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13. Let P divides AB in ratio k : 1. Then co-ordinates of point P are

$(\frac{k(-1)+1(2)}{k+1},\frac{k(2)+1(-3)}{k+1},\frac{k(1)+1(4)}{k+1})$

= $\left(\frac{-k+2}{k+1},\frac{2k-3}{k+1},\frac{k+4}{k+1}\right)$

Let us examine whether the value of k, the point P coincides with point C

Putting $\frac{-k+2}{k + 1}=0$

=> $-k+2=0$

=> $k=2$

Put $k=2$ in

$\frac{2k - 3}{k + 1}$

= $\frac{2\left(2\right) - 3}{2 + 1}$

= $\frac{4 - 3}{3}$

= $\frac{1}{3}$

And put $k=2$ in

$\frac{k + 4}{k + 1}$

= $\frac{2 + 4}{2 + 1}$

= $\frac{6}{3}$

= 2

Therefore, C $\left(0,\frac{1}{3},2\right)$ is a point which divides AB internally in ratio 2 : 1 and is same as P. Hence A, B and C are collinear.

Both Bharathiar University Distance Education and Periyar Maniammai Institute of Science and Technology are good options to pursue an MBA. However, in terms of affordability, Bharathiar University Distance Education is more affordable since the tuition fee to pursue an MBA at Bharathiar University Distance Education is INR 21,100, and the tuition fee to pursue an MBA at Periyar Maniammai Institute of Science and Technology is INR 1.3 lakh.

Note: The fee mentioned above is as per the official sources. However, it is indicative and subject to change.

12. Let YZ-plane divides the line segment joining A (–2, 4, 7) and B (3, –5, 8) at point P (x, y, z) in the ratio k : 1.

Then the co-ordinates of P are.

$\left(\frac{k(3)+1(-2)}{k+1},\frac{k(-5)+1(4)}{k+1},\frac{k(8)+1(7)}{k+1}\right)$

$\left(\frac{3k-2}{k+1},\frac{-5k+4}{k+1},\frac{8k+7}{k+1}\right)$

As P lies on YZ-plane its x-coordinate is zero.

i.e. $\frac{3k-2}{k + 1}=0$

=> $3k-2=0$

=> $k=\frac{2}{3}$

Hence the YZ-plane divides AB internally in ratio.

$\frac{2}{3}$ : 1 = 2 : 3

BBA at Jaipur National University is a three- to four-year undergraduate course,  spread over six to eight semesters,  and offered in full-time mode. The course offers core and elective subjects in the BBA course. Names of the subjects offered in the first semester of the course are:

• Environmental Management 
• Business Organisation
• Managerial Economics
• Financial Accounting 
• Business Statistics
• Entrepreneurship & Skill Development

11. Let point Q divides PR in the k : 1. Then co-ordinate of Q will be

$(\frac{k(9)+1(3)}{k+1},\frac{k(8)+1(2)}{k+1},\frac{k(-10)+1(-4)}{k+1})$

=> (5, 4, –6) = $·\left(\frac{9k+3}{k+1}·,·\frac{8k+2}{k+1}·,·\frac{-10k-4}{k+1}·\right)$

Equating the co-ordinates we get,

$\frac{9k+3}{k + 1}$ = 5

=> $9k+3=5\left(k+1\right)$

=> $9k+3=5k+5$

=> $9k-5k=5-3$

=> $4k=2$

=> $k=\frac{2}{4}$

=> $k=\frac{1}{2}$

Putting $k=\frac{1}{2}$ in y-coordinate and z-coordinate

$\frac{8k + 2}{k + 1}$

= $\frac{\left(8 x\frac{1}{2}\right) + 2}{\frac{1}{2} + 1}$

= (4 + 2) ÷ $\frac{3}{2}$

= 6 x $\frac{2}{3}$

= 4

And

$\frac{\left(-1\mathrm{0x}\frac{1}{2} \right) - 4}{\frac{1}{2} + 1}$

= (–5 – 4) ÷ $\frac{3}{2}$

= – 9 x $\frac{2}{3}$

= – 6

Which is matching with the given co-ordinates of Q.

Hence, the ration in which Q divides PR is k : 1

= $\frac{1}{2}$ : 1

= 1 : 2

The course fees for two years MBA in University College of Commerce and Business Management, Osmania University is around INR 40,000. Candidates who qualify for the cutoff list, which is released by the university and get selected in the counselling process, are required to complete the further admission process. After seat allotment, candidates must complete the admission formalities, which include document verification and fee payment.  

NOTE: This information is sourced from the official website/ sanctioning body and is subject to change.

Yes, it is possible to get admission to Nirma University with 20000 rank in NATA. The cutoff was released for students seeking admission to the BArch course. The cutoff was released category-wise for All India and Home State quota candidates. The cutoff rank for the General AI category was 21005. For the General HS catrgory candidates, the cutoff was closed at 11086.

The candidates can see below the details of the RRB JE 2024 minimum qualifying marks:

This percentage of marks for eligibility may be relaxed by 2% for PwBD candidates, in case of shortage of PwBD candidates against vacancies reserved for them.

Nirma University accepts GUJCET scores for admission to BArch course. As per Nirma University cutoff 2024, the last round closing ranks for Bachelor of Pharmacy (B.Pharm.) was 487 and for Bachelor of Architecture (B.Arch.) was 12057 for the General category Home State candidates. 

10. i. Let P(x, y, z) be the point which divides line segment joining (–2, 3, 5) and (1, –4, 6) internally in the ratio 2 : 3

Therefore,

x = $\frac{2\left(1\right) + 3\left(-2\right)}{2 + 3}$ = $\frac{2 - 6}{5}$ = $\frac{-4}{5}$

y = $\frac{2\left(-4\right) + 3\left(3\right)}{2 + 3}$ = $\frac{-8 + 9}{5}$ = $\frac{1}{5}$

z = $\frac{2\left(6\right) + 3\left(5\right)}{2 + 3}$ = $\frac{12 + 15}{5}$ = $\frac{27}{5}$

Thus, the required points are $\left(\frac{-4}{5},\frac{1}{5},\frac{27}{5}\right)$

ii. Let P(x, y, z) be the point which divides line segment joining (–2, 3, 5) and (1, –4, 6) externally in the ratio 2 : 3

Therefore,

x = $\frac{2\left(1\right) - 3\left(-2\right)}{2 - 3}$ = $\frac{2 + 6}{-1}$ = –8

y = $\frac{2\left(-4\right) - 3\left(3\right)}{2 - 3}$ = $\frac{-8 - 9}{-1}$ = 17

z = $\frac{2\left(6\right) - 3\left(5\right)}{2 - 3}$ = $\frac{12 - 15}{-1}$ = 3

Thus, the required points are (–8, 17, 3).

The total fees to pursue the Bharathiar University Distance Education MBA course is a composition of multiple fee elements essential to be paid by the students to complete the course. According to the fee structure, students are required to pay four major components: tuition fees, hostel fees, other fees, and a one-time fee. Upon adding all,  the total fees for the MBA programme amount to INR 44,250. Check the below table to learn the component-wise bifurcation of the total fees:

Note: The above-mentioned fee is as per the official sources. However, it is indicative and subject to change.

IcfaiTech has a good track record of placements for its BCA course. The course-wise placement stats are yet to be released, However, the institute recorded 72% placements so far for the overall Class of 2024. The key highlights of IcfaiTech placements for the Class of 2024 are tabulated below:

Note: The placements are going on for the Class of 2024. The above-mentioned placement stats for 2025 may vary once the final placement report is out.

The highest package offered during the 2024 placement drive at IcfaiTech stood at INR 46 LPA. The same is presented below: 

9. Let P have the co-ordinates (x, y, z).

Given that,

PA + PB = 10

More than 74 recruiters participated during IcfaiTech placements 2024. Some of the top recruiters of IcfaiTech include Cognizant, HCL, Cisco, HP, TCS, Accenture, Capgemini, Leoforce, Dark Horse, etc..

As per the latest report, the average package offered during IcfaiTech placements in 2024 stood at INR 6.01 LPA. The same is tabulated below:    

The exam pattern of CBT 2 is as follows