JEE Main Preparation Resources for Competitive Exams

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JEE Main MCQ & Objective Questions

The JEE Main exam is a crucial step for students aspiring to enter prestigious engineering colleges in India. It tests not only knowledge but also the ability to apply concepts effectively. Practicing MCQs and objective questions is essential for scoring better, as it helps in familiarizing students with the exam pattern and enhances their problem-solving skills. Engaging with practice questions allows students to identify important questions and strengthen their exam preparation.

What You Will Practise Here

Fundamental concepts of Physics, Chemistry, and Mathematics
Key formulas and their applications in problem-solving
Important definitions and theories relevant to JEE Main
Diagrams and graphical representations for better understanding
Numerical problems and their step-by-step solutions
Previous years' JEE Main questions for real exam experience
Time management strategies while solving MCQs

Exam Relevance

The topics covered in JEE Main are not only significant for the JEE exam but also appear in various CBSE and State Board examinations. Many concepts are shared with the NEET syllabus, making them relevant across multiple competitive exams. Common question patterns include conceptual applications, numerical problems, and theoretical questions that assess a student's understanding of core subjects.

Common Mistakes Students Make

Misinterpreting the question stem, leading to incorrect answers
Neglecting units in numerical problems, which can change the outcome
Overlooking negative marking and not managing time effectively
Relying too heavily on rote memorization instead of understanding concepts
Failing to review and analyze mistakes from practice tests

FAQs

Question: How can I improve my speed in solving JEE Main MCQ questions?
Answer: Regular practice with timed quizzes and focusing on shortcuts can significantly enhance your speed.

Question: Are the JEE Main objective questions similar to previous years' papers?
Answer: Yes, many questions are based on previous years' patterns, so practicing them can be beneficial.

Question: What is the best way to approach JEE Main practice questions?
Answer: Start with understanding the concepts, then attempt practice questions, and finally review your answers to learn from mistakes.

Now is the time to take charge of your preparation! Dive into solving JEE Main MCQs and practice questions to test your understanding and boost your confidence for the exam.

Chemistry Syllabus (JEE Main) Mathematics Syllabus (JEE Main) Physics Syllabus (JEE Main)

Q. If the data set has a mean of 30 and a standard deviation of 10, what is the z-score of a value 40?

A. 1
B. 0
C. 2
D. -1

Solution

Z-score = (X - Mean) / Standard Deviation = (40 - 30) / 10 = 1.

Correct Answer: C — 2

Q. If the data set has a mean of 30 and a standard deviation of 10, what is the z-score of the value 40?

A. 0
B. 1
C. 2
D. 3

Solution

Z-score = (X - Mean) / Standard Deviation = (40 - 30) / 10 = 1

Correct Answer: C — 2

Q. If the data set has a mean of 30 and a variance of 16, what is the standard deviation?

A. 4
B. 5
C. 6
D. 7

Solution

Standard Deviation = √Variance = √16 = 4.

Correct Answer: A — 4

Q. If the data set has a mean of 50 and a median of 45, what can be said about the data distribution?

A. Symmetric
B. Positively skewed
C. Negatively skewed
D. Uniform

Solution

Since the mean is greater than the median, the distribution is positively skewed.

Correct Answer: B — Positively skewed

Q. If the data set has a mean of 50 and a standard deviation of 10, what is the z-score of the value 70?

A. 1
B. 2
C. 3
D. 4

Solution

Z-score = (X - Mean) / Standard Deviation = (70 - 50) / 10 = 2.

Correct Answer: B — 2

Q. If the data set has a mean of 50 and a variance of 16, what is the standard deviation?

A. 2
B. 4
C. 8
D. 16

Solution

Standard Deviation = √Variance = √16 = 4.

Correct Answer: B — 4

Q. If the data set is 1, 2, 2, 3, 4, 4, 4, 5, what is the mode?

A. 2
B. 3
C. 4
D. 5

Solution

Mode = 4 (most frequent value).

Correct Answer: C — 4

Q. If the data set is 4, 4, 4, 5, 5, 6, what is the mode?

A. 4
B. 5
C. 6
D. None

Solution

Mode = 4 (most frequent value).

Correct Answer: A — 4

Q. If the data set is {5, 7, 7, 8, 10}, what is the mode?

A. 5
B. 7
C. 8
D. 10

Solution

Mode = 7 (most frequently occurring value).

Correct Answer: B — 7

Q. If the data set is {5, 7, 8, 9, 10}, what is the interquartile range?

A. 2
B. 3
C. 4
D. 5

Solution

Q1 = 7, Q3 = 9; Interquartile Range = Q3 - Q1 = 9 - 7 = 2.

Correct Answer: B — 3

Q. If the data set is {5, 7, 8, 9, 10}, what is the standard deviation?

A. 1.58
B. 2.58
C. 3.58
D. 4.58

Solution

Mean = 7.8. Variance = [(5-7.8)² + (7-7.8)² + (8-7.8)² + (9-7.8)² + (10-7.8)²]/5 = 2.5. Standard Deviation = √2.5 ≈ 1.58.

Correct Answer: A — 1.58

Q. If the data set is: 3, 7, 7, 19, what is the median?

A. 7
B. 10
C. 11
D. 12

Solution

Median = (7 + 7) / 2 = 7.

Correct Answer: A — 7

Q. If the data set is: 5, 7, 8, 9, 10, what is the median?

A. 7
B. 8
C. 9
D. 10

Solution

Median is the middle value. Here, the middle values are 7 and 8, so Median = (7+8)/2 = 7.5.

Correct Answer: B — 8

Q. If the data set {1, 2, 3, 4, 5} is transformed to {2, 3, 4, 5, 6}, what happens to the standard deviation?

A. Increases
B. Decreases
C. Remains the same
D. Cannot be determined

Solution

The standard deviation remains the same because the transformation is a shift.

Correct Answer: C — Remains the same

Q. If the data set {10, 20, 30, 40, 50} is transformed to {x + 5}, what happens to the standard deviation?

A. Increases
B. Decreases
C. Remains the same
D. Cannot be determined

Solution

Standard deviation remains the same as adding a constant does not affect dispersion.

Correct Answer: C — Remains the same

Q. If the data set {3, 7, 8, 12, 14} has a median of 8, what is the first quartile?

A. 3
B. 7
C. 8
D. 12

Solution

Q1 is the median of the first half of the data set {3, 7}, which is 7.

Correct Answer: B — 7

Q. If the data set {3, 7, 8, 12, 14} is given, what is the median?

A. 8
B. 7
C. 12
D. 10

Solution

Median is the middle value, which is 8.

Correct Answer: A — 8

Q. If the data set {5, 7, 8, 9, 10} has a mean of 7.8, what is the sum of the deviations from the mean?

A. 0
B. 1
C. 2
D. 3

Solution

The sum of deviations from the mean is always 0.

Correct Answer: A — 0

Q. If the density of a substance is calculated as 8.0 g/cm³ with an uncertainty of ±0.2 g/cm³, what is the relative uncertainty?

A. 0.025
B. 0.02
C. 0.005
D. 0.01

Solution

Relative uncertainty = (absolute uncertainty / density) = 0.2 / 8.0 = 0.025.

Correct Answer: B — 0.02

Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.5 g/cm³, what is the range of possible values for the density?

A. 7.5 to 8.5 g/cm³
B. 8.0 to 8.5 g/cm³
C. 8.0 to 9.0 g/cm³
D. 7.0 to 9.0 g/cm³

Solution

Range = (8.0 - 0.5) to (8.0 + 0.5) = 7.5 to 8.5 g/cm³.

Correct Answer: A — 7.5 to 8.5 g/cm³

Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.1 g/cm³, what is the absolute error in the density?

A. 0.1 g/cm³
B. 0.01 g/cm³
C. 0.5 g/cm³
D. 0.2 g/cm³

Solution

The absolute error is given directly as ±0.1 g/cm³.

Correct Answer: A — 0.1 g/cm³

Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.1 g/cm³, what is the fractional error in the density?

A. 0.0125
B. 0.01
C. 0.005
D. 0.02

Solution

Fractional error = (absolute error / measured value) = 0.1 / 8.0 = 0.0125.

Correct Answer: B — 0.01

Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.2 g/cm³, what is the absolute error in the volume calculated from this density?

A. 0.025 cm³
B. 0.1 cm³
C. 0.2 cm³
D. 0.5 cm³

Solution

Volume = mass/density; if mass is constant, the absolute error in volume = (mass * absolute error in density) / (density²).

Correct Answer: A — 0.025 cm³

Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.2 g/cm³, what is the relative uncertainty in the density?

A. 0.025
B. 0.02
C. 0.005
D. 0.1

Solution

Relative uncertainty = (absolute uncertainty / measured value) = 0.2 / 8.0 = 0.025.

Correct Answer: B — 0.02

Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.2 g/cm³, what is the range of possible densities?

A. 7.8 to 8.2 g/cm³
B. 7.5 to 8.5 g/cm³
C. 8.0 to 8.4 g/cm³
D. 8.0 to 8.2 g/cm³

Solution

Range = 8.0 ± 0.2 gives 7.8 to 8.2 g/cm³.

Correct Answer: A — 7.8 to 8.2 g/cm³

Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.1 g/cm³, what is the relative uncertainty in the density?

A. 0.0125
B. 0.01
C. 0.005
D. 0.02

Solution

Relative uncertainty = (absolute uncertainty / measured value) = 0.1 / 8.0 = 0.0125.

Correct Answer: B — 0.01

Q. If the determinant | x 2 | | 3 4 | = 0, find x.

A. 1
B. 2
C. 3
D. 4

Solution

Setting the determinant to zero gives x*4 - 2*3 = 0, thus x = 1.5.

Correct Answer: B — 2

Q. If the directrix of a parabola is given by the equation y = -p, what is the equation of the parabola?

A. y^2 = 4px
B. x^2 = 4py
C. y^2 = -4px
D. x^2 = -4py

Solution

The equation of a parabola with directrix y = -p is y^2 = -4px.

Correct Answer: C — y^2 = -4px

Q. If the distance between the object and the image formed by a lens is 70 cm, and the object distance is 30 cm, what is the image distance?

A. 40 cm
B. 50 cm
C. 60 cm
D. 70 cm

Solution

Image distance (v) = Object distance (u) + Distance between object and image = 30 cm + 70 cm = 40 cm.

Correct Answer: A — 40 cm

Q. If the distance between the plates of a capacitor is doubled, what happens to its capacitance?

A. It doubles
B. It halves
C. It remains the same
D. It quadruples

Solution

Capacitance is inversely proportional to the distance between the plates. If the distance d is doubled, the capacitance C becomes C/2.

Correct Answer: B — It halves

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