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  1. Prepare for an exam
  2. /CUET UG
Exam preparation

CUET UG preparation

The Common University Entrance Test for undergraduate admission to central and other taking universities, run by the National Testing Agency. Physics, Chemistry, Mathematics and Biology practice from the Class 12 chapters.

752 questions · 595 problems

With a Standard plan

Question sets

No timer. Work at your own pace.

  • MathematicsVolumes, Averages and Other Uses: Think It Through10 questions
  • MathematicsArea Between Curves: Concept Check10 questions
  • MathematicsArea Under a Curve: Check Your Understanding10 questions
  • MathematicsDefinite Integrals: Think It Through10 questions
  • MathematicsMethods of Integration: Concept Check10 questions
  • MathematicsAntiderivatives and Substitution: Check Your Understanding10 questions

All CUET UG question sets →

Practice questions and problems

Hardest first. Try each one on paper before you see the answer.

Physics

Questions

  • AdvancedA sample starts as a pure radioactive nuclide A, of half-life 6.0 h. Each nucleus of A decays into a nucleus of B, which is itself radioactive, with a half-life of 2.0 h, and decays into a stable nuclide. After how long is the activity of B in the sample greatest?
  • AdvancedIn a double-slit experiment the slits are 0.40 mm apart and the screen is 1.00 m away. The slits are lit at the same time by light of wavelengths 600 nm and 450 nm. Which of the following statements are correct?

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Advanced
Two long, smooth, horizontal metal rails, 0.50 m apart, lie in a uniform vertical magnetic field of 0.80 T. At one end they are joined by an uncharged capacitor of 0.50 F. A metal rod of mass 0.20 kg lies across the rails, as in the figure, and is given a push so that it starts sliding away from the capacitor at 7.0 m/s. No other force acts along the rails. The rod and rails together have a resistance of 2.0 Ω. How much heat is produced in the circuit in all, by the time the current has stopped?
  • AdvancedA uniform magnetic field of 0.20 T fills the region to the right of a straight boundary and points out of the page, as in the figure. A proton moving at 2.0 × 10⁶ m/s crosses the boundary into the field, at 30° to the normal, tilted towards the top of the page. Take the proton's mass as 1.67 × 10⁻²⁷ kg and its charge as 1.6 × 10⁻¹⁹ C. Which of the following statements are correct?
  • AdvancedA metal sphere of radius 12 cm carries no net charge. Inside it there is a small spherical cavity, not at the centre, and a point charge q = +3.0 nC sits inside the cavity, away from the cavity's centre. A second point charge Q = +5.0 nC is held outside, 40 cm from the centre of the sphere. Take 1/4πε₀ = 9.0 × 10⁹ N m²/C². Which of the following statements are correct?
    • More Physics questions for CUET UG →

    Problems with worked solutions

    • AdvancedA radio antenna stands on the edge of a cliff, at a height h = 120 m above a calm sea, and points…
    • AdvancedA large flat coil of 500 turns and radius R = 20 cm carries a steady current of 4.0 A…
    • AdvancedIn a vacuum chamber there is a uniform electric field of 2.0 × 10⁴ V/m along +y and a uniform…
    • AdvancedTwo equal capacitors, each of C = 100 µF, and two equal resistors, each of R = 10 kΩ, make a…
    • AdvancedA metal sphere of radius R = 10.0 cm stands on an insulating stand in a large empty room…
    More Physics problems for CUET UG →

    Chemistry

    Questions

    • HardAn octahedral d⁴ ion is first bound to a weak ligand and shows 4 unpaired electrons. A stronger ligand then replaces it, and the complex shows 2 unpaired electrons. Which statement explains this?
    • HardHow many stereoisomers, counting each enantiomer, has the octahedral ion [Co(en)(NH₃)₂Cl₂]⁺?
    • HardA polarimeter reads -6.0° for a tube of the pure (-) enantiomer of a chiral complex. Another tube, filled to the same level at the same concentration, holds a mixture of 95 percent (-) and 5 percent (+). What does the polarimeter read for the mixture?
    • HardA student names K₂[Zn(CN)₄] as potassium tetracyanidozinc(II). What is the mistake?
    • HardEvery two ammonia ligands of [Zn(NH₃)₄]²⁺ are replaced by one ethane-1,2-diamine to give [Zn(en)₂]²⁺. What happens to the coordination number and the charge?
    More Chemistry questions for CUET UG →

    Problems with worked solutions

    • AdvancedHydrogen peroxide breaks down slowly in water, but iodide ions speed it up: 2 H₂O₂(aq) → 2 H₂O(l) +…
    • AdvancedNitric oxide and chlorine form nitrosyl chloride: 2 NO(g) + Cl₂(g) → 2 NOCl(g)…
    • AdvancedCane sugar (sucrose) is hydrolysed in dilute hydrochloric acid at 298 K: C₁₂H₂₂O₁₁ + H₂O → C₆H₁₂O₆…
    • AdvancedA compound A in solution reacts by two paths at once, as many organic compounds do when one…

    Mathematics

    Questions

    • AdvancedThe figure shows the graph of a function f on [0, 12]. It is made of three straight pieces joining the points (0, 0), (3, 6), (9, 0) and (12, -3): a steep rise, a slow fall, and a dip below the axis. For 0 ≤ x ≤ 9 let F(x) = ∫xˣ⁺³ f(t) dt, the area under the graph over a window of width 3 that slides along the axis. The window catches the most area when its two ends are at the same height, but the peak of f need not sit in the middle of the window. What is the greatest value of F(x) for 0 ≤ x ≤ 9?
    • AdvancedThe figure shows the curve y = eˣ and its tangent at the point where x = s, for some s > 0. The curve bends upwards, so the tangent lies below it. The curve, the tangent and the y-axis enclose a region, shaded in the figure. Let A(s) be its area. For larger s the tangent crosses the y-axis below the origin, but the region is still bounded by the same three lines and curves. Find A(s) as a formula in s, and then check each statement. Which of the following statements are true?
    • AdvancedA function f is continuous on the whole real line and satisfies ∫₀ˣ f(t) dt = x f(x) - x² for every real x. Differentiating both sides turns this into a differential equation for f, but take care. The right side contains x f(x), so differentiating it needs f'(x), and you must first make sure that f is differentiable, at least for x ≠ 0. Also ask whether the equation says anything about the value of f at 0, where the factor x on the right side vanishes. Continuity of f at 0 may matter in the end. Which of the following statements are true?
    • AdvancedLet F(x) = ∫₀^(x²) sin√ t dt for every real x. The upper limit x² is the same for x and for -x, so F is an even function. Near t = 0 the integrand behaves like √ t, and that decides how fast F(x) goes to 0. Recall that √(x²) = |x|, not x, which matters as soon as x is negative. Two of the statements are about what happens very close to x = 0, from one side or from both sides, and one is about the sign of F far from 0. The substitution t = w² gives F in closed form, but most of the statements can be decided without it. Which of the following statements are true?
    • AdvancedFor every whole number n ≥ 0 let In = ∫₀¹ xⁿ eˣ dx. So I₀ = e - 1. Integration by parts, with xⁿ as the part to differentiate, links each In to the one before it. Then the values can be found one after another without integrating again, starting from I₀. Some of the statements below follow from that link; others need a comparison of the integrands, and one is about the size of In for large n. Decide about each statement on its own. Which of the following statements are true?
    More Mathematics questions for CUET UG →

    Problems with worked solutions

    • AdvancedA ranger in Cornwall is protecting a sand dune from walkers…
    • AdvancedLet f(x) = x³ + x. Since f'(x) = 3x² + 1 > 0, the function f increases on the whole real line, and…
    • AdvancedA definite integral is a limit of sums, and this works in both directions…
    • AdvancedSome definite integrals look impossible until a mirror is used…
    • Advanced

    Biology

    Problems with worked solutions

    • AdvancedA pea plant heterozygous for seed shape (round R over wrinkled r) and seed colour (yellow Y over…
    • AdvancedA woman is healthy. Her parents are healthy, and her brother has an autosomal recessive condition…
    • AdvancedIn the fruit fly Drosophila melanogaster, a female heterozygous for three genes (a⁺b⁺c⁺ on one…
    • AdvancedRed-green colour vision loss is X-linked and recessive…
    More Biology problems for CUET UG →
    • All 595 CUET UG problems →
    • All 752 CUET UG questions →
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    • Hard
    Cadmium(II) adds ammonia in four steps with log K = 2.6, 2.1, 1.4 and 0.9…
    More Chemistry problems for CUET UG →
    For x > 0 let F(x) = ∫x^(x²) ln t dt.. Both limits of this integral move with x…
    More Mathematics problems for CUET UG →