JEE Advanced Mixed Practice Set 1
Pattern-based JEE Advanced practice with a mix of physics, chemistry, and mathematics questions.
Exam Pattern & Rules
Negative Marking: May apply for some questions
Note: Both papers are compulsory. Pattern is not fixed in the same way as JEE Main.
Practice Set Details
JEE Advanced Mixed Practice Set 1: all 6 questions with answers
Try each question first, then open “Show answer” to check the correct option and explanation.
Q1.If sinθ = 3/5 and θ is acute, what is cosθ?
- A.4/5
- B.3/4
- C.5/3
- D.1/5
Show answer
Correct answer: A. 4/5
For an acute angle, cosθ = √(1 − sin²θ) = √(1 − 9/25) = 4/5.
Q2.Which compound is the conjugate base of acetic acid?
- A.CH3COOH
- B.CH3COO−
- C.HCO3−
- D.CH3CHO
Show answer
Correct answer: B. CH3COO−
The conjugate base of acetic acid is the acetate ion CH3COO−.
Q3.A particle moves with displacement x = 2t² − 5t + 3. What is its acceleration?
- A.4 m/s²
- B.−5 m/s²
- C.4t − 5
- D.2 m/s²
Show answer
Correct answer: A. 4 m/s²
Acceleration is the second derivative of displacement: d²x/dt² = 4.
Q4.Which of these matrices is singular?
- A.[[1,0],[0,1]]
- B.[[1,2],[2,4]]
- C.[[2,0],[0,2]]
- D.[[0,1],[1,0]]
Show answer
Correct answer: B. [[1,2],[2,4]]
The determinant of [[1,2],[2,4]] is 1×4 − 2×2 = 0, so it is singular.
Q5.If a solution has pH 3, its hydrogen ion concentration is 10⁻³ M. What is its hydroxide ion concentration?
- A.10⁻¹ M
- B.10⁻³ M
- C.10⁻¹¹ M
- D.10⁻⁷ M
Show answer
Correct answer: C. 10⁻¹¹ M
Kw = 10⁻¹⁴, so [OH−] = 10⁻¹¹ M.
Q6.A circle has radius 5. What is the length of an arc subtended by a 60° angle?
- A.(5π)/3
- B.(π)/3
- C.(10π)/3
- D.(5π)/6
Show answer
Correct answer: A. (5π)/3
Arc length = θ (in radians) × r = (π/3) × 5 = 5π/3.