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(a+b+c)² = a²+b²+c²+2 (ab+bc+ca)
1² = a²+b²+c²+2 (2) ⇒ a²+b²+c² = -3.
a²b²+b²c²+c²a² = (ab+bc+ca)² - 2abc (a+b+c) = 2² - 2 (3) (1) = -2.
a? +b? +c? = (a²+b²+c²)² - 2 (a²b²+b²c²+c²a²) = (-3)² - 2 (-2) = 9+4=13.

Δ = |1,1, -1; 1,2, α 2, -1,1| = 1 (2+α)-1 (1-2α)-1 (-1-4) = 2+α+2α-1+5 = 3α+6=0 ⇒ α=-2.
Δ? = |2,1, -1; 1,2, α β, -1,1| = 2 (2+α)-1 (1-αβ)-1 (-1-2β) = 4+2α-1+αβ+1+2β = 4+2α+αβ+2β=0.
4-4-2β+2β=0. This holds.
Δ? = |1,2, -1; 1,1, α 2, β,1| = 1 (1-αβ)-2 (1-2α)-1 (β-2) = 1-αβ-2+4α-β+2 = 1+4α-αβ-β=0.
1-8+2β-β=0 ⇒ -7+β=0 ⇒ β=7.
α+β = -2+7 = 5.

CITM Kolkata admission is based on entrance exam scores. Some of the popular entrance exams accepted by the college are JEE Main, AIEEE,  WBJEE, etc. CITM courses are offered to students at the UG and Diploma levels. To get admitted to CITM, candidates must meet the eligibility criteria set by the institute. Further, candidates seeking admission to the BTech programme must be Class 12 passed with a 45% aggregate with PCM. 

sec y dy/dx = 2sinxcosy.
sec²y dy = 2sinx dx.
tan y = -2cosx + C.
y (0)=0 ⇒ 0=-2+C ⇒ C=2.
tan y = 2-2cosx.
y' = (-2sinx)/sec²y.
5y' (π/2) = 5 (2sin (π/2)/sec² (π/2)
sec²y dy/dx = 2sinx.
y' (π/2)? At x=π/2, tan y = 2. sec²y = 1+tan²y = 5.
5 (2sin (π/2) = 5 (2)=10.

The highest package offered during Great Lakes Institute of Management, Gurgaon placements 2025  stood at  INR 22.7 LPA. The table below presents the highest package provided to PGDM and PGPM students:

P (x) = a (x-2)² + b (x-2) + c.
lim (x→2) P (x)/sin (x-2) = lim (x→2) P (x)/ (x-2) = P' (2) = 7.
P' (x) = 2a (x-2) + b. P' (2) = b = 7.
P' (x) = 2a.
P (3) = a (1)² + b (1) + c = a+b+c = 9.
Continuity at x=2 means lim f (x) = f (2).
lim (x→2) (a (x-2)²+b (x-2)+c)/ (x-2) = P' (2) = b=7. This is given.
The problem states f (2)=7.
P (x) = (x-2) (ax+b) form used in solution. Let's use this.
lim (x→2) (x-2) (ax+b)/sin (x-2) = lim (x→2) ax+b = 2a+b = 7.
P (3) = (3-2) (3a+b) = 3a+b=9.
Solving: a=2, b=3.
P (x) = (x-2) (2x+3).
P (5) = (5-2) (2*5+3) = 3 * 13 = 39.

Great Lakes Institute of Management, Gurgaon  provides great placement to its students. During the 2025  Great Lakes Institute of Management, Gurgaon.  placement season the highest package recorded was  INR 22.7 LPA. Refer to the table below to know more about the placement statistics at Great Lakes Institute of Management, Gurgaon. :

Mean = (6+10+7+13+a+12+b+12)/8 = (60+a+b)/8 = 9 ⇒ a+b=12.
Variance = (Σx? ²/n) - (mean)² = 37/4.
Σx? ²/8 - 81 = 37/4.
Σx? ² = 8 (81+9.25) = 8 (90.25) = 722.
Σx? ² = 36+100+49+169+a²+144+b²+144 = 642+a²+b².
642+a²+b²=722 ⇒ a²+b²=80.
(a+b)²=144 ⇒ a²+b²+2ab=144 ⇒ 80+2ab=144 ⇒ 2ab=64.
(a-b)² = a²+b²-2ab = 80-64 = 16.

At DAITM Kolkata, the 180 seats for the BBA programme are divided between the general BBA and the BBA in Hospital Management. Out of the total, 120 seats are allotted for the general BBA course, while 60 seats are reserved for the Hospital Management specialisation, giving students the flexibility to choose their career path.

The total seat intake for the BBA course at DAITM Kolkata is 180. This includes both the general BBA programme and the BBA in Hospital Management specialisation. With limited seats available in each discipline, students are encouraged to apply early and ensure they meet the eligibility and entrance requirements.

x? + 2 (20)¹/? x³ + (20)¹/²x² + . No.
x² = - (20)¹/? x - (5)¹/².
α+β = - (20)¹/? , αβ=5¹/².
α²+β² = (α+β)²-2αβ = (20)¹/² - 2 (5)¹/² = 0.
α? +β? = (α²+β²)² - 2 (αβ)² = 0 - 2 (5) = -10.
α? +β? = (α? +β? )² - 2 (αβ)? = (-10)² - 2 (5)² = 100 - 50 = 50.

Students seeking admission to the BBA programme at DAITM Kolkata are required to submit specific documents during the admission process. Key documents typically include the Class 12 mark sheet, MAKAUT CET scorecard, passport-sized photographs, a government-issued ID, and any additional documents as specified by the university during the counselling process.

The last step in the admission process at DAITM Kolkata is document verification followed by fee payment. This step finalises the admission and confirms the student's seat in the BBA programme. As per official guidelines, the total tuition fee for the BBA course falls within the range of INR 2.25 Lacs - INR 3 Lakh.

Using L'Hopital Rule:
lim (x→2) (2xf (2) - 4f' (x)/1 = 2 (2)f (2) - 4f' (2) = 4 (4) - 4 (1) = 12.

DAITM Kolkata evaluates applications by considering both the candidate's Class 12 marks and MAKAUT CET scores. Only those who meet the eligibility requirements and hold a valid entrance exam score move forward in the selection process. Shortlisted candidates receive further instructions through their registered email ID or mobile number provided during the application.

I = ∫? π/? π/? dx/ (1+e^ (xcosx) (sin? x+cos? x). Using ∫? f (x)dx = ∫? f (a+b-x)dx. a+b=0.
I = ∫? π/? π/? dx/ (1+e? ) (sin? x+cos? x) = ∫? π/? π/? e? dx/ (e? +1) (sin? x+cos? x).
2I = ∫? π/? π/? dx/ (sin? x+cos? x) = 2∫? π/? dx/ (sin? x+cos? x).
I = ∫? π/? sec? xdx/ (tan? x+1). Let t=tanx.
I = ∫? ¹ (t²+1)dt/ (t? +1) = ∫? ¹ (1+1/t²)dt/ (t²-√2t+1) (t²+√2t+1). No, this is hard.
I = ∫? ¹ (1+1/t²)dt/ (t-1/t)²+2). Let u=t-1/t. I = ∫ du/ (u²+2) = (1/√2)tan? ¹ (u/√2).
= π/ (2√2).