All questions

• A projectile is fired so that its horizontal range equals its maximum height. The angle of projection with the horizontal is Answer: C. tan⁻¹(4) 2u²sinθcosθ/g=u²sin²θ/2g⇒tanθ=4 . Motion in a Plane 1 answer
• Blocks of mass 2 kg and 3 kg are in contact on a frictionless horizontal surface. A horizontal force of 10 N is applied to the 2 kg block. The contact force between the blocks is Answer: C. 6 N a=10/5=2 m/s²; force on 3 kg block =3×2=6 N. Laws of Motion 1 answer
• A ball of mass 0.15 kg moving at 20 m/s is hit straight back with the same speed. If the contact lasts 0.01 s, the average force on the ball is Answer: C. 600 N Δ p=0.15×40=6 N s; F=6/0.01=600 N. Laws of Motion 1 answer
• A planet has the same mean density as the earth but twice its radius. If the escape speed on earth is 11.2 km/s, the escape speed on the planet is Answer: A. 22.4 km/s v_e=√(2GM/R)=R√(8π Gρ/3)∝ R for equal density, so 2×11.2=22.4 km/s. Gravitation 1 answer
• At what height above the earth's surface does the acceleration due to gravity become one-fourth of its value on the surface? (R = 6400 km) Answer: A. 6400 km g/4=g/(1+h/R)²⇒1+h/R=2⇒ h=R . Gravitation 1 answer
• 100 g of water at 80 °C is mixed with 200 g of water at 20 °C. Neglecting heat losses, the final temperature is Answer: D. 40 °C 100(80-T)=200(T-20)⇒ T=40 °C. Thermal Properties of Matter 1 answer
• A source of frequency 900 Hz moves towards a stationary observer at 34 m/s. If the speed of sound is 340 m/s, the frequency heard is Answer: A. 1000 Hz n'=nv/v-v_s=900×340/306=1000 Hz. Sound 1 answer
• A convex lens of focal length 20 cm is placed in contact with a concave lens of focal length 40 cm. The combination behaves as a Answer: D. convex lens of focal length 40 cm 1/F=frac120-frac140=frac140 ; positive, so converging, F = 40 cm. Optics 1 answer
• The critical angle for light going from glass (\(\mu=1.5\)) to air is Answer: B. sin⁻¹(2/3) sin C=frac1μ=2/3 . Optics 1 answer
• A wire of resistance R is stretched uniformly until its length is doubled. Its new resistance is Answer: C. 4R Volume constant: A→ A/2 . R=ρl/A→ρ2l/A/2=4R . Electric Current Through Conductors 1 answer
• The packing efficiency of a body-centred cubic (bcc) unit cell is Answer: C. 68% In bcc, 4r=sqrt3a ; two atoms occupy 2·4/3π r³/a³≈0.68 of the cell. Solid State 1 answer
• An element with molar mass 60 g mol-1 forms an fcc lattice with edge length 400 pm. Its density is approximately (\(N_A=6.022\times10^{23}\)) Answer: D. 6.23 g cm-3 ρ=ZM/a³N_A=frac4×60(4×10⁻⁸)³×6.022×10²³=240/38.54≈6.23 g cm⁻³. Solid State 1 answer
• In a cubic solid, atoms A occupy the corners and atoms B occupy the face centres. If one A atom is missing from one corner of each unit cell, the formula of the compound is Answer: D. A7B24 A =7×1/8=7/8 , B =6×1/2=3 . Ratio 7/8:3=7:24 . Solid State 1 answer
• Which of the following defects does NOT change the density of an ionic crystal? Answer: D. Frenkel defect In a Frenkel defect an ion only shifts to an interstitial site, so mass and volume stay the same. Solid State 1 answer
• 1.8 g of glucose (molar mass 180 g mol-1) is dissolved in 100 g of water. The elevation in boiling point is (\(K_b=0.52\) K kg mol-1) Answer: D. 0.052 K m=0.01/0.1=0.1 mol kg⁻¹; Δ T_b=0.52×0.1=0.052 K. Solutions 1 answer
• The osmotic pressure of a 0.1 M aqueous solution of a non-electrolyte at 300 K is (R = 0.082 L atm K-1 mol-1) Answer: C. 2.46 atm π=CRT=0.1×0.082×300=2.46 atm. Solutions 1 answer
• Which of the following liquid pairs shows a negative deviation from Raoult's law? Answer: C. Acetone + chloroform Acetone and chloroform form hydrogen bonds with each other, so the A–B attraction is stronger than A–A and B... Solutions 1 answer
• The pH of 0.1 M acetic acid (\(K_a=1.8\times10^{-5}\)) is approximately Answer: B. 2.87 [H^+]=√(K_aC)=sqrt1.8×10⁻⁶=1.34×10⁻³ M; pH ≈2.87 . Ionic Equilibria 1 answer
• The solubility of Ag2CrO4 in water is \(1\times10^{-4}\) mol L-1. Its solubility product is Answer: A. 4×10⁻¹² K_sp=(2s)²s=4s³=4×10⁻¹² . Ionic Equilibria 1 answer
• A buffer contains 0.02 M acetic acid and 0.2 M sodium acetate. If p\(K_a\) of acetic acid is 4.74, the pH of the buffer is Answer: B. 5.74 pH =pK_a+log[salt]/[acid]=4.74+log10=5.74 . Ionic Equilibria 1 answer
• For the reaction \(\mathrm{N_2(g)+3H_2(g)\rightarrow2NH_3(g)}\) at 298 K, \(\Delta H-\Delta U\) is approximately Answer: A. -4.96 kJ Δ n_g=2-4=-2 ; Δ H-Δ U=Δ n_gRT=-2×8.314×298≈-4955 J. Chemical Thermodynamics 1 answer
• For a reaction \(\Delta H=+30\) kJ mol-1 and \(\Delta S=+100\) J K-1 mol-1. The reaction becomes spontaneous above Answer: B. 300 K Δ G<0 when T>Δ H/Δ S=30000/100=300 K. Chemical Thermodynamics 1 answer
• Given: \(\mathrm{C(s)+O_2(g)\rightarrow CO_2(g)}\), \(\Delta H=-393.5\) kJ; \(\mathrm{CO(g)+\frac12O_2(g)\rightarrow CO_2(g)}\), \(\Delta H=-283.0\) kJ. The standard enthalpy of formation of CO(g) is Answer: D. -110.5 kJ mol-1 Subtract the second equation from the first: Δ_fH(CO)=-393.5-(-283.0)=-110.5 kJ mol⁻¹. Chemical Thermodynamics 1 answer
• For the Daniell cell \(\mathrm{Zn|Zn^{2+}(1M)||Cu^{2+}(1M)|Cu}\), \(E^\circ_{\mathrm{Zn}}=-0.76\) V and \(E^\circ_{\mathrm{Cu}}=+0.34\) V. The standard Gibbs energy change is Answer: C. -212.3 kJ E^°_cell=0.34-(-0.76)=1.10 V; Δ G^°=-nFE^°=-2×96500×1.10=-212.3 kJ. Electrochemistry 1 answer