JEE Advanced Mi...

An object of specific gravity ρ is hung from a thin steel wire. The fundamental frequency for transverse standing waves in the wire is 300 Hz. The object is immersed in water, such that one half of its volume is submerged. The new fundamental frequency (in Hz) is

What is the minimum possible radius of wire passed over a pulley which supports two blocks of masses m and 2m, if the breaking stress of the wire is σ?

The probability of survival of a radioactive nucleus for one mean life is:

The electrochemical cell shown below is a concentration cell.

M | M2+ (saturated solution of a sparingly soluble salt, MX₂) || M²⁺ (0.001 mol dm^-3) | M

The emf of the cell depends on the difference in concentrations of M2+ ions at the two electrodes. (The emf of the cell at 298 K is 0.059 V)

The value of ΔG (kJ mol^-1) for the given cell is

(Take 1F = 96500 C mol^-1)

'I' is an aromatic aldehyde, which does not have alpha hydrogens. When reacted with an anhydride of a carboxylic acid in the presence of a sodium salt of the same acid to give an unsaturated acid 'J', which undergoes a series of reactions as depicted in the equation below, to form 'K'.

J gives effervescence on treatment with NaHCO₃ and a positive Baeyer's test.

In the following reaction sequence, the compound K is

AValue of gas constant R, is

Statement-1: If chlorine is passed into toluene at room temperature in the presence of Anhydrous AlCl₃, electrophilic substitution reaction takes place giving o- and p-chlorotoluenes.

Statement-2: If chlorine is passed through boiling toluene in the presence of UV light, substitution reaction in the aliphatic side chain occurs.

If the transversal y = m_rx; r = 1, 2, 3 cut off equal intercepts on the transversal x + y = 1, then 1 + m₁, 1 + m₂, 1 + m₃ are in

m & n are integers with 0< n < m. AA is the point (m,n) on the Cartesian plane. B is the reflection of A in the line y = x. C is the reflection of B in the yy-axis, D is the reflection of C in the x-axis and E is the reflection of D in the yy-axis. The area of the pentagon ABCDE is

Consider the polynomial: f(x) = 1 + 2x + 3x² + 4x³

Let s be the sum of all distinct real roots of f(x) and let t = |s|.

The real number 's' lies in the interval