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P (x) = x² + bx + c.
Given ∫? ¹ P (x) dx = 1.
∫? ¹ (x² + bx + c) dx = [x³/3 + bx²/2 + cx] from 0 to 1 = 1/3 + b/2 + c = 1.
2 + 3b + 6c = 6 => 3b + 6c = 4 - (i)
When P (x) is divided by (x-2), the remainder is 5. So, P (2) = 5.
(2)² + b (2) + c = 5 => 4 + 2b + c = 5 => 2b + c = 1 - (ii)
From (ii), c = 1 - 2b. Substitute into (i):
3b + 6 (1 - 2b) = 4
3b + 6 - 12b = 4
-9b = -2 => b = 2/9.
c = 1 - 2 (2/9) = 1 - 4/9 = 5/9.
We need to find 9 (b+c).
9 (2/9 + 5/9) = 9 (7/9) = 7.

No, candidates cannot apply for NIC BSc admissions in offline mode. Candidates need to apply for CUET exam in order to qualify for admissions into BSc at NIC. However, candidates cannot apply for the CUET entrance exam in offline mode as the applications are only accepted in the prescribed format. Candidates will need to visit the official website of NIC to apply for the CUET entrance exam.

dy/dx + (tanx)y = sinx. This is a linear differential equation.
Integrating Factor (I.F.) = e^ (∫tanx dx) = e^ (ln|secx|) = secx.
The solution is y * I.F. = ∫ (sinx * I.F.) dx + C.
y * secx = ∫ (sinx * secx) dx = ∫tanx dx = ln|secx| + C.
Given y (0) = 0.
0 * sec (0) = ln|sec (0)| + C => 0 = ln (1) + C => C = 0.
So, y * secx = ln (secx).
y = cosx * ln (secx).
At x = π/4:
y = cos (π/4) * ln (sec (π/4) = (1/√2) * ln (√2) = (1/√2) * (1/2)ln (2) = ln (2) / (2√2).

IIM Amritsar shortlists candidates based on their entrance exam scores at the first level. Aspirants must have a valid score in CAT, GATE, GMAT, GRE or JAM for admission. Shortlisted candidates are further called for a personal interview round for admission. The institute also considers Class 10, Class 12, qualifying degree marks and work experience and gender diversity for final selection. 

The University of Suffolk and Solent University both are among the top choices of international students in the UK. Every university offers something unique for its international students to stand out of the herd. Both universities have its advantages and disadvantages. 

Check the comparison listed below between University of Suffolk and Solent University. The below comparison will help students in gaining more clarity on these universities respectively:

The MBA packages offered at BIBS Kolkata have seen a surge as compared to last years'. The MBA packages offered during the BIBS Kolkata placements 2024-2025 are listed below:

Candidates must pass a bachelor's or a master's degree or any other equivalent degree, preferably involving Management, Mathematics, Computer Science or allied fields with at least 60% aggregate or 6.0 CGPA or first class to apply for MSc programme at IIM Amritsar. Besides, aspirants must also have a valid score in CAT, GATE, GMAT, GRE or JAM for admission.

Yes, candidates are required to pay a non-refundable counselling fee during the registration process. The exact amount will be specified on the official counselling portal.

It is not advised for any candidate to miss the counselling date. It can result in losing the seat as well as the admission. You can confirm with the respective RIE if you can attend the next round of counselling or any other available solution.

No, you can't change the allotted RIE after admission. Try to choose carefully during choice-filling round.

For BTech in Information Technology, the maximum JEE Main required cutoff rank was 6926 in the General category under the AI quota. Therefore, a cutoff rank below the rank mentioned here is considered to be a good rank for getting an IT branch at IIIT Allahabad. The category-wise maximum cutoff rank required in 2025 is given below for BTech in IT course. 

Yes, some dates regarding CUET exam 2026 have been announcedat this point. The CUET 2026 entrance exam will be open for registrations in the month of March from 1st March 2026 - 26th March 2026. The CUET 2026 exam is scheduled to take place from 15th May 2026 - 3rd June 2026. The results are expected to be announced on 4th July 2026.

 BSSS Institute of Advanced Studies offers various PG courses along with multiple specialisations. It is affiliated with Barkatullah University, Bhopal and approved by the AICTE. Though, it's important to consider other factors such as infrastructure, faculty, curriculum, fees structure, etc. while taking admission. Candidates can visit the campus or check alumni/student reviews. 

The inequality is experience ( (|z|+3) (|z|-1) / (|z|+1) * log?2 ) ≥ log√? 16.
The right side is log? (1/2) 16 = log? (2? ¹) 2? = (4/-1)log?2 = -4. This seems incorrect.
Let's assume the base of the log on the right is √2. log√? 16 = log? (1/2) 2? = 2 * log?2? = 8.
The inequality becomes: 2^ (|z|+3) (|z|-1) / (|z|+1) ≥ 8 = 2³.
So, (|z|+3) (|z|-1) / (|z|+1) ≥ 3.
Let |z| = t. (t+3) (t-1) / (t+1) ≥ 3
t² + 2t - 3 ≥ 3t + 3
t² - t - 6 ≥ 0
(t-3) (t+2) ≥ 0
Since t = |z| ≥ 0, we must have t-3 ≥ 0.
So, t ≥ 3, which means |z| ≥ 3.
The minimum value of |z| is 3.

No, the BSc course admissions at NIU are no longer open in 2025. The BSc admissions at NIU are decided by the scores obtained by a candidate in the CUET entrance exams. The last date to register for the CUET exam ended in the month of March in 2025. The exam has already been concluded in the month of July. Candidates need to wait for the announcement of the CUET 2026 exam for BSc admissions at NIU.

No, candidates cannot complete MS at BSSS Institute of Advanced Studies in one year. The duration of this course is 16-18 months. Admissions are merit based and merit of graduation is accepted. Interested candidates can apply online or offline for admission at BSSS Institute of Advanced Studies.