Mistake book

Full mock test 6 · Q 12Sun 27 Sep −1 mark

A solid sphere rolls without slipping on a level floor. What fraction of its total kinetic energy is rotational?

1. A2/5Your answer
2. B2/7Right answer
3. C5/7
4. D1/2

Why: I = 2/5 MR² and ω = v/R, so rotational KE = 1/5 Mv² and translational KE = ½ Mv². Total = 7/10 Mv², so the rotational share is (1/5) ÷ (7/10) = 2/7. The 2/5 is the factor in I, not the energy share.

Full mock test 6 · Q 17Sun 27 Sep −1 mark

A disc spins freely at angular speed ω about its axis. An identical disc, at rest, is gently placed on it so they share the axis and finally turn together. Their common angular speed is:

1. Aω
2. Bω/2Right answer
3. Cω/√2Your answer
4. D2ω

Why: No outside torque acts, so angular momentum is conserved: Iω = (I + I)ω′, giving ω′ = ω/2. Kinetic energy is not conserved — friction between the discs turns half of it into heat. Using energy gives ω/√2, which is the trap.

Full mock test 5 · Q 9Sun 13 Sep −1 mark

What is the moment of inertia of a thin uniform ring of mass M and radius R about one of its diameters?

1. AMR²/4
2. BMR²/2Right answer
3. CMR²Your answer
4. D3MR²/2

Why: About the axis through the centre and perpendicular to the ring, I = MR². By the perpendicular axis theorem, two equal diameters share this: I_d + I_d = MR², so I_d = MR²/2.

Full mock test 5 · Q 16Sun 13 Sep −1 mark

A solid disc and a ring of the same mass and radius are released together from rest at the top of the same incline. Both roll without slipping. Which reaches the bottom first?

1. AThe discRight answer
2. BThe ring
3. CBoth reach togetherYour answer
4. DIt depends on the angle of the incline

Why: Acceleration when rolling = g sin θ / (1 + I/MR²). For a disc I/MR² = ½, for a ring it is 1, so the disc accelerates faster at any angle. Mass and radius cancel — only the shape matters.

Full mock test 6 · Q 31Sun 27 Sep Skipped

Two cells, 2 V with internal resistance 1 Ω and 1.5 V with internal resistance 0.5 Ω, are joined in parallel (positive to positive). The emf of the combination is:

1. A1.75 V
2. B5/3 V (about 1.67 V)Right answer
3. C3.5 V
4. D1.5 V

Why: For cells in parallel, $E = \dfrac{E_1/r_1 + E_2/r_2}{1/r_1 + 1/r_2} = \dfrac{2 + 3}{1 + 2} = \dfrac{5}{3}$ V. You left it blank after 4 minutes — learn the one-line formula.

Full mock test 6 · Q 34Sun 27 Sep Skipped

In a potentiometer, a cell balances at 60 cm. When a 5 Ω resistor is connected across the cell, the balance point moves to 50 cm. The internal resistance of the cell is:

1. A1 ΩRight answer
2. B1.5 Ω
3. C2 Ω
4. D0.5 Ω

Why: $r = R\left(\dfrac{l_1}{l_2} - 1\right) = 5 \times \left(\dfrac{60}{50} - 1\right) = 5 \times 0.2 = 1\ \Omega$, where l₁ is the balance length with the cell open and l₂ with the resistor connected.

Full mock test 5 · Q 31Sun 13 Sep −1 mark

Two bulbs rated 100 W, 220 V and 60 W, 220 V are connected in series across a 220 V supply. Which one glows brighter?

1. AThe 100 W bulbYour answer
2. BThe 60 W bulbRight answer
3. CBoth glow equally
4. DNeither glows

Why: R = V²/P, so the 60 W bulb has the higher resistance. In series the current is the same, and power = I²R is larger for the larger R. (In parallel, the 100 W bulb would be brighter.)

Today's 10 practice · Q 6Sat 3 Oct Practice

The refractive index of a glass is √2. What is the critical angle for light going from this glass into air?

1. A30°
2. B60°Your answer
3. C45°Right answer
4. D90°

Why: sin C = 1/n = 1/√2, so C = 45°. Your rough work had sin C = 1/√2 right — then you matched it with sin 60° instead of sin 45°.

Full mock test 6 · Q 52Sun 27 Sep −1 mark

Which of these has the highest first ionisation enthalpy?

1. AB
2. BC
3. CNRight answer
4. DOYour answer

Why: Ionisation enthalpy rises across period 2 with one break: nitrogen's half-filled 2p³ is extra stable, and oxygen's fourth 2p electron is paired and easier to remove. So N (1402 kJ/mol) beats O (1314 kJ/mol).

Full mock test 6 · Q 77Sun 27 Sep Skipped

How many geometrical isomers does the octahedral complex [Co(NH₃)₄Cl₂]⁺ have?

1. A1
2. B2Right answer
3. C3
4. D4

Why: An [MA₄B₂] octahedral complex has two arrangements: the two Cl next to each other (cis, 90°) or opposite each other (trans, 180°). So there are 2 geometrical isomers.

Full mock test 5 · Q 58Sun 13 Sep −1 mark

As a solution of a strong electrolyte such as KCl is diluted, its molar conductivity (Λ_m):

1. AIncreases slightlyRight answer
2. BDecreasesYour answer
3. CStays exactly the same
4. DIncreases sharply

Why: Conductivity (κ) falls on dilution, but molar conductivity rises because ions move more freely. For strong electrolytes the rise is small ($\Lambda_m = \Lambda^\circ_m - A\sqrt{c}$); it is sharp only for weak electrolytes.

Full mock test 5 · Q 70Sun 13 Sep −1 mark

An inert gas such as argon is added to the equilibrium \ce{N2 + 3H2 <=> 2NH3} at constant volume. The equilibrium:

1. AShifts forwardYour answer
2. BShifts backward
3. CIs not affectedRight answer
4. DStops completely

Why: At constant volume the partial pressures (and concentrations) of N₂, H₂ and NH₃ do not change, so Q still equals K. Adding inert gas at constant pressure would shift it backward.

Full mock test 5 · Q 81Sun 13 Sep −1 mark

Which of these is the most acidic?

1. AEthanol
2. BPhenolYour answer
3. Cp-Cresol (4-methylphenol)
4. Dp-Nitrophenol (4-nitrophenol)Right answer

Why: The –NO₂ group pulls electrons away and spreads out the negative charge of the phenoxide ion, making it more stable, so p-nitrophenol loses H⁺ most easily. –CH₃ in p-cresol does the opposite.

Full mock test 6 · Q 118Sun 27 Sep −1 mark

In the Calvin cycle, how many ATP and NADPH are used to fix one molecule of CO₂?

1. A2 ATP and 3 NADPHYour answer
2. B3 ATP and 2 NADPHRight answer
3. C2 ATP and 2 NADPH
4. D3 ATP and 3 NADPH

Why: Two ATP and two NADPH reduce the two 3-PGA formed per CO₂; one more ATP regenerates RuBP. So each CO₂ needs 3 ATP and 2 NADPH (18 ATP and 12 NADPH per glucose). You swapped the numbers — read the options twice.

Biology unit test 4 · Q 44Thu 1 Oct −1 mark

Which cells in the testis secrete testosterone?

1. ALeydig (interstitial) cellsRight answer
2. BSertoli cellsYour answer
3. CSpermatogonia
4. DPrimary spermatocytes

Why: Leydig cells lie between the seminiferous tubules and make androgens such as testosterone. Sertoli cells, inside the tubules, nourish the developing sperm.

Full mock test 5 · Q 152Sun 13 Sep −1 mark

Which of these pteridophytes is heterosporous?

1. ALycopodium
2. BSelaginellaRight answer
3. CEquisetumYour answer
4. DDryopteris

Why: Selaginella (and Salvinia) make two kinds of spores — large megaspores and small microspores. Lycopodium, Equisetum and Dryopteris make only one kind (homosporous).