#mht-cet pcm
- A 6 V Zener diode is used with a series resistance of 200 Ω across a 10 V supply. A load of 1 kΩ is connected across the Zener. The current through the Zener diode is Answer: C. 14 mA Series current =10-6/200=20 mA; load current =6/1000=6 mA; Zener current =14 mA. 1
- 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 . 1
- Nylon-6,6 is obtained by condensation polymerisation of Answer: D. hexamethylenediamine and adipic acid n H₂N(CH₂)₆NH₂+n HOOC(CH₂)₄COOH→ Nylon-6,6 + 2n H₂O . 1
- The number of molecules in 4.4 g of CO2 is Answer: A. 6.022×10²² n=4.4/44=0.1 mol ⇒0.1×6.022×10²³ molecules. 1
- A compound contains 40% C, 6.67% H and 53.3% O by mass. Its empirical formula is Answer: D. CH2O Mole ratio C : H : O =40/12:6.67/1:53.3/16=3.33:6.67:3.33=1:2:1 . 1
- 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. 1
- 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. 1
- 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. 1
- 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 . 1
- 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. 1
- 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. 1
- The number of radial nodes in a 3p orbital is Answer: B. 1 Radial nodes =n-l-1=3-1-1=1 . 1
- The maximum number of electrons in an atom that can have \(n=3\) and \(m_s=+\frac12\) is Answer: B. 9 The n=3 shell has n²=9 orbitals, and each holds one electron with m_s=+1/2 . 1
- The bond order of the superoxide ion O2− is Answer: D. 1.5 O₂⁻ has 17 electrons: bonding 10, antibonding 7. Bond order =10-7/2=1.5 . 1
- 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. 1
- 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. 1
- 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 . 1
- 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. 1
- 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. 1
- The shape of the ClF3 molecule is Answer: B. T-shaped Cl has 3 bond pairs and 2 lone pairs (sp³d). The lone pairs occupy equatorial positions, giving a T-shape. 1
- The oxidation number of oxygen in OF2 is Answer: A. +2 F is always −1: x+2(-1)=0⇒ x=+2 . 1
- The negation of \(p\rightarrow q\) is Answer: B. pwedgesim q p→ qequivsim pvee q ; its negation is pwedgesim q . 1
- Which of the following statements is a tautology? Answer: A. (pwedge q)→ p If pwedge q is true then p is true, so the implication is always true. The others fail for (T,F), (F,T) and always,... 1
- 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... 1