According to Bohr's model of the hydrogen atom, the ratio of the kinetic energy to the total energy of an electron in \(3^{rd}\) excited state is?

• (A) \( 1 : 1 \)
• (B) \( 1 : -1 \)
• (C) \( -1 : 1 \)
• (D) \( 1 : 2 \)

A radioactive sample has a half-life of 10 days. The fraction of the initial nuclei decayed after 40 days is:

• (A) \( 1/4 \)
• (B) \( 3/4 \)
• (C) \( 1/16 \)
• (D) \( 15/16 \)

A block of mass \(M\) attached to a horizontal spring of spring constant \(k\) executes SHM with amplitude \(A\). When the block passes through its mean position, a small piece of mass \(m\) is dropped vertically onto it and sticks to it. The new amplitude of oscillation is:

• (A) \( A\sqrt{\left(\frac{M}{M+m}\right)} \)
• (B) \( A\left(\frac{M}{M+m}\right) \)
• (C) \( A\sqrt{\left(\frac{M+m}{M}\right)} \)
• (D) \( A \)

The dimensions of magnetic flux are identical to the dimensions of:

• (A) EMF \(\times\) Time
• (B) Electric field \(\times\) Velocity
• (C) Force/Current
• (D) Magnetic field \(\times\) Current

If the ionic product of \(Ni(OH)_2\) is \(1.9 \times 10^{-15}\), then the molar solubility of \(Ni(OH)_2\) in \(1.0 M NaOH\) is

• (A) \( 2.9 \times 10^{-18} M \)
• (B) \( 1.9 \times 10^{-13} M \)
• (C) \( 1.9 \times 10^{-15} M \)
• (D) \( 2.9 \times 10^{-14} M \)

The solubility of \(Pb(OH)_2\) in water is \(6.7 \times 10^{-6} M\). Its solubility in a buffer solution of \(pH = 8\) would be:

• (A) \( 1.2 \times 10^{-2} \)
• (B) \( 1.6 \times 10^{-3} \)
• (C) \( 1.6 \times 10^{-2} \)
• (D) \( 1.2 \times 10^{-3} \)

\(0.1 m\) of urea and \(0.05 m\) of \(CaCl_2\) are dissolved separately in equal volumes of water. Which solution will have higher elevation in boiling point?

• (A) Urea solution
• (B) \(CaCl_2\) solution
• (C) Both will show equal elevation
• (D) None will show elevation

A decimolar solution of potassium ferrocyanide is \(50%\) dissociated at \(300K\). The osmotic pressure of the solution is (\(R = 8.314 JK^{-1}mol^{-1}\))

• (A) \( 7.48 atm \)
• (B) \( 4.99 atm \)
• (C) \( 3.74 atm \)
• (D) \( 6.23 atm \)

Given a real valued function \(f\) such that \(f(x) = \begin{cases} \frac{\tan^2\{x\}}{x^2 - [x]^2} & for x > 0
1 & for x = 0
\sqrt{\{x\} \cot\{x\}} & for x < 0 \end{cases}\) then

• (A) \( LHL = 1 \)
• (B) \( RHL = \sqrt{\cot 1} \)
• (C) \( \lim_{x \to 0} f(x) exist \)
• (D) \( \lim_{x \to 0} f(x) does not exists \)

If the eccentricity and length of latus rectum of a hyperbola are \(\frac{\sqrt{13}}{3}\) and \(\frac{10}{3}\) units respectively, then what is the length of the transverse axis?

• (A) \( 7/2 unit \)
• (B) \( 12 unit \)
• (C) \( 15/2 unit \)
• (D) \( 15/4 unit \)

The eccentricity of the ellipse whose major axis is three times the minor axis is:

• (A) \( \sqrt{2}/3 \)
• (B) \( \sqrt{3}/2 \)
• (C) \( 2\sqrt{2}/3 \)
• (D) \( 2/\sqrt{3} \)

Let \(L_1\) be the length of the common chord of the curves \(x^2 + y^2 = 9\) and \(y^2 = 8x\), and \(L_2\) be the length of the latus rectum of \(y^2 = 8x\), then:

• (A) \( L_1 > L_2 \)
• (B) \( L_1 = L_2 \)
• (C) \( L_1 < L_2 \)
• (D) \( L_1/L_2 = \sqrt{2} \)