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Capacity of the tube

$\pi {(1)}^2(7-1)+\frac{2}{3}\pi {(1)}^3=\frac{20}{3}\pi$

If D < 0 roots are imaginary.

i.e. q² – 4pr < 0 $\Rightarrow$ q² < 4pr 

Discriminant $={(2\sqrt[]{5})}^2-4(1)(3)=20-12=8$

So, the roots are real and irrational.

400 students × 80 days = 240 students × d days

d = $\frac{400}{3}=133.33days$  

The food was to last 80 more days but now it is lasting 53.33 days more.

5x + 4y = 253         …. (1)

3x + 7y = 161         …. (2)

On solving equations (1) & (2), we get

x = 49 and y = 2.

Hence, type I Alloy = 392 kg, and Type II Alloy = 22 kg

The distances covered by them are in the ratio 3:5 and difference is 30 m. This means 5x – 3x = 30 or 2x = 30 or x = 15 m

Therefore, the total distance covered is equal to 120 m. Their speeds are also in the ratio 3 : 5. Since the speed of the first person is 6 m/s, the speed of the second person will be 10 m/s and he has to cover a distance of 45 m.

Therefore time taken $=\frac{45}{10}=4.5seconds$

Let R be the radius of the recast sphere

$\frac{4}{3}\pi R^3=\frac{4}{3}\pi (3^3+4^3+5^3)$

R³ = 216 $\Rightarrow$ R = 6

Total surface area of 3 spheres

$=4\pi (3^2+4^2+5^2)=4\pi \times 50=200\pi {}^{}$

Surface area of the recast sphere = 4π (6²)=144

% reduction in area $=\frac{(200\pi -144\pi )}{200\pi }\times 100\mathrm{\%}=28\mathrm{\%}$

ar¹⁰ * ar¹⁷ * ar¹⁹ = ar²⁷ * ar⁴

a³r⁴⁶ = a²r³¹

ar¹⁵ = 1

NSHM Kolkata offers a total of 390 seats for the BBA course, whereas FEM offers 180 seats. The difference between these seats might be a reason that NSHM Kolkata offers various specialisations for the BBA course, and has two specialised schools for Bachelor in Business Administration courses - NSHM Business School, NSHM Knowledge Campus - Kolkata Campus, and NSHM Institute of Hotel & Tourism Management, NSHM Knowledge Campus - Kolkata Campus. On the other hand, FIEM only have two specialisations in the BBA course.

Let A (4, 3), B (6, −2), C (−11, −3) be the vertices of triangle ABC.

AB² = (6 – 4)² + (−2 −3)² = 29

BC² = (−11 −6)² + [−3 – (−2)]² = 290

AC² = (−11 −4)² + [ (−3 −3)]² = 261

As AB²+ AC²= BC²

 ABC is a right-angled triangle.

Slope of given line = $-\frac{2}{3}$ perpendicular line has slope = $\frac{2}{3}$

Now c = −3 (given)

Putting in general equation y = mx + c

2y = 3x ⇒ 3x-2y=6

Total expenses = (35% of 7500) + 712 + 1880 + 272 + 400 + 75 = 6024

Total receipts = 7500 Total profit = 7500 – 6024 = 1476

% profit = $\left(\frac{1476}{6024}\right)\times 100=24.5\mathrm{\%}$

We can see that men, women & children are in the ratio = $\frac{12}{6},\frac{15}{5},\frac{16}{4},$ or 2: 3: 4.Number of men, women & children = 10, 15, 20. Now if each man gets 6a, we have10 × 6a + 15 × 5a + 20 × 4a = 1720 or a = 8. So, the answers are Rs. 48, 40, 32.

Only possibility is if 1950 is divided by a multiple of 13, because the other glasses have a capacity that is not a multiple of 13.

Hence 1209 is the only choice.

Alternative method:

As the glasses filled by same fractions,

$\frac{a}{750}=\frac{b}{1950}=\frac{c}{600}=\frac{a+b+c}{750+1950+600}$

a + b + c = 2046 $\therefore \frac{b}{1950}=\frac{2046}{3300}$

b = 1209 litres

The university selects candidates based on entrance exam or merit-based as per the course requirements. NFSU offers a plethora of courses, including MA, MSc, MTech, MBA and BTech. For BTech course, admission aspirants must have a valid JEE Main score. Similarly, for courses like BBA LLB, LLM, etc., students are selected based on CLAT score + merit. 

You can get direct admission into merit-based courses such as MA or MSc with 80% in Class 12 if you have all other eligibility criteria. In entrance-based courses such as BTech or MBA, Class 12 marks assist in making you eligible but the entrance exam score is still required.

The total seat intake for the BBA course at FIEM is 180. The college divided an equal number of seats for both the BBA course, i.e., 90. Candidates who wish to secure a seat in the BBA course must complete their Class 12 from any stream with an aggregate of 50%. Additionally, secure a valid score in the accepted entrance exam—MAKAUT CET.