1 Cp and Cv are specific heats at constant pressure and constant volume, respectively. It is observed that Cp - Cv =a for hydrogen gas Cp - Cv =b for nitrogen gas. The correct relation between a and b is A) a=b B) a=14b C) a=28b D) $a=\frac{1}{14}b$
2 Which of the following statements is false? A) In a balanced Wheatstone bridge, if the cell and the galvanometer are exchanged, the null point is disturbed B) A rheostat can be used as a potential divider C) Kirchhoff 's second law represents energy conservation D) Wheatstone bridge is the most sensitive when all the four resistances are of the same order of magnitude.
3 In amplitude modulation. sinusoidal carrier frequency used is denoted by ωc and the signal frequency is denoted by ωm . The bandwidth (Δωm) of the signal is such that Δωm << ωc . Which of the following frequencies is not contained in the modulated wave ? A) $\omega_{c}$ B) $\omega_{m}+\omega_{c}$ C) $\omega_{c}-\omega_{m}$ D) $\omega_{m}$
4 A time-dependent force F =6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done by the force during the first 1 s will be A) 22J B) 9 J C) 18 J D) 4.5 J
5 A magnetic needle of magnetic moment 6.7 × 10-2 Am2 and moment of inertia 7.5 × 10-6 kg m2 is performing simple harmonic oscillations in a magnetic field of 0.01 T. Time taken for 10 complete oscillations is A) 8.89 s B) 6.98 s C) 8.76 s D) 6.65 s
6 A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that this density remains the same, the stress in the leg will change by a factor of A) $\frac{1}{9}$ B) 81 C) $\frac{1}{81}$ D) 9
7 The radius of the second Bohr orbit for hydrogen atom is [Planck's constant (h)= 6.6262 × 10-34 Js; mass of electron =9.1091 × 10-31kg ; charge of electron (e) = 1.60210 × 10-19 C : permitivity of vacuum (ε0)=8.854185 × 10-12 kg-1 m-3 A2) A) $1.65 \dot{A}$ B) $4.76 \dot{A}$ C) $0.529 \dot{A}$ D) $2.12 \dot{A}$
8 pKa of a weak acid (HA) and pKb of a weak base (BOH) are 3.2 and 3.4 respectively. The pH of their salt (AB) solution is A) 7.2 B) 6.9 C) 7.0 D) 1.0
9 3-methyl-pent-2-ene on reaction with HBr in presence of peroxide forms an addition product . The number of possible stereoisomers for the product is A) six B) zero C) two D) four
10 Two reactions R1 and R2 have identical pre-exponential factors. The activation energy of R1 exceeds that of R2 by 10 kj mol-1 . If k1 and k2 are rate constants for reactions R1 and R2, respectively at 300 K. then ln $(\frac{k_{2}}{k_{1}})$ is equal to (R=8.314 J mol-1 K-1) A) 8 B) 12 C) 6 D) 4
11 The products obtained when chlorine gas reacts with cold and dilute aqueous NaOH are A) $ClO^{-}$ and $ClO_{3}^{-}$ B) $ClO_{2}^{-}$ and $ClO_{3}^{-}$ C) $Cl^{-}$ and $ClO_{}^{-}$ D) $Cl^{-}$ and $ClO_{2}^{-}$
12 The major products obtained in the following reaction is A) $(\pm)C_{6}H_{5}CH(O^{t}Bu)CH_{2}C_{6}H_{5}$ B) $C_{6}H_{5}CH= CHC_{6}H_{5}$ C) $(+)C_{6}H_{5}CH(O^{t}Bu)CH_{2}C_{6}H_{5}$ D) $(-)C_{6}H_{5}CH(O^{t}Bu)CH_{2}C_{6}H_{5}$
13 A water sample has ppm level concentration of following anions $F^{-} =10 $: $SO_{4}^{2-} =100 $ : $NO_{3}^{-}=50$ the anion /anions that, make/makes the water sample unsuitable for drinking is/are A) Only $NO_{3}^{-}$ B) Both $SO_{4}^{2-} and NO_{3}^{-}$ C) only $F^{-} $ D) Only $SO_{4}^{2-} $
14 If the image of the point P(1,-2,3) in the plane 2x+3y-4z+22=0 measured parallel to the line $\frac{x}{1}=\frac{y}{4}=\frac{z}{5}$ is Q, then PQ is equal to A) $3\sqrt{5}$ B) $2\sqrt{42}$ C) $\sqrt{42}$ D) $6\sqrt{5}$
15 The function $f:R\rightarrow [-\frac{1}{2},\frac{1}{2}]$ defined as $f(x)=\frac{x}{1+x^{2}} is$ A) invertible B) injective but not surjective C) surjective but not injective D) neither injective nor surjective
