Ask & Answer: India's Largest Education Community

Bohr's theory accounts for the line spectrum of single electron species but Li? has two electrons. Bohr's theory fails to explain splitting of spectral lines in presence of magnetic field i.e. Zeeman effect.

To find the sum Σ[r=0 to 6] (?C?)².
This is the coefficient of x? in the expansion of (1+x)?(x+1)? = (1+x)¹².
By the binomial theorem, (1+x)¹² = Σ[k=0 to 12] ¹²C? x?.
The coefficient of x? is ¹²C?.
¹²C? = (12 * 11 * 10 * 9 * 8 * 7) / (6 * 5 * 4 * 3 * 2 * 1) = 11 * 2 * 3 * 2 * 7 = 924.

I? = I? + I? ⇒ I? /I? = 1 + I? /I? ⇒ 1/α = 1 + 1/β = (β+1)/β ⇒ α = β/ (1+β)

⇒ 1/β = 1/α - 1 = (1-α)/α ⇒ β = α/ (1-α)

IIT Palakkad JEE Advanced cutoff 2025 for BTech admission ranged between 5736 and 16753 for the General AI category students. This is overall cutoff range, including all six rounds for BTech. The cutoff range differs for different rounds and categories. Considering 2025 cutoff ranks BTech in CSE had lowest rank of 5736 in first round and 6454 during last round of admission. Students can refer to the table below to view IIT Palakkad branch-wise cutoff 2025 for both the first and last rounds. 

g? = g - ω²R ⇒ 0 = g - ω²R ⇒ ω = √ (g/R)

⇒ T = 2π/ω = 2π√ (R/g) = 2 × 3.14 × √ (6400 × 10³)/10)

(A) sin (ωt) + cos (ωt) = √2 sin (ωt + π/4) ⇒ T = 2π/ω
(B) sin² (ωt) = 1/2 - (1/2)cos (2ωt) ⇒ T = 2π/ (2ω) = π/ω
(C) 3cos (π/4 - 2ωt) ⇒ T = 2π/ (2ω) = π/ω
(D) cos (ωt) + cos (2ωt) + cos (3ωt)
Time period of cos (ωt) = 2π/ω
Time period of cos (2ωt) = 2π/ (2ω)
Time period of cos (3ωt) = 2π/ (3ω)
Time period of combined function = 2π/ω

Find the number of solutions for 2tan(x) = π/2 - x in [0, 2π].
This is equivalent to finding the number of intersection points of the graphs y = tan(x) and y = (π/4) - x/2.
Let's sketch the graphs:

y = tan(x) has vertical asymptotes at x = π/2, 3π/2.

y = (π/4) - x/2 is a straight line with a negative slope.
At x=0, y=π/4.
At x=π/2, y=0.
At x=π, y=-π/4.
At x=2π, y=-3π/4.
By observing the graphs, there will be one intersection in (0, π/2), one in (π/2, 3π/2), and one in (3π/2, 2π].
Total number of solutions is 3.

Always possible as it is associated only with β? decay

Last date to apply for NCHM JEE exam 2025 was 15th January 2025. The registrations for the exam started from 16th December 2024. The NCHM JEE 2025 exam was held on 27th April 2025. 

A = Area swept ⇒ dA/dt = (1/2)r² (dθ/dt) = (1/2) (Mr²ω)/M = L / (2M)

θ? > I = θ ⇒ sinθ? > sinθ ⇒ 1/μ > sinθ

⇒ μ < 1/sinθ

Note: If we assume θ = 45° ⇒ μ < 1.414, then red colour light ray will come out from face PR of prism.

No, the BSc admissions at IHM, Ahmedabad for the year 2025 have now been closed. Candidates need to appear for the NCHM JEE exam to gain admissions at IHM, Ahmedabad BSc courses. The NCHM JEE 2025 exam has been concluded. Candidates who appeared for the exam have already received the results of their exam performance. The dates for the NCHM JEE 2026 will be announced soon.

Given that x, y, z are in A.P., so 2y = x + z.
The determinant is:
| 3 4√2 x |
| 4 5√2 y | = 0
| 5 k z |

Apply the operation R? → R? + R? - 2R?:
The first row becomes:
(3 + 5 - 24) (4√2 + k - 25√2) (x + z - 2y)
= 0 (k - 6√2) (0)
So the determinant becomes:
| 0 k-6√2 0 |
| 4 5√2 y | = 0
| 5 k z |

Expanding along the first row:
-(k - 6√2)(4z - 5y) = 0.
This implies k - 6√2 = 0 or 4z - 5y = 0.
k = 6√2 or y = 4z/5.
The condition y = 4z/5 is stated as not possible.
Therefore, k = 6√2, which means k² = (6√2)² = 36 * 2 = 72.

PV? = C ⇒ V? (dP/dV) + P (γV^ (γ-1) = 0 ⇒ dP/dV = -γ (P/V) ⇒ dP/P = -γ (dV/V)

U = mV (r) = -Cm/r

F = -dU/dr = -Cm/r² ⇒ The force which provides required centripetal force

⇒ mv²/r = Cm/r² ⇒ r = C/v²

NCHM JEE is compulsory for every candidate who wishes to take admissions into the IHM, Ahmedabad BSc exams. The last date to register for the exam is Jan 2025, 2026. The exam is scheduled to take place 25th April 2026. 

The institution offers good placements to its PG and UG graduating students. The overall key highlights of Thiagarajar College of Engineering placements 2025 as compared with 2024 and 2023 are presented below: