1 Consider a hydrogen atom with its electron in the nth orbital. An electromagnetic radiation of wavelength 90mm is used to ionize the atom. If the kinetic energy of the ejected electron is 10.4 eV, then the value of n is (hc= 1242 eV nm) A) 2 B) 3 C) 1 D) 4
2 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
4 If the freezing point of a 0.01 molal aqueous solution of a cobalt (III) chloride -ammonia complex (which behaves as a strong electrolyte) is -0.0558° C, the number of chloride (s) in the coordination sphere of the complex is [Kf of water =1.86 K kg mol-1] A) 1 B) 2 C) 3 D) 4
5 Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then, the value of $\frac{m}{n}$ is A) 4 B) 5 C) 6 D) 3
6 Let $f:R\rightarrow R$ be a function defined by $f(x)=\begin{cases}[x], & x \leq 2\\0 & x > 2\end{cases}$ , where [x] denotes the greatest integer less than or equal to x. If $I= \int_{-1}^{2} \frac{x f(x^{2})}{2+f(x+1)}dx, $, then the value of (4l-1) is A) 1 B) 3 C) 2 D) 0
7 An electron in an excited state of Li2+ ion has angular momentum $\frac{3h}{2\pi}$. The de Broglie wavelength of the electron in this state is $p\pi a_{0}$ (where $a_{0}$ is the Bohr radius). The value of p is A) 4 B) 3 C) 2 D) 1
8 A parallel plate capacitor having plates of area S and plate separation d, has capacitance C1 in air. When two dielectrics of different relative permittivities (ε1= 2 and ε2 =4) are introduced between the two plates as shown in the figure, the capacitance becomes C2. The ratio $\frac{C_{2}}{C_{1}}$ is A) $\frac{6}{5}$ B) $\frac{5}{3}$ C) $\frac{7}{5}$ D) $\frac{7}{3}$
9 An ideal monoatomic gas is confined ina horizontal cylinder by a spring-loaded piston (as shown in the figure). Initially, the gas is at temperature T1, pressure P1 and volume V1 and the spring is in its relaxed state. The gas is then heated very slowly to temperature T2, pressure P2 and volume V2 . during this process the piston moves out by a distance of x, Ignoring the friction between the piston and the cylinder, the correct statements is/are A) If $V_{2}=2V_{1}$ and $T_{2}=3T_{1}$ , then the energy stored in the spring is $\frac{1}{4}p_{1}V_{1}$ B) If $V_{2}=2V_{1}$ and $T_{2}=3T_{1}$ , then the change in internal energy $3p_{1}V_{1}$ C) If $V_{2}=3V_{1}$ and $T_{2}=4T_{1}$, then the work done by the gas $\frac{7}{3}p_{1}V_{1}$ D) If $V_{2}=3V_{1}$ and $T_{2}=4T_{1}$, then the heat supplied to the gas is $\frac{17}{6}p_{1}V_{1}$
10 Light guidance in an optical fibre can be understood by considering a structure comprising of thin solid glass cylinder of refractive index n1 surrounded by a medium of lower refractive index n2. The light guidance in the structure takes place due to successive total internal reflections at the interface of the media n1 and n2 as shown in the figure. All rays with the angle of incidence i less than a particular value im are confined in the medium of refractive index n1. The numerical aperture (NA) of the structure is defined as sin I'm. For two structures namely S1 with $n_{1}=\frac{\sqrt{45}}{4}$ and $n_{2}=\frac{3}{2}$ and S2 with $n_{1}=\frac{8}{5}$ and $n_{2}=\frac{7}{5}$ and taking the refractive index of water to be $\frac{4}{3}$ and that to air to be 1. the correct options is/are A) NA of $S_{1}$ immersed in water is the same as that of $S_{2}$ immersed in a liquid of refractive index $\frac{16}{3\sqrt{15}}$ B) NA of $S_{1}$ immersed in liquid of refractive index $\frac{6}{\sqrt{15}}$ is the same as that of $S_{2}$ immersed in water. C) NA of $S_{1}$ placed in air is the same as that $S_{2}$ immersed in liquid of refractive index $\frac{4}{\sqrt{15}}$ D) NA of $S_{1}$ placed in air is the same as that of $S_{2}$ placed in water
11 Under hydrolysis conditions, the compounds used for preparation of linear polymer and for chain termination m respectively are A) $CH_{3}SiCl_{3}$ and $Si(CH_{3})_{4}$ B) $(CH_{3})_{2}SiCl_{2}$ and $(CH_{3})_{3}SiCl_{}$ C) $(CH_{3})_{}SiCl_{2}$ and $(CH_{3})_{}SiCl_{3}$ D) $SiCl_{4}$ and $(CH_{3})_{3}SiCl_{}$
12 The correct statement(s) regarding, $(i) HClO,(ii) HClO_{2},(iii) HClO_{3}$ and $HClO_{4}$ is(are) A) the number of Cl=O bonds in(ii) and (iii) together is two B) the number of lone pair of electrons on Cl in(ii) and (iii) together in three. C) the hybridisatin of Cl in(iv) in $sp^{3}$ D) amongest (i) and (iv) , the strongest acid is(i)
13 When 100 mL of 1.0 M HCl was mixed with 100mL of 1.0 M NaOH in an insulated beaker at constant pressure, a temperature increase of 5.7° C was measured for the beaker and its contents (Expt. I). Because the enthalpy of neutralisation of a strong acid with a strong base is a constant (-57.0kJmol-1), this experiment could be used to measure the calorimeter constant. In a second experiment (Expt.2), 100mL of 2.0 M acetic acid (Ka = 2.0 x 10-5) was mixed with 100 mL of 1.0 M NaOH (under identical conditions to Expt. 1) where a temperature rise of 5.6° C was measured. Enthalpy of disscociation (in KJmol-1) of acetiic acid obtained from the Expt. 2 is A) 1.0 B) 10.0 C) 24.5 D) 51.4
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. A ball is drawn at random from box I and transferred to box II. If the probability of drawing a red ball from box I, after this transfer is $\frac{1}{3}$, then the correct option(s) with the possible values of n1 and n2 is/are A) $n_{1}=4$ and $n_{2}=6$ B) $n_{1}=2$ and $n_{2}=3$ C) $n_{1}=10$ and $n_{2}=20$ D) $n_{1}=3$ and $n_{2}=6$
