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4. i. The x-axis and y-axis taken together determine a plane known as XY plane.

ii. The coordinates of points in the XY-plane are of the form (x, y, 0).

iii. Coordinate planes divide the space into 8 (eight) octants.

3. 

(1, 2, 3) lies in octant I.

(4, –2, 3) lies in octant IV.

(4, –2, –5) lies in octant VIII.

(4, 2, –5) lies in octant V.

(–4, 2, –5) lies in octant VI.

(–4, 2, 5) lies in octant II.

(–3, –1, 6) lies in octant III.

(–2, –4, –7) lies in octant VII.

If you belong to the General AI category, the DY Patil Akurdi JEE Main cutoff 2025 ranged between 35834 and 99038. The cutoff ranks vary for different specialisations, rounds and categories. For General AI quota, the specialisation-wise BE cutoff 2025 is tabulated below for the first and the last round. 

Since there are no restrictions on being a student, you are welcome to apply for the Civil Services coaching programme offered by Jamia Millia Islamia (JMI) while you are working toward your degree. You must, however, fulfill the prerequisites for UPSC preparation, which include being at least 21 years old by the Civil Services Exam year. There is no set age limit for the coaching itself.

For studying BSc in IT, students need to meet the describes eligibility. According to it, the students must pass the class 12 exam from any stream with Mathematics or Statistics as a subject from a recognised board. Therefore, yes, students from other streams are welcomed to participate in the admission process of Gokul Global University.

Yes, candidates can join Jaipur National University without entrance examination scores for the BBA course because the university also accepts the scores of the last qualifying examination for admissions to the BBA course and releases the merit according to that. Therefore, candidates can get admission to the BBA course through the scores of the entrance examination and by Class 12 merit too. 

2. When a point lies on XZ-plane, its y-coordinate is zero.

1. When a point lies on x-axis, its y-coordinate and z-coordinate are zero.

International students can apply at the University of Alberta for MBA programs and they are required to pay the tuition and living accomodation cost too. The table below mentions the cost of living on campus:

Yes. There are several entrance exams through which students can get admission to the top MCA colleges in Kolkata. You can check the table below for some details about these exams.

Disclaimer: This info. is taken from the official website and may differ.

(c) Given, f(x)=(x-a)(x-b)

where a and b are constants.

So,

$f^{\prime }(x)=(x-a)\frac{d}{dx}(x-b)+(x-b)\frac{d}{dx}(x-a)$

=(x-a)+(x-b)

= 2x– a- b. $$

(ii) Given f(x)= ${\left(a{x}^2+b\right)}^2.$ where ab are constant

So, $f^{\prime }(x)=\frac{d}{dx}{\left(a{x}^2+b\right)}^2$

$=\frac{d}{dx}\left(a^2{x}^4+b^2+2a{x}^{2}b\right)$

$=\frac{d}{dx}{a}^2{x}^4+\frac{d}{dx}{b}^2+\frac{d}{dx}2a{x}^{2}b$

= $4a^2{x}^3+0+4axb$

= $4ax\left(a{x}^2+b\right).$

(iii) Given, f(x)= $\frac{x-9}{x-b}$ where a and bare constants

So, $f(x)=\frac{(x-b)\frac{d}{dx}(x-a)-(x-a)\frac{d}{dx}(x-b)}{{(x-b)}^2}$

$=\frac{(x-b)-(x-a)}{{(x-b)}^2}$

$=\frac{a-b}{{(x-b)}^2}$

KTU - APJ Abdul Kalam Technological University accepts multiple entrance exams for its MBA course. CAT, CMAT,  KMAT Kerala, KMAT, etc., are few of the entrance exams accepted by the university for its MBA course. Candidates can appear for any one of the entrance exams to be eligible for the MBA course. However, it is mandatory for students to have completed Graduation with a minimum aggregate of 50% from a recognised university. 

The table given below compares the fees and the salary package after completing an MCA from the top MCA colleges in Kolkata.

Disclaimer: This info. is taken from the official website and may differ.

38. Given, $f(x)=x^n+a{x}^{n-1}+a^2{x}^{n-2}+?+a^{n-1}x+a^n.$

We know that,

$\frac{d}{dx}\left(x^x\right)=n{x}^{x-1}$

So,

$f^{\prime }(x)=\frac{d}{dx}{x}^x+\frac{d}{dx}a{x}^{x-1}+\frac{d}{dx}{a}^2{x}^{x-2}+?+\frac{d}{dx}$ $a^{x-1}x+\frac{d}{dx}{a}^x=n{x}^{n-1}+a(n-1)x^{n-2}+a^2(n-2)x^{n-3}+?+a^{n-1}+0.$

$\begin{array}{l}(?\frac{dax}{dx}=a\frac{dx}{dx}\frac{\mathrm{and\; d}a}{dx}=\mathrm{0whereaisconstant}\end{array}$$\begin{array}{l}\end{array}$$\begin{array}{l}\end{array}$

Pursuing a Master of Computer Applications from colleges in Kolkata can be valuable if the college has good faculty, infrastructure, and industry connections. It offers opportunities to gain strong technical skills and access local job markets. However, it is important to research each college's reputation and placement record before making a decision.

The students often are curious about the professional outlook after studying the BSc Course. The students are given opportunities to participate in the placement drive at the Gokul Global University. However, there are a multiple array of job positions that students can opt for after studying BSc. Some of them are noted below:

• Research & Developmentvarious scientific roles.
• Quality Control/Assurance
• Teaching at schools or coaching institutes, or pursuing further studies and become lecturers or professors.
• Sales & Marketing
• Data Analysis

37. 

Given $f(x)=\frac{x^{100}}{100}+\frac{x^{99}}{99}+?+\frac{x^2}{2}+x+1$

$\underset{h\to 0}{lim}\frac{{(x+h)}^{100}-x^{100}}{100\cdot h}+\underset{h\to 0}{lim}\frac{{(x+h)}^{99}-x^{99}}{99\cdot h}+\dots +\underset{x\to 0}{lim}\frac{{(x+h)}^2-x^2}{2h}$ $+\underset{x\to 0}{lim}x+\underset{x\to 0}{lim}1$

$=\frac{100\cdot x^{99}}{100}+\frac{99x^{98}}{99}+?+\frac{2x}{2}+0+1$

$=x^{99}+x^{98}+?+x+1$

At x=0,

f(X)  =1.

and at x=1,

$f^{\prime }(1)=1^{99}+1^{98}+\dots +1^2+1+1$

=100 $\times$ 1

=100 $\times f^{\prime }(0)$

Hence, $f^{\prime }(1)=100f^{\prime }(0)$

KTU - APJ Abdul Kalam Technological University doesn't offer direct admission to the MBA course. Candidates seeking admission to the MBA programme, which is offered in both full-time and part-time modes, need to have a valid score in an entrance exam, followed by an institute-level GD & PI round. The basic eligibility is to pass graduation in the relevant field from a recognised university. Interested candidates can visit the official website of the college to learn further. 

The students can read the table given below for details about the placement package and top recruiting companies that hire students from the top MCA colleges in Kolkata-

Disclaimer: This info. is taken from the official website and may differ.