Class 11th
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New answer posted
a year ago
Contributor-Level 10
U = mV (r) = -Cm/r
F = -dU/dr = -Cm/r² ⇒ The force which provides required centripetal force
⇒ mv²/r = Cm/r² ⇒ r = C/v²
New answer posted
a year ago
Contributor-Level 10
(v/v? ) + (x/x? ) = 1 ⇒ v = - (v? /x? )x + v?
⇒ a = dv/dt = - (v? /x? ) (v) = - (v? /x? ) [- (v? /x? )x + v? ] ⇒ a = (v? ²/x? ²)x - v? ²/x?
- Concept involved: Graph of kinematics
- Topic: Kinematics
- Difficulty level: Moderate
- Note: IIT-Jee-2005
- Point of Error: Writing Equation of straight line and differentiation
New answer posted
a year agoContributor-Level 10
Limit (θ→0) [tan(πcos²θ) / sin(2πsin²θ)]
Let θ → 0. Then cos²θ → 1 and sin²θ → 0.
Let u = πsin²θ. As θ → 0, u → 0.
cos²θ = 1 - sin²θ = 1 - u/π.
The expression becomes:
Limit (u→0) [tan(π(1 - u/π)) / sin(2u)]
= Limit (u→0) [tan(π - u) / sin(2u)]
= Limit (u→0) [-tan(u) / sin(2u)]
= Limit (u→0) [-tan(u) / (2sin(u)cos(u))]
= Limit (u→0) [-(sin(u)/cos(u)) / (2sin(u)cos(u))]
= Limit (u→0) [-1 / (2cos²(u))] = -1 / (2 * 1²) = -1/2.
New answer posted
a year agoContributor-Level 9
Combustion of ethane: C? H? + 7/2 O? → 2CO? + 3H? O.
Moles of C? H? = 3g / 30 g/mol = 0.1 mol.
Moles of H? O produced = 0.3 mol.
Number of H? O molecules = 0.3 * 6.023 * 10²³ ≈ 18.06 * 10²².
So, x = 18.
New answer posted
a year agoContributor-Level 10
P(O at even place) = 1/2, P('O' at odd place) = 1/3
P(1 at even place) = 1 - 1/2 = 1/2
P(1 at odd place) = 1 - 1/3 = 2/3
The probability that 10 is followed by 01 is given by a sequence of probabilities, which seems to represent a specific arrangement or transition. The calculation is:
P(10 is followed by 01) = (2/3) * (1/2) * (1/3) * (1/2) * (1/2) * (1/3) * (1/2) * (2/3) = 1/18 + 1/18 = 1/9.
The calculation seems incomplete or context is missing.
New answer posted
a year agoContributor-Level 9
3-Hydroxy propanal
If 7.8g of C? H? O (molar mass 56 g/mol ) is formed, calculate the initial weight of 3-hydroxy propanal (molar mass 74 g/mol ).
Weight = (7.8/56) * 74 * (100/64) [Assuming 64% yield, though the number seems out of place].
Ans ≈ 16 g.
New answer posted
a year agoContributor-Level 9
AX is a diatomic molecule with a bond order of 2.5.
The compound is NO. The total number of electrons = 15 (7+8).
New answer posted
a year agoContributor-Level 10
- Given vectors OP = xi + yj - k and OQ = -i + 2j + 3xk.
- PQ = OQ - OP = (-1 - x)i + (2 - y)j + (3x + 1)k
- Given |PQ| = √20, so |PQ|² = 20.
(-1 - x)² + (2 - y)² + (3x + 1)² = 20
(1 + x)² + (2 - y)² + (3x + 1)² = 20 .(i) - Given OP ⊥ OQ, so OP · OQ = 0.
(x)(-1) + (y)(2) + (-1)(3x) = 0
-x + 2y - 3x = 0 ⇒ -4x + 2y = 0 ⇒ y = 2x .(ii)
Substitute (ii) into (i):
(1 + x)² + (2 - 2x)² + (3x + 1)² = 20
1 + 2x + x² + 4 - 8x + 4x² + 9x² + 6x + 1 = 20
14x² = 14 ⇒ x² = 1 ⇒ x = ±1.
When x = 1, y = 2. When x = -1, y = -2.
So, (x, y) can be (1, 2) or (-1, -2).- Given that OR, OP, and OQ are coplanar, their scalar triple product is 0: [OR OP OQ]
- Given OP ⊥ OQ, so OP · OQ = 0.
New answer posted
a year agoContributor-Level 9
Phosphorous Trichloride + Phosphorous acid
O-H bond is polar, so the number of ionisable hydrogens are 2.
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