ATMA
• PGCET

Based on scores obtained in any one of the exams, students are shortlisted for further evaluation. Those who have a valid score and fulfil the eligibility criteria can apply for the course.