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Physics · Mechanics · JEE Main level
1. A block of mass 2 kg is pushed against a vertical wall by a horizontal force of 50 N. The coefficient of static friction between block and wall is 0.4. Taking g = 10 m/s², what is the friction force acting on the block?
Answer: A. First decide whether the block is moving. The weight pulling it down is mg = 20 N. The maximum friction available is μN = 0.4 × 50 = 20 N. Since the maximum available (20 N) is not less than the weight (20 N), the block does not slide, so friction is static and takes whatever value balances the weight — 20 N, directed upward. The common error is to answer 20 N by computing μN and accidentally getting the right number for the wrong reason, or to pick 8 N by using the weight instead of the normal force in μN.
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Physics · Modern physics · NEET level
2. Light of wavelength 400 nm falls on a metal whose work function is 2.0 eV. Taking hc = 1240 eV·nm, the maximum kinetic energy of the emitted photoelectrons is approximately
Answer: B. Photon energy E = hc/λ = 1240 / 400 = 3.1 eV. Einstein's equation gives KEmax = E − φ = 3.1 − 2.0 = 1.1 eV. Option C is the photon energy itself, which is the trap; option D adds instead of subtracting. Memorise hc = 1240 eV·nm — it turns this whole chapter into one-line arithmetic.
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Physics · Current electricity · JEE Main level
3. A wire of resistance R is stretched uniformly until its length is doubled. Its new resistance is
Answer: C. Stretching conserves volume: if the length doubles, the cross-sectional area halves. R = ρL/A, so doubling L and halving A multiplies the resistance by four. In general, stretching to n times the length gives n²R. This single result is examined almost every year in some form.
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Chemistry · Mole concept · JEE Main level
4. How many grams of oxygen are required for the complete combustion of 4.4 g of propane (C₃H₈)? (C = 12, H = 1, O = 16)
Answer: C. Balance first: C₃H₈ + 5O₂ → 3CO₂ + 4H₂O. Moles of propane = 4.4 / 44 = 0.1. The equation needs 5 moles of O₂ per mole of propane, so 0.5 mol of O₂ is required, which is 0.5 × 32 = 16 g. Nearly every mistake on this question is a failure to balance the equation before starting the arithmetic.
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Chemistry · General Organic Chemistry · JEE level
5. Which of the following carbocations is the most stable?
Answer: C. Stability rises with the number of alkyl groups donating electron density by hyperconjugation and the inductive effect: primary < secondary < tertiary. The tertiary butyl cation has nine hyperconjugative structures and is the most stable of these four. The allyl cation in D is resonance-stabilised and is more stable than a primary cation, but not more than a tertiary one — that comparison is the point of the question.
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Chemistry · Coordination compounds · NEET and JEE
6. What is the oxidation state of chromium in the complex [Cr(H₂O)₄Cl₂]Cl?
Answer: C. Water is neutral, each chloride is −1, and the complex ion must balance the one chloride outside the square brackets, so the complex ion carries +1. Therefore x + 0 + (2 × −1) = +1, giving x = +3. The commonest error is to forget the chloride outside the brackets and answer +2.
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Mathematics · Quadratic equations · JEE Main level
7. If the roots of x² − px + q = 0 differ by 1, then which relation holds?
Answer: A. Let the roots be α and β. Then α + β = p and αβ = q. The difference satisfies (α − β)² = (α + β)² − 4αβ = p² − 4q. If the roots differ by 1, then (α − β)² = 1, so p² − 4q = 1, that is p² = 4q + 1. This identity — the square of the difference equals the square of the sum minus four times the product — is worth having automatic.
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Mathematics · Calculus · JEE Main level
8. The value of the definite integral of sin²x from 0 to π/2 is
Answer: B. Use sin²x = (1 − cos 2x)/2. The integral becomes ½∫₀^{π/2}(1 − cos 2x)dx = ½[x − (sin 2x)/2]₀^{π/2} = ½[(π/2 − 0) − (0 − 0)] = π/4. Alternatively, use the symmetry result that the integrals of sin²x and cos²x over 0 to π/2 are equal and together add to π/2, so each is π/4 — a one-line method worth knowing under time pressure.
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Mathematics · Probability · JEE Main level
9. Two fair dice are thrown. Given that the sum is 8, what is the probability that both dice show the same number?
Answer: A. This is conditional probability, and the trap is to use 36 as the denominator. The outcomes giving a sum of 8 are (2,6), (3,5), (4,4), (5,3), (6,2) — five of them. Exactly one of those, (4,4), has both dice equal. So the answer is 1/5. Whenever a question says 'given that', reduce the sample space first and only then count.
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Biology · Molecular basis of inheritance · NEET level
10. In the Meselson–Stahl experiment, after one round of replication in ¹⁴N medium, DNA originally labelled with ¹⁵N showed
Answer: C. After a single replication every molecule has one heavy parental strand and one light new strand, so all the DNA is hybrid and forms a single intermediate band. This result rules out conservative replication, which would have given two bands (option D) after the first generation. The distinction between semi-conservative and dispersive replication appears only at the second generation.
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Biology · Human physiology · NEET level
11. Which of the following is the main site of absorption of digested food in humans?
Answer: C. Most chemical digestion is completed in the duodenum, but the bulk of absorption occurs in the jejunum and ileum, whose villi and microvilli create an enormous surface area. The stomach absorbs very little (some water, alcohol and certain drugs) and the large intestine chiefly absorbs water and some minerals. NEET regularly tests the difference between where digestion happens and where absorption happens.
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Biology · Plant physiology · NEET level
12. In C₄ plants, the initial fixation of carbon dioxide takes place in the
Answer: B. In the C₄ pathway, CO₂ is first fixed in the mesophyll by PEP carboxylase, which has no oxygenase activity, producing a four-carbon acid. That acid moves to the bundle sheath cells, where it releases CO₂ for RuBisCO in an environment of high CO₂ concentration — which is precisely how C₄ plants avoid photorespiration. The Kranz anatomy that makes this possible is examined just as often as the biochemistry.
