LearnQuiz - Educational Quizzes

1. Compute: ∫₀¹ln(1+x)dx=?

ln2−1/2 2ln2-1 1 1/2

2. Evaluate the line integral ∮_C(ydx+xdy), C: x²+y²=1

0 2π π -π

3. Solve the differential equation: dy/dx=y, y(0)=1

y = eᕽ y = e⁻ᕽ y = x y = 1

4. The radius of convergence of the power series ∑^∞_𝑛=0(x^𝑛/𝑛!) is:

0 1 ∞ Does not exist

5. Evaluate the double integral: ∬_[0,1]×[0,1](x+y)dxdy

1/2 3/2 2 1

1. Mechanics: A projectile is launched at 20 m/s at 45°. Find the maximum height reached. (𝑔=9.8 m/s²)

5.8 m 7.5 m 10.2 m 15.6 m

2. Mechanics: The approximate formula for the period of a simple pendulum, T=2π√(l/g) is applicable when:

Any amplitude Small amplitude Large amplitude Independent of amplitude

3. Optics: In Young’s double-slit experiment, wavelength 𝜆=600 nm, slit separation 𝑑=0.3 mm, screen distance 𝐿=2 m. What is the fringe spacing?

2 mm 3 mm 4 mm 5 mm

4. Electromagnetism: A solenoid has 500 turns, length 0.5 m, carries 2 A current. Find the magnetic field inside (μ₀=4π×10⁻⁷).

2.5×10⁻³ T 4.0×10⁻³ T 2.5×10⁻² T 4.0×10⁻² T

5. Electromagnetism: A 0.1 m² loop is in a perpendicular magnetic field 𝐵=0.5sin(100𝑡) T. Find the maximum induced emf.

2 V 3 V 5 V 10 V

1. For the reaction 2A(g) + B(s) ⇌ C(g) + D(g) (ΔH° > 0), at equilibrium, which change will definitely increase the partial pressure of C?

Adding inert gas at constant volume. Increasing the temperature. Adding more B(s). Decreasing the volume of the container.

2. In the Latimer diagram for chlorine in acidic solution: ClO₄⁻ ──⟶^1.19 ClO₃⁻ ──⟶^1.21 HClO₂ ──⟶^1.65 HClO ──⟶^1.63 Cl₂ ──⟶^1.36 Cl⁻, which species is unstable with respect to disproportionation?

ClO₃⁻ HClO₂ HClO Cl₂

3. The [Ni(CN)₄]²⁻ ion is diamagnetic and square planar, while [NiCl₄]²⁻ is paramagnetic and tetrahedral. This difference is primarily due to the:

Larger crystal field splitting energy (Δ_t) of Cl⁻ compared to CN⁻. Ability of CN⁻ to cause spin-pairing, making Δ > P (pairing energy) for the square planar complex. Difference in the oxidation state of nickel in the two complexes. Cl⁻ ligand being a stronger field ligand than CN⁻.

4. What is the final major product of this multi-step synthesis?
    Benzene → (with CH₃CH₂COCl / AlCl₃) → A
    A → (with Zn(Hg) / HCl) → B
    B → (with NBS / hv) → C
    C → (with KOC(CH₃)₃ / heat) → D

(E)-Ph-CH=CH-CH₃ Ph-CH₂-CH=CH₂ Ph-CH=CH₂ o-Br-C₆H₄-CH₂CH₂CH₃

5. Rank the following compounds in order of decreasing rate of electrophilic aromatic substitution (EAS) with Br₂/FeBr₃ (fastest to slowest).
    (I) Toluene
    (II) Benzoic acid
    (III) Phenol
    (IV) Bromobenzene

III > I > IV > II I > III > II > IV II > IV > I > III III > II > I > IV

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