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JEE MAIN 2019 – Reworked Practice Paper Date & Shift: 12th April 2019 – Morning Session (Shift 1) Mode: Computer-Based Test (CBT) 📚 For: B.E. / B.Tech Aspirants 🧠 Subjects: Physics | Chemistry | Mathematics 🔢 Total Questions: 90 ( With Answers & Concepts ) ✍ Prepared & Rewritten by: Hope Zilper™ Academic Content Creator | Docsity Seller 📧 hopezilper@gmail.com 🔒 Authenticated & Watermarked This material is 100% original, rewritten for safe resale & digital distribution. Unauthorized copying or reposting is strictly prohibited. “Original work, created to help students revise and succeed.”
Question 1 Two vectors have magnitudes 3 and 5 units respectively. If the angle between them is 60°, what is the magnitude of their resultant? Options: (A) 7 (B) \sqrt{37} (C) 4 (D) 6 ✅ Answer: (B) \sqrt{37} 📌 Tip: Use the vector addition formula involving cosine of the angle. 🔸 Question 2 Which among the following compounds exhibits aromaticity? Options: (A) Cyclooctatetraene (B) Cyclopentadienyl anion (C) Cyclobutadiene (D) Cycloheptatrienyl cation ✅ Answer: (B) Cyclopentadienyl anion
📌 Tip: Use the Balmer series formula: \frac{1}{\lambda} = R\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right) 🔸 Question 5 Let f(x) = x^2 + 1. The area under the curve from x = 0 to x = 2 is: Options: (A) \frac{10}{3} (B) \frac{8}{3} (C) \frac{14}{3} (D) \frac{16}{3} ✅ Answer: (C) \frac{14}{3} 📌 Concept: Area under curve = definite integral of f(x) from 0 to 2. 🔸 Question 6 Which of the following is not a property of electromagnetic waves? Options: (A) They are transverse waves (B) They require a medium (C) They travel at the speed of light (D) They can be polarized ✅ Answer: (B) They require a medium
📌 Key Point: EM waves do not need a medium to travel. 🔸 Question 7 What is the value of the determinant: \left| \begin{matrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \ \end{matrix} \right| Options: (A) 0 (B) 1 (C) 3 (D) 6 ✅ Answer: (A) 0 📌 Shortcut: Rows are in arithmetic progression → determinant is zero. 🔸 Question 8 Which of the following shows the maximum number of lone pairs on the central atom? Options: (A) \text{NH}_ (B) \text{H}2\text{O} (C) \text{XeF}
✅ Answer: (C) 6 cm 📌 Apply: Mirror equation \frac{1}{f} = \frac{1}{v} - \frac{1}{u} Question 11 Which of the following complex ions is colorless? Options: (A) [ \text{Ti(H}_2\text{O})_6 ]^{3+} (B) [ \text{Zn(H}_2\text{O})_6 ]^{2+} (C) [ \text{Fe(H}_2\text{O})_6 ]^{2+} (D) [ \text{Cr(H}_2\text{O})_6 ]^{3+} ✅ Answer: (B) [ \text{Zn(H}_2\text{O})6 ]^{2+} 📌 Concept: Zn²⁺ has fully filled d-orbitals → no d–d transition → colorless. 🔸 Question 12 Evaluate the limit: \lim{x \to 0} \frac{e^{2x} - 1}{x} Options: (A) 1 (B) 2 (C) 0
(D) e^ ✅ Answer: (B) 2 📌 Trick: Differentiate numerator and denominator using L’Hospital’s Rule. 🔸 Question 13 Which of these molecules has the highest dipole moment? Options: (A) CO₂ (B) BF₃ (C) NH₃ (D) CCl₄ ✅ Answer: (C) NH₃ 📌 Reasoning: All others are symmetrical → net dipole cancels out. 🔸 Question 14 What is the integral of \frac{1}{x^2 + 1} with respect to x? Options: (A) \arctan(x) + C (B) \ln(x^2 + 1) + C (C) \arcsin(x) + C (D) \ln|x - 1| + C
🔸 Question 17 Find the derivative of x \sin x. Options: (A) x \cos x + \sin x (B) x \cos x (C) \cos x + x \sin x (D) x \sin x + \cos x ✅ Answer: (A) x \cos x + \sin x 📌 Use: Product rule of differentiation. 🔸 Question 18 A spring has a spring constant k = 200 , \text{N/m} and is compressed by 0.1 m. What is the stored potential energy? Options: (A) 1 J (B) 0.5 J (C) 2 J (D) 5 J ✅ Answer: (B) 0.5 J 📌 Formula: U = \frac{ 1 }{ 2 } k x^ 2 🔸 Question 19
Which of the following is not a greenhouse gas? Options: (A) CO₂ (B) CH₄ (C) N₂ (D) O₃ ✅ Answer: (C) N₂ 📌 Explanation: N₂ does not absorb IR radiation — hence not a greenhouse gas. 🔸 Question 20 What is the general solution of the differential equation: \frac{dy}{dx} = y Options: (A) y = e^x (B) y = ce^x (C) y = \ln x (D) y = x \ln x ✅ Answer: (B) y = ce^x 📌 Concept: Standard exponential growth equation. 🔸 Question 21
Options: (A) \text{C}^2 \cdot \text{N}^{-1} \cdot \text{m}^{-2} (B) \text{N} \cdot \text{m}^2/\text{C}^ (C) \text{F/m} (D) \text{C/m} ✅ Answer: (C) \text{F/m} 📌 Note: Farad per meter is standard SI unit for permittivity. ⸻ 🔸 Question 24 Which functional group is present in aspirin? Options: (A) Aldehyde (B) Ketone (C) Ester (D) Ether ✅ Answer: (C) Ester 📌 Structure: Aspirin = acetylsalicylic acid → contains ester linkage. ⸻ 🔸 Question 25
Find the slope of the tangent to the curve y = \ln(x^2 + 1) at x = 1. Options: (A) \frac{2}{2} (B) \frac{1}{1} (C) \frac{2}{2} (D) \frac{2}{x^2 + 1} ✅ Answer: (A) \frac{2}{2} = 1 📌 Use: Differentiate using chain rule. ⸻ 🔸 Question 26 Which law explains the pressure difference across a curved liquid surface? Options: (A) Bernoulli’s Law (B) Pascal’s Law (C) Laplace’s Law (D) Hooke’s Law ✅ Answer: (C) Laplace’s Law 📌 Used in: Surface tension and capillarity contexts. ⸻
🔸 Question 29 A particle is projected vertically upward with speed u. At its highest point, the velocity is: Options: (A) u (B) 0 (C) −u (D) g ✅ Answer: (B) 0 📌 Concept: Vertical velocity becomes zero at maximum height. ⸻ 🔸 Question 30 Which among the following shows geometrical isomerism? Options: (A) 1-butene (B) But- 2 - ene (C) Propene (D) Ethane ✅ Answer: (B) But- 2 - ene
📌 Reason: It has different groups on both sides of double bond → cis-trans forms. ⸻ 🔸 Question 31 Find the integral: \int x \cdot \ln x , dx Options: (A) \frac{x^2 \ln x}{2} - \frac{x^2}{4} + C (B) \frac{x^2}{2} \ln x + C (C) x \ln x - x + C (D) x^2 \ln x + C ✅ Answer: (A) 📌 Apply: Integration by parts. ⸻ 🔸 Question 32 Which of the following is not a colligative property? Options: (A) Boiling point elevation (B) Osmotic pressure (C) Surface tension
(B) (-2, 2)
(C) (-\infty, - 2] \cup [2, \infty) (D) [-2, 2] ✅ Answer: (C) 📌 Reason: The expression under root must be ≥ 0. ⸻ 🔸 Question 35 What is the equivalent resistance when three 6-ohm resistors are connected in parallel? Options: (A) 2 Ω (B) 18 Ω (C) 6 Ω (D) 1 Ω ✅ Answer: (A) 2 Ω 📌 Formula: R_{eq} = \frac{R}{n} when all resistors are equal. ⸻ 🔸 Question 36 Which of the following compounds is most acidic?
Options: (A) Ethanol (B) Phenol (C) Water (D) Acetic acid ✅ Answer: (D) Acetic acid 📌 Reason: Carboxylic acids are more acidic than alcohols and phenols. ⸻ 🔸 Question 37 Evaluate: \lim_{x \to \infty} \frac{2x^2 + 3}{x^2 + 5} Options: (A) 1 (B) 2 (C) 0 (D) ∞ ✅ Answer: (B) 2 📌 Strategy: Divide numerator and denominator by x^ 2. ⸻ 🔸 Question 38
