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!
Q. Which of the following is the correct dimension for pressure? (2021)
A.
M^1L^-1T^-2
B.
M^1L^1T^-2
C.
M^1L^0T^-2
D.
M^0L^1T^-1
Show solution
Solution
Pressure is defined as force per unit area, hence its dimension is M^1L^-1T^-2.
Correct Answer:
A
— M^1L^-1T^-2
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Q. Which of the following is the correct dimension for velocity? (2021)
A.
M^1L^1T^-1
B.
M^0L^1T^-1
C.
M^1L^0T^-1
D.
M^1L^1T^0
Show solution
Solution
The dimension of velocity is M^0L^1T^-1.
Correct Answer:
B
— M^0L^1T^-1
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Q. Which of the following is the correct dimensional formula for acceleration? (2022)
A.
[M^0 L^1 T^-2]
B.
[M^1 L^0 T^-2]
C.
[M^1 L^1 T^-1]
D.
[M^0 L^0 T^-2]
Show solution
Solution
Acceleration is defined as the change in velocity per unit time, so its dimensional formula is [M^0 L^1 T^-2].
Correct Answer:
A
— [M^0 L^1 T^-2]
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Q. Which of the following is the correct dimensional formula for electric charge?
A.
[M^1 L^2 T^-3 A^-1]
B.
[M^0 L^0 T^0 A^1]
C.
[M^0 L^1 T^-2 A^1]
D.
[M^1 L^1 T^-2 A^-1]
Show solution
Solution
The dimensional formula for electric charge is [M^1 L^2 T^-3 A^-1], derived from the definition of current.
Correct Answer:
A
— [M^1 L^2 T^-3 A^-1]
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Q. Which of the following is the correct dimensional formula for energy? (2023)
A.
[M^1 L^2 T^-2]
B.
[M^1 L^1 T^-1]
C.
[M^0 L^2 T^-1]
D.
[M^2 L^1 T^-2]
Show solution
Solution
Energy has the dimensional formula [M^1 L^2 T^-2], as it is defined as work done, which is force times distance.
Correct Answer:
A
— [M^1 L^2 T^-2]
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Q. Which of the following is the correct dimensional formula for frequency? (2021)
A.
[M^0 L^0 T^-1]
B.
[M^0 L^1 T^-1]
C.
[M^1 L^0 T^-1]
D.
[M^0 L^0 T^1]
Show solution
Solution
Frequency has the dimensional formula [M^0 L^0 T^-1].
Correct Answer:
A
— [M^0 L^0 T^-1]
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Q. Which of the following is the correct direct speech for: 'She told me that she would help me.'?
A.
She said, I will help you.
B.
She said, I would help you.
C.
She said, I am helping you.
D.
She said, I help you.
Show solution
Solution
The correct direct speech form is 'I will help you' as it reflects the future intention.
Correct Answer:
A
— She said, I will help you.
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Q. Which of the following is the correct expansion of (x - 3)²?
A.
x² - 6x + 9
B.
x² + 6x + 9
C.
x² - 9
D.
x² - 3
Show solution
Solution
(x - 3)² = x² - 2(3)x + 3² = x² - 6x + 9.
Correct Answer:
A
— x² - 6x + 9
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Q. Which of the following is the correct expansion of (x - y)³?
A.
x³ - 3x²y + 3xy² - y³
B.
x³ - y³
C.
x³ - 3xy² + 3x²y - y³
D.
3x²y - 3xy²
Show solution
Solution
(x - y)³ = x³ - 3x²y + 3xy² - y³ by the binomial theorem.
Correct Answer:
A
— x³ - 3x²y + 3xy² - y³
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Q. Which of the following is the correct expression for gravitational potential energy (U) of an object of mass m at a height h? (2020)
A.
mgh
B.
mg/h
C.
mgh^2
D.
m^2gh
Show solution
Solution
The gravitational potential energy is given by U = mgh, where h is the height above the reference point.
Correct Answer:
A
— mgh
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Q. Which of the following is the correct expression for the van der Waals equation?
A.
(P + a(n/V)^2)(V - nb) = nRT
B.
(P - a(n/V)^2)(V + nb) = nRT
C.
PV = nRT + a(n/V)^2
D.
PV = nRT - nb
Show solution
Solution
The van der Waals equation is (P + a(n/V)^2)(V - nb) = nRT.
Correct Answer:
A
— (P + a(n/V)^2)(V - nb) = nRT
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Q. Which of the following is the correct factorization of a² - b²?
A.
(a + b)(a - b)
B.
(a - b)(a - b)
C.
(a + b)(a + b)
D.
a² - 2ab + b²
Show solution
Solution
a² - b² = (a + b)(a - b) by the difference of squares identity.
Correct Answer:
A
— (a + b)(a - b)
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Q. Which of the following is the correct factorization of the quadratic equation x^2 - 5x + 6?
A.
(x - 2)(x - 3)
B.
(x + 2)(x + 3)
C.
(x - 1)(x - 6)
D.
(x + 1)(x + 6)
Show solution
Solution
The quadratic x^2 - 5x + 6 factors to (x - 2)(x - 3).
Correct Answer:
A
— (x - 2)(x - 3)
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Q. Which of the following is the correct factorization of the quadratic expression x^2 - 5x + 6?
A.
(x - 2)(x - 3)
B.
(x + 2)(x + 3)
C.
(x - 1)(x - 6)
D.
(x + 1)(x + 6)
Show solution
Solution
The expression factors to (x - 2)(x - 3) since -2 and -3 are the roots.
Correct Answer:
A
— (x - 2)(x - 3)
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Q. Which of the following is the correct factorization of x^2 + 10x + 21?
A.
(x + 3)(x + 7)
B.
(x + 1)(x + 21)
C.
(x + 2)(x + 10)
D.
(x + 5)(x + 5)
Show solution
Solution
To factor x^2 + 10x + 21, we look for two numbers that multiply to 21 and add to 10, which are 3 and 7. Thus, it factors to (x + 3)(x + 7).
Correct Answer:
A
— (x + 3)(x + 7)
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Q. Which of the following is the correct factorization of x² + 10x + 25?
A.
(x + 5)²
B.
(x + 10)(x + 5)
C.
(x - 5)(x + 5)
D.
(x + 25)(x + 1)
Show solution
Solution
x² + 10x + 25 = (x + 5)².
Correct Answer:
A
— (x + 5)²
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Q. Which of the following is the correct factorization of x² + 6x + 9?
A.
(x + 3)²
B.
(x + 2)(x + 4)
C.
(x + 1)(x + 8)
D.
(x + 3)(x + 3)
Show solution
Solution
x² + 6x + 9 is a perfect square trinomial, which factors to (x + 3)².
Correct Answer:
A
— (x + 3)²
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Q. Which of the following is the correct factorization of x² - 16?
A.
(x - 4)(x + 4)
B.
(x - 8)(x + 2)
C.
(x + 8)(x - 2)
D.
(x - 2)(x + 2)
Show solution
Solution
x² - 16 = (x - 4)(x + 4) (Difference of squares)
Correct Answer:
A
— (x - 4)(x + 4)
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Q. Which of the following is the correct factorization of x² - 9x + 20?
A.
(x - 4)(x - 5)
B.
(x + 4)(x + 5)
C.
(x - 2)(x - 10)
D.
(x - 5)(x + 4)
Show solution
Solution
x² - 9x + 20 = (x - 4)(x - 5) by finding two numbers that multiply to 20 and add to -9.
Correct Answer:
A
— (x - 4)(x - 5)
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Q. Which of the following is the correct formula for ethyne?
A.
C2H2
B.
C2H4
C.
C2H6
D.
C2H8
Show solution
Solution
Ethyne, also known as acetylene, has the formula C2H2, which indicates it is an alkyne.
Correct Answer:
A
— C2H2
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Q. Which of the following is the correct formula for the sine of a sum?
A.
sin(a + b) = sin(a) + sin(b)
B.
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
C.
sin(a + b) = sin(a)sin(b)
D.
sin(a + b) = cos(a) + cos(b)
Show solution
Solution
The sine of a sum is given by sin(a + b) = sin(a)cos(b) + cos(a)sin(b).
Correct Answer:
B
— sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
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Q. Which of the following is the correct identity for (a - b)(a + b)? (2019)
A.
a² + b²
B.
a² - b²
C.
ab
D.
a - b
Show solution
Solution
(a - b)(a + b) = a² - b² by the difference of squares formula.
Correct Answer:
B
— a² - b²
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Q. Which of the following is the correct identity for (a - b)²?
A.
a² - 2ab + b²
B.
a² + 2ab + b²
C.
a² - b²
D.
2a² - 2b²
Show solution
Solution
(a - b)² = a² - 2ab + b² by the expansion of the square of a binomial.
Correct Answer:
A
— a² - 2ab + b²
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Q. Which of the following is the correct identity for (x + y + z)³?
A.
x³ + y³ + z³ + 3(x + y)(y + z)(z + x)
B.
x³ + y³ + z³ + 3xyz
C.
x³ + y³ + z³ + 3xy + 3yz + 3zx
D.
x³ + y³ + z³ - 3xyz
Show solution
Solution
(x + y + z)³ = x³ + y³ + z³ + 3xyz.
Correct Answer:
B
— x³ + y³ + z³ + 3xyz
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Q. Which of the following is the correct identity for (x + y)³?
A.
x³ + y³ + 3xy(x + y)
B.
x³ + y³ - 3xy(x + y)
C.
x³ + y³ + 3xy²
D.
x³ - y³
Show solution
Solution
(x + y)³ = x³ + y³ + 3xy(x + y) by the binomial expansion.
Correct Answer:
A
— x³ + y³ + 3xy(x + y)
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Q. Which of the following is the correct identity for sin(2A)?
A.
2sinAcosA
B.
sin^2A + cos^2A
C.
sinA + cosA
D.
sinAcosA
Show solution
Solution
The double angle formula states that sin(2A) = 2sinAcosA.
Correct Answer:
A
— 2sinAcosA
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Q. Which of the following is the correct indirect speech for: 'He said, I will call you tomorrow.'?
A.
He said that he would call me the next day.
B.
He said that he will call me tomorrow.
C.
He said he called me tomorrow.
D.
He said he is calling me tomorrow.
Show solution
Solution
In indirect speech, 'will' changes to 'would' and 'tomorrow' changes to 'the next day'.
Correct Answer:
A
— He said that he would call me the next day.
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Q. Which of the following is the correct indirect speech for: 'John said, I can help you.'?
A.
John said that he could help me.
B.
John said that he can help me.
C.
John said that he will help me.
D.
John said that he helps me.
Show solution
Solution
In indirect speech, 'can' changes to 'could'.
Correct Answer:
A
— John said that he could help me.
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Q. Which of the following is the correct indirect speech for: 'She asked, Where are you going?'?
A.
She asked where I was going.
B.
She asked where I am going.
C.
She asked where I will go.
D.
She asked where I go.
Show solution
Solution
In indirect speech, 'are' changes to 'was'.
Correct Answer:
A
— She asked where I was going.
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Q. Which of the following is the correct indirect speech for: 'She exclaimed, What a beautiful day!'?
A.
She exclaimed that it was a beautiful day.
B.
She exclaimed that it is a beautiful day.
C.
She exclaimed that it was a beautiful days.
D.
She exclaimed that it was beautiful day.
Show solution
Solution
In indirect speech, the exclamatory sentence is reported with 'that' and the tense changes accordingly.
Correct Answer:
A
— She exclaimed that it was a beautiful day.
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