Major Competitive Exams

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Major Competitive Exams

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Major Competitive Exams MCQ & Objective Questions

Major Competitive Exams play a crucial role in shaping the academic and professional futures of students in India. These exams not only assess knowledge but also test problem-solving skills and time management. Practicing MCQs and objective questions is essential for scoring better, as they help in familiarizing students with the exam format and identifying important questions that frequently appear in tests.

What You Will Practise Here

Key concepts and theories related to major subjects
Important formulas and their applications
Definitions of critical terms and terminologies
Diagrams and illustrations to enhance understanding
Practice questions that mirror actual exam patterns
Strategies for solving objective questions efficiently
Time management techniques for competitive exams

Exam Relevance

The topics covered under Major Competitive Exams are integral to various examinations such as CBSE, State Boards, NEET, and JEE. Students can expect to encounter a mix of conceptual and application-based questions that require a solid understanding of the subjects. Common question patterns include multiple-choice questions that test both knowledge and analytical skills, making it essential to be well-prepared with practice MCQs.

Common Mistakes Students Make

Rushing through questions without reading them carefully
Overlooking the negative marking scheme in MCQs
Confusing similar concepts or terms
Neglecting to review previous years’ question papers
Failing to manage time effectively during the exam

FAQs

Question: How can I improve my performance in Major Competitive Exams?
Answer: Regular practice of MCQs and understanding key concepts will significantly enhance your performance.

Question: What types of questions should I focus on for these exams?
Answer: Concentrate on important Major Competitive Exams questions that frequently appear in past papers and mock tests.

Question: Are there specific strategies for tackling objective questions?
Answer: Yes, practicing under timed conditions and reviewing mistakes can help develop effective strategies.

Start your journey towards success by solving practice MCQs today! Test your understanding and build confidence for your upcoming exams. Remember, consistent practice is the key to mastering Major Competitive Exams!

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Q. If two charges of +2 µC and -2 µC are placed 1 m apart, what is the net electric field at the midpoint? (2023)

A. 0 N/C
B. 4 N/C
C. 2 N/C
D. 8 N/C

Solution

The electric fields due to both charges at the midpoint cancel each other out, resulting in a net electric field of 0 N/C.

Correct Answer: A — 0 N/C

Q. If two charges of +3μC and +5μC are placed 0.3m apart, what is the magnitude of the force between them?

A. 0.15 N
B. 0.25 N
C. 0.45 N
D. 0.75 N

Solution

Using Coulomb's law, F = k * |q1 * q2| / r² = (9 × 10^9 N m²/C²) * |(3 × 10^-6 C) * (5 × 10^-6 C)| / (0.3 m)² = 0.45 N.

Correct Answer: C — 0.45 N

Q. If two charges of +3μC and -3μC are placed 0.1m apart, what is the net electric field at the midpoint?

A. 0 N/C
B. 54000 N/C
C. 27000 N/C
D. 81000 N/C

Solution

The electric fields due to both charges at the midpoint cancel each other out, resulting in a net electric field of 0 N/C.

Correct Answer: A — 0 N/C

Q. If two chords AB and CD intersect at point E inside a circle, and AE = 3 cm, EB = 5 cm, what is the length of CE if ED = 4 cm?

A. 6
B. 8
C. 12
D. 10

Solution

Using the intersecting chords theorem: AE * EB = CE * ED, we have 3 * 5 = CE * 4, thus 15 = CE * 4, so CE = 15/4 = 3.75, which rounds to 4.

Correct Answer: A — 6

Q. If two chords AB and CD intersect at point E inside a circle, and AE = 3, EB = 5, CE = 4, what is the length of ED?

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

Solution

Using the intersecting chords theorem: AE * EB = CE * ED. Thus, 3 * 5 = 4 * ED, so 15 = 4 * ED, giving ED = 15/4 = 3.75.

Correct Answer: A — 2

Q. If two chords intersect inside a circle and the lengths of the segments are 3 cm and 4 cm for one chord, and 2 cm and x cm for the other, what is the value of x?

A. 5
B. 6
C. 7
D. 8

Solution

Using the intersecting chords theorem: 3 * 4 = 2 * x, so 12 = 2x, thus x = 6.

Correct Answer: B — 6

Q. If two chords intersect inside a circle, and the lengths of the segments of one chord are 4 cm and 6 cm, what is the length of the other chord if its segments are x cm and y cm?

A. 10
B. 12
C. 14
D. 16

Solution

Using the intersecting chords theorem: 4 * 6 = x * y. If x + y = 10, then x = 4 and y = 6.

Correct Answer: C — 14

Q. If two circles intersect at points A and B, and the distance between their centers is 10 cm, what is the maximum possible radius of each circle? (2021)

A. 5 cm
B. 10 cm
C. 15 cm
D. 20 cm

Solution

The maximum radius of each circle can be half the distance between the centers, which is 10 cm.

Correct Answer: B — 10 cm

Q. If two circles intersect at two points, what can be said about their centers?

A. They are the same.
B. They are equidistant from the intersection points.
C. They lie on the same line.
D. They are at a fixed distance apart.

Solution

The centers of two intersecting circles are equidistant from the points of intersection.

Correct Answer: B — They are equidistant from the intersection points.

Q. If two circles intersect at two points, what can be said about their relationship?

A. They are concentric.
B. They are tangent to each other.
C. They are secant to each other.
D. They do not intersect.

Solution

Circles that intersect at two points are said to be secant to each other.

Correct Answer: C — They are secant to each other.

Q. If two circles intersect at two points, which of the following statements is true? (2021)

A. The centers of the circles are equidistant from the intersection points.
B. The line joining the centers of the circles passes through the intersection points.
C. The circles are tangent to each other.
D. The area of intersection is always a triangle.

Solution

The centers of the circles are equidistant from the intersection points, making option 0 true.

Correct Answer: A — The centers of the circles are equidistant from the intersection points.

Q. If two coherent sources of light are in phase, what type of interference pattern will be observed?

A. No interference pattern
B. Destructive interference
C. Constructive interference
D. Random interference

Solution

When two coherent sources are in phase, they produce constructive interference, resulting in bright fringes.

Correct Answer: C — Constructive interference

Q. If two coherent sources of light are in phase, what type of interference will occur?

A. Destructive interference
B. Constructive interference
C. No interference
D. Random interference

Solution

When two coherent sources are in phase, they produce constructive interference, resulting in bright fringes.

Correct Answer: B — Constructive interference

Q. If two coherent sources of light are in phase, what will be the phase difference at a point where the path difference is λ/4?

A. 0 radians
B. π/2 radians
C. π radians
D. 3π/2 radians

Solution

The phase difference (Δφ) is given by (2π/λ) * path difference. For a path difference of λ/4, Δφ = (2π/λ) * (λ/4) = π/2 radians.

Correct Answer: B — π/2 radians

Q. If two coherent sources of light are in phase, what will be the phase difference at a point where the path difference is λ/2?

A. 0 radians
B. π/2 radians
C. π radians
D. 2π radians

Solution

A path difference of λ/2 corresponds to a phase difference of π radians, leading to destructive interference.

Correct Answer: C — π radians

Q. If two coherent sources of light are in phase, what will be the result at a point where the path difference is λ/2?

A. Constructive interference
B. Destructive interference
C. No interference
D. Partial interference

Solution

A path difference of λ/2 results in destructive interference, as the waves will be out of phase.

Correct Answer: B — Destructive interference

Q. If two coins are tossed, what is the probability of getting at least one head?

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

Solution

Total outcomes = 4 (HH, HT, TH, TT). At least one head = 3 outcomes. Probability = 3/4.

Correct Answer: C — 3/4

Q. If two coins are tossed, what is the probability of getting at least one tail? (2023)

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

Solution

The possible outcomes are HH, HT, TH, TT. The outcomes with at least one tail are HT, TH, TT (3 outcomes). So, the probability is 3/4.

Correct Answer: C — 3/4

Q. If two dice are rolled, what is the probability of getting a sum of 7?

A. 1/6
B. 1/12
C. 1/36
D. 1/18

Solution

Possible combinations for sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 combinations. Total outcomes = 36. Probability = 6/36 = 1/6.

Correct Answer: A — 1/6

Q. If two dice are rolled, what is the probability that the sum is 7?

A. 1/6
B. 1/12
C. 1/36
D. 5/36

Solution

Possible combinations for sum 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 combinations. Total outcomes = 36. Probability = 6/36 = 1/6.

Correct Answer: D — 5/36

Q. If two dice are rolled, what is the probability that the sum is greater than 10?

A. 1/12
B. 1/6
C. 1/8
D. 1/4

Solution

The combinations for a sum greater than 10 are (5,6), (6,5), (6,6), giving a probability of 3/36 = 1/12.

Correct Answer: B — 1/6

Q. If two dice are rolled, what is the probability that the sum of the numbers on the dice is 7?

A. 1/6
B. 1/12
C. 1/36
D. 5/36

Solution

The combinations that give a sum of 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1), totaling 6 combinations. The total outcomes are 36, so the probability is 6/36 = 1/6.

Correct Answer: A — 1/6

Q. If two equal and opposite forces are applied at the ends of a lever arm of length 1 m, what is the net torque about the center?

A. 0 Nm
B. 1 Nm
C. 2 Nm
D. 4 Nm

Solution

The net torque is zero because the forces are equal and opposite, producing no rotational effect.

Correct Answer: A — 0 Nm

Q. If two equal and opposite forces are applied at the ends of a lever arm of length 4 m, what is the net torque about the center?

A. 0 Nm
B. 8 Nm
C. 4 Nm
D. 16 Nm

Solution

The net torque is zero because the forces are equal and opposite, resulting in no rotational effect.

Correct Answer: A — 0 Nm

Q. If two equal and opposite forces are applied at the ends of a lever arm, what is the net torque about the center?

A. Zero
B. Equal to the force
C. Depends on the distance
D. Twice the force

Solution

The net torque is zero because the forces are equal and opposite, producing no rotational effect.

Correct Answer: A — Zero

Q. If two forces of 10 N and 15 N act in the same direction on an object, what is the resultant force?

A. 5 N
B. 10 N
C. 15 N
D. 25 N

Solution

The resultant force is the sum of the two forces: 10 N + 15 N = 25 N.

Correct Answer: D — 25 N

Q. If two forces of 10 N and 15 N act on an object in the same direction, what is the net force acting on the object?

A. 5 N
B. 10 N
C. 15 N
D. 25 N

Solution

Net force = 10 N + 15 N = 25 N.

Correct Answer: D — 25 N

Q. If two forces of 10 N and 5 N act in the same direction on an object, what is the net force?

A. 15 N
B. 5 N
C. 10 N
D. 20 N

Solution

The net force is the sum of the forces: 10 N + 5 N = 15 N.

Correct Answer: A — 15 N

Q. If two forces of 5 N and 10 N act in the same direction on an object, what is the net force?

A. 15 N
B. 5 N
C. 10 N
D. 0 N

Solution

Net force = 5 N + 10 N = 15 N.

Correct Answer: A — 15 N

Q. If two forces of 5 N and 10 N are applied at the same distance from a pivot, which force produces more torque?

A. 5 N
B. 10 N
C. Both produce the same torque
D. It depends on the angle of application

Solution

Torque is directly proportional to the force applied; hence, the 10 N force produces more torque.

Correct Answer: B — 10 N

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