1 Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits 104 times the power emitted from B. The ratio $\left(\frac{\lambda_{A}}{\lambda_{B}}\right)$ of their wavelengths $\lambda_{A}$ and $\lambda_{B}$ at which the peaks occur in their respective radiation curves is A) 3 B) 2 C) 4 D) 1
2 A nuclear power plant supplying electrical power to a village uses a radioactive material of half-life T years as fuel.The amount of fuel at the beginning is such that the total power requirement of the village is 12.5% of the electrical power available from the plant at that time. If the plant is able to meet the total power needs of the village for a maximum period of nT years, then the value of n is A) 4 B) 2 C) 3 D) 1
4 For the octahedral complexes of Fe3+ in SCN- (thiocyanate- S) and in CN- ligand environments, the difference between the spin only magnetic moments in Bohr magnetons (when approximated to the nearest integer) is [ atomic number of Fe=26} A) 3 B) 4 C) 1 D) 2
5 Not considering the electronic spin, the degeneracy of the second excited state (n=3) of H-atom is 9, while the degeneracy of the second excited state of H- is A) 4 B) 3 C) 2 D) 1
6 All the energy released from the reaction $X\rightarrow Y,\triangle_{r}G^{0}=-193kJmol^{-1}$ is used for oxidising M+ as $M^{+}\rightarrow M^{3+}+2\overline{e}$, E0 =-0.25 V. Under standard conditions , the number of moles of M+ oxidised when one mole of X is converted to Y is [F=96500 C mol-] A) 4 B) 3 C) 2 D) 1
7 Fe3+ is reduced to Fe2+ by using A) $ H_{2}O_{2}$ in presence of NaOH B) $ Na_{2}O_{2}$ in water C) $ H_{2}O_{2}$ in presence of $H_{2}SO_{4}$ D) $ Na_{2}O_{2}$ in presence of $H_{2}SO_{4}$
8 The densities of two solids spheres A and B of the same radii R vary with radial distance r as $\rho_{A}(r)=k\left(\frac{r}{R}\right)$ and $\rho_{B}(r)=k\left(\frac{r}{R}\right)^{5}$ , respectively where k is a constant. The moment of inertia of the individual spheres about axes passing through their centres are IA and IB, respectively. If $\frac{I_{B}}{I_{A}}=\frac{n}{10}$, the value of n is A) 6 B) 4 C) 5 D) 2
9 Consider a uniform spherical charge distribution of radius R1 centred at the origin O. In this distribution, a spherical cavity of radius R2, centred at P with distance OP=a=R1- R2 (see figure) is made. If the electric field inside the cavity at position r is E(r), then the correct statements is /are A) E is uniform , its magnitude is independent of $R_{2}$ but its direction depends on r B) E is uniform , its magnitude depends on $R_{2}$ and its direction depends on r C) E is uniform , its magnitude is independent of 'a' but its direction depends on a D) E is uniform and both its magnitude and direction depends on a
10 Two spheres P and Q for equal radii have densities ρ1 and ρ2, respectively, The spheres are connected by a massless string and placed in liquids L1 and L2 of densities σ1 and σ 2 and viscosities η1 and η2, respectively. They float in equilibrium with the sphere P in L1 and sphere Q in L2 and the string being taut (see figure). If sphere P alone in L2 has terminal velocity vp and Q alone in L1 has terminal velocity vQ, then A) $\frac{|V_{P}|}{|V_{Q}|}=\frac{\eta_{1}}{\eta_{2}}$ B) $\frac{|V_{P}|}{|V_{Q}|}=\frac{\eta_{2}}{\eta_{1}}$ C) $[V_{P}.V_{Q}>0$ D) $V_{P}.V_{Q}<0$
11 When O2 is absorbed on a metallic surface, electron transfer occurs from the metal to O2. The true statement (s) regarding this adsorption is(are) A) $O_{2}$ is physisorbed B) heat released C) Occupancy of $^{*}\pi_{2\rho}$ of $O_{2}$ is increased D) bond length of $O_{2}$ is increased
12 The pair(s) of ions where both the ions are precipitated upon passing H2S gas in presence of dilute HCl, is (are) A) $Ba^{2+},Zn^{2+}$ B) $Bi^{3+},Fe^{3+}$ C) $Cu^{2+},Pb^{2+}$ D) $Hg^{2+},Bi^{3+}$
13 Consider the hyperbola H: x2-y2=1 and a circle S with centre N(x2,0). Suppose that H and S touch each other at a point P(x1,y1) with x1>1 and y1>0. The common tangent to H and S at P intersects the X-axis at point M. If (l,m) is the centroid of $\triangle PMN$, then the correct expression(s) is/are A) $\frac{dl}{dx_{1}}=1-\frac{1}{3x_1^2}$ for $x_{1}>0$ B) $\frac{dm}{dx_{1}}=\frac{x_{1}}{3(\sqrt{x_1^2-1}}$ for $x_{1}>0$ C) $\frac{dl}{dx_{1}}=1+\frac{1}{3x_1^2}$ for $x_{1}>0$ D) $\frac{dm}{dy_{1}}=\frac{1}{3}$ for $y_{1}>0$
14 Let $F:R\rightarrow R$ be a thrice differentiable function. Suppose that F(1)=0,F(3)=-4 and F'(x)<0 for x ε (1,3) , Let f(x)=xF(X) for all x ε R. The correct statement(s) is/are A) $f^{1}(1)<0$ B) $f(2)<0$ C) $ f'(x)\neq 0$ for any $x\epsilon (1,3)$ D) f'(x) =0 for same $x\epsilon (1,3)$
15 Let n1 and n2 be the number of red and black balls. respectively in box I. Let n3 and n4 be the number of red and black balls respectively in box II. One of the two boxes, box I and box II a was selected at random and a ball was drawn randomly out of this box. The ball was found to be red. If the probability that this red ball was drawn from box II, is $\frac{1}{3}$, then the correct option(s) with the possible values of n1,n2,n3 and n4 is/are A) $n_{1}=3,n_{2}=3,n_{3}=5,n_{4}=15$ B) $n_{1}=3,n_{2}=6,n_{3}=10,n_{4}=50$ C) $n_{1}=8,n_{2}=6,n_{3}=5,n_{4}=20$ D) $n_{1}=6,n_{2}=12,n_{3}=5,n_{4}=20$