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JEE Advanced Mathematics 2027 Free

JEE Advanced Mock Test 1 (Paper 1 shape)

JEE Advanced mock test 1 in the Paper 1 shape: 3 hours, multi-concept questions, with the marking scheme disclosed at the start as the real exam does.

54Questions
180Minutes
197Marks
-1 Negative
11-12Grades

About this test

JEE Advanced Mock Test 1 (Paper 1 shape) is a full 54-question paper you attempt online in 180 minutes. It follows the Joint Entrance Examination Advanced pattern, so the timing, the question style and the marking match the real exam. Marks are banded: Q1 score 4 and lose 1 if wrong; Q2 score 4 and lose 2 if wrong; Q3 score 4 and lose 1 if wrong; Q4 score 3 with no penalty; Q5 score 4 and lose 1 if wrong; Q6 score 4 and lose 2 if wrong; Q7 score 3 with no penalty; Q8 score 4 and lose 1 if wrong; Q9 score 3 with no penalty; Q10 score 4 and lose 1 if wrong; Q11 score 4 and lose 2 if wrong; Q12 score 3 with no penalty; Q13 score 4 and lose 1 if wrong; Q14 score 3 with no penalty; Q15 score 4 and lose 1 if wrong; Q16 score 4 and lose 2 if wrong; Q17 score 3 with no penalty; Q18-19 score 4 and lose 1 if wrong; Q20 score 4 and lose 2 if wrong; Q21 score 3 with no penalty; Q22 score 4 and lose 1 if wrong; Q23 score 4 and lose 2 if wrong; Q24 score 4 and lose 1 if wrong; Q25 score 3 with no penalty; Q26 score 4 and lose 1 if wrong; Q27 score 4 and lose 2 if wrong; Q28 score 3 with no penalty; Q29 score 4 and lose 1 if wrong; Q30 score 3 with no penalty; Q31 score 4 and lose 1 if wrong; Q32 score 4 and lose 2 if wrong; Q33 score 4 and lose 1 if wrong; Q34 score 3 with no penalty; Q35 score 4 and lose 1 if wrong; Q36 score 3 with no penalty; Q37 score 4 and lose 1 if wrong; Q38 score 4 and lose 2 if wrong; Q39 score 3 with no penalty; Q40 score 4 and lose 1 if wrong; Q41 score 3 with no penalty; Q42 score 4 and lose 2 if wrong; Q43 score 4 and lose 1 if wrong; Q44 score 3 with no penalty; Q45 score 4 and lose 1 if wrong; Q46 score 4 and lose 2 if wrong; Q47 score 3 with no penalty; Q48 score 4 and lose 1 if wrong; Q49 score 3 with no penalty; Q50 score 4 and lose 1 if wrong; Q51 score 4 and lose 2 if wrong; Q52 score 3 with no penalty; Q53 score 4 and lose 1 if wrong; and Q54 score 3 with no penalty. Guessing carries a real cost, exactly as it does on the day.

You get your score the moment you submit, question by question, with a step-by-step solution to every problem. Two papers, mixed question types, partial marking.

What it covers

Rotational + energy SHM + springs Electromagnetic induction Electrostatics + capacitance Thermodynamics Modern physics Optics Current electricity Rotational dynamics Waves + Doppler Gravitation Kinematics (relative motion) Magnetism Nuclear physics Fluid mechanics Semiconductors Collisions Dimensional analysis Chemical bonding Electrochemistry Chemical kinetics Coordination chemistry Organic - mechanism Mole concept + stoichiometry Solid state Periodic properties Ionic equilibrium Organic - aromatic Atomic structure p-block Organic - isomerism Surface chemistry Solutions - colligative d-block Equilibrium Functional equations Quadratic + roots Definite integration Application of derivatives Complex numbers Matrices Probability Sequences and series Coordinate geometry - circles Vectors Limits Differential equations Binomial theorem Trigonometry Continuity and differentiability 3D geometry Permutations Area under curves

Sections

  • Physics — 18 questions
  • Chemistry — 18 questions
  • Mathematics — 18 questions

Difficulty spread

  • 54 hard questions

Before you start

Pattern. One paper of 3 hours, in the shape of JEE Advanced Paper 1. Physics, Chemistry and Mathematics sections, with single-correct, multiple-correct, numerical and matching questions.

Marking scheme for this paper: +4 / -1 for single-correct; +4 with partial credit and -2 for multiple-correct; +3 / 0 for numerical.

Why the scheme changes between papers. JEE Advanced does not publish its marking scheme in advance. The official brochure states only that negative marks may be awarded for some questions, and that the details appear in the question paper itself. The organising IIT sets the rules each year and reveals them on screen on exam day. Read the scheme above before you begin and set your attempt threshold accordingly β€” that habit is worth more marks than any single topic.

Before you start. Phone in another room, single screen, no reference material, full three hours in one sitting. Remember that the real examination is two such papers on one day, and appearing in both is compulsory.

A look at the questions

Q1. A uniform solid cylinder of mass $M$ and radius $R$ rolls without slipping down an incline of angle $\theta$. After descending a vertical height $h$ from rest, the speed of its centre of mass is:
A) $\sqrt{2gh}$
B) $\sqrt{\dfrac{4gh}{3}}$
C) $\sqrt{\dfrac{10gh}{7}}$
D) $\sqrt{\dfrac{6gh}{5}}$
Q2.

A block of mass $m$ is connected to two identical springs of stiffness $k$, one on each side, both horizontal and initially unstretched. Which statements are correct for small horizontal oscillations?

One or more options are correct. Partial credit applies; any incorrect selection scores βˆ’2.

A) The effective stiffness is $2k$
B) The time period is $2\pi\sqrt{\dfrac{m}{2k}}$
C) The motion is simple harmonic
D) The time period is $2\pi\sqrt{\dfrac{2m}{k}}$
52 more questions in the full paper, each with a worked solution.

Questions people ask

What is the marking scheme for this paper?

+4 / -1 for single-correct; +4 with partial credit and -2 for multiple-correct; +3 / 0 for numerical. It is disclosed here because the real examination discloses its own scheme on the day rather than in advance.

How long is the paper?

Three hours, matching one real JEE Advanced paper. The actual exam is two such papers on a single day and appearing in both is compulsory.

What does this paper focus on?

Full syllabus - baseline diagnostic.

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