Q. In an arithmetic progression, if the 2nd term is 10 and the 4th term is 14, what is the first term? (2023)
Show solution
Solution
Let the first term be a and the common difference be d. From the equations a + d = 10 and a + 3d = 14, we can solve for a and find it to be 8.
Correct Answer:
B
— 8
Learn More →
Q. In an arithmetic progression, if the 2nd term is 8 and the 4th term is 14, what is the 1st term?
Show solution
Solution
Let the first term be a and the common difference be d. From the equations a + d = 8 and a + 3d = 14, solving gives a = 6.
Correct Answer:
A
— 6
Learn More →
Q. In an arithmetic progression, if the 3rd term is 12 and the 7th term is 24, what is the common difference?
Show solution
Solution
Let the first term be a and the common difference be d. From the equations a + 2d = 12 and a + 6d = 24, we can find d = 3.
Correct Answer:
C
— 4
Learn More →
Q. In an arithmetic progression, if the 3rd term is 15 and the 6th term is 24, what is the common difference?
Show solution
Solution
Let the first term be a and the common difference be d. From the equations a + 2d = 15 and a + 5d = 24, we can solve for d, which gives d = 3.
Correct Answer:
B
— 4
Learn More →
Q. In an arithmetic progression, if the 4th term is 20 and the 7th term is 26, what is the first term?
Show solution
Solution
Let the first term be a and the common difference be d. From the equations a + 3d = 20 and a + 6d = 26, we can solve for a and find it to be 12.
Correct Answer:
B
— 12
Learn More →
Q. In an arithmetic progression, if the 5th term is 20 and the 10th term is 35, what is the first term?
Show solution
Solution
Let the first term be a and the common difference be d. From the given terms, we have a + 4d = 20 and a + 9d = 35. Solving these gives a = 10.
Correct Answer:
B
— 10
Learn More →
Q. In an arithmetic progression, if the first term is 10 and the common difference is 5, what is the sum of the first 8 terms?
A.
120
B.
130
C.
140
D.
150
Show solution
Solution
The sum of the first n terms is given by S_n = n/2 * (2a + (n-1)d). Here, S_8 = 8/2 * (20 + 35) = 4 * 55 = 220.
Correct Answer:
C
— 140
Learn More →
Q. In an arithmetic progression, if the first term is 12 and the last term is 48, and there are 10 terms, what is the common difference?
Show solution
Solution
Using the formula for the last term, 48 = 12 + (10-1)d. Solving gives d = 4.
Correct Answer:
A
— 4
Learn More →
Q. In an arithmetic progression, if the first term is 4 and the last term is 40, and there are 10 terms, what is the common difference?
Show solution
Solution
Using the nth term formula, we have 40 = 4 + (10-1)d. Solving gives d = 4.
Correct Answer:
B
— 5
Learn More →
Q. In an arithmetic progression, if the first term is 5 and the common difference is 3, what is the 10th term?
Show solution
Solution
The nth term of an AP is given by a + (n-1)d. Here, a = 5, d = 3, and n = 10. So, the 10th term = 5 + (10-1) * 3 = 5 + 27 = 32.
Correct Answer:
A
— 32
Learn More →
Q. In an arithmetic progression, if the first term is 7 and the common difference is -2, what is the 6th term?
Show solution
Solution
Using the nth term formula, a + (n-1)d = 7 + 5*(-2) = 7 - 10 = -3.
Correct Answer:
A
— -1
Learn More →
Q. In an arithmetic progression, if the sum of the first 10 terms is 100, what is the first term if the common difference is 2?
Show solution
Solution
Using the formula S_n = n/2 * (2a + (n-1)d), we have 100 = 10/2 * (2a + 9*2). Solving gives a = 10.
Correct Answer:
B
— 10
Learn More →
Q. In an arithmetic progression, if the sum of the first 10 terms is 250, what is the first term if the common difference is 5?
Show solution
Solution
Using the formula S_n = n/2 * (2a + (n-1)d), we can substitute n = 10 and d = 5 to find a = 20.
Correct Answer:
B
— 20
Learn More →
Q. In an arithmetic progression, if the sum of the first 5 terms is 50 and the first term is 5, what is the common difference?
Show solution
Solution
Using the sum formula S_n = n/2 * (2a + (n-1)d), we have 50 = 5/2 * (10 + 4d). Solving gives d = 7.
Correct Answer:
C
— 7
Learn More →
Q. In an arithmetic progression, if the sum of the first 5 terms is 50, what is the first term if the common difference is 2?
Show solution
Solution
Using the sum formula S_n = n/2 * (2a + (n-1)d), we have 50 = 5/2 * (2a + 8). Solving gives a = 10.
Correct Answer:
C
— 10
Learn More →
Q. In an arithmetic progression, if the sum of the first 5 terms is 50, what is the value of the first term if the common difference is 2?
Show solution
Solution
The sum of the first n terms is given by S_n = n/2 * (2a + (n-1)d). Here, 50 = 5/2 * (2a + 8). Solving gives a = 10.
Correct Answer:
B
— 10
Learn More →
Q. In an arithmetic series, if the first term is 5 and the last term is 45, and there are 10 terms, what is the common difference?
Show solution
Solution
Using the formula for the nth term: a_n = a + (n-1)d, we have 45 = 5 + 9d. Solving gives d = 4.
Correct Answer:
A
— 4
Learn More →
Q. In an ecosystem, which of the following organisms is known as a primary consumer? (2019)
A.
Herbivores
B.
Carnivores
C.
Decomposers
D.
Producers
Show solution
Solution
Herbivores are primary consumers as they feed directly on producers (plants).
Correct Answer:
A
— Herbivores
Learn More →
Q. In an ecosystem, which of the following organisms is known as a primary producer? (2021)
A.
Herbivores
B.
Carnivores
C.
Decomposers
D.
Plants
Show solution
Solution
Plants are primary producers as they convert sunlight into chemical energy through photosynthesis.
Correct Answer:
D
— Plants
Learn More →
Q. In an electric circuit, if the voltage is 12 V and the current is 3 A, what is the power?
A.
36 W
B.
9 W
C.
4 W
D.
12 W
Show solution
Solution
Power in an electric circuit is given by P = V * I. Here, P = 12 V * 3 A = 36 W.
Correct Answer:
A
— 36 W
Learn More →
Q. In an electric circuit, if the voltage is doubled while the resistance remains constant, what happens to the power?
A.
It remains the same
B.
It doubles
C.
It quadruples
D.
It halves
Show solution
Solution
Power in an electric circuit is given by P = V^2/R. If V is doubled, P becomes (2V)^2/R = 4V^2/R, which is quadrupled.
Correct Answer:
C
— It quadruples
Learn More →
Q. In an electrochemical cell, the anode is where: (2019)
A.
Oxidation occurs
B.
Reduction occurs
C.
Electrons are gained
D.
Ions are produced
Show solution
Solution
In an electrochemical cell, oxidation occurs at the anode.
Correct Answer:
A
— Oxidation occurs
Learn More →
Q. In an endothermic reaction, the enthalpy of the products is ____ than that of the reactants.
A.
higher
B.
lower
C.
equal
D.
unpredictable
Show solution
Solution
In an endothermic reaction, the enthalpy of the products is higher than that of the reactants.
Correct Answer:
A
— higher
Learn More →
Q. In an experiment, a student measures the mass of an object as 200 g with an uncertainty of ±5 g. What is the range of possible values for the mass?
A.
195 g to 205 g
B.
200 g to 210 g
C.
195 g to 210 g
D.
200 g to 205 g
Show solution
Solution
Range = Measured value ± Uncertainty = 200 g ± 5 g = 195 g to 205 g.
Correct Answer:
A
— 195 g to 205 g
Learn More →
Q. In an experiment, the length of a rod is measured as 12.0 m with an uncertainty of ±0.5 m. What is the total uncertainty if the length is used in a calculation involving multiplication by 3?
A.
±1.5 m
B.
±0.5 m
C.
±0.75 m
D.
±0.25 m
Show solution
Solution
Total uncertainty = 3 * (0.5 m) = ±1.5 m.
Correct Answer:
A
— ±1.5 m
Learn More →
Q. In an experiment, the mass of an object is measured as 5.0 kg with an uncertainty of ±0.2 kg. What is the absolute error?
A.
0.2 kg
B.
0.5 kg
C.
0.1 kg
D.
0.3 kg
Show solution
Solution
Absolute error is the uncertainty in the measurement, which is ±0.2 kg.
Correct Answer:
A
— 0.2 kg
Learn More →
Q. In an experiment, the measured value of a voltage is 12.0 V with an uncertainty of ±0.2 V. What is the maximum possible error?
A.
0.2 V
B.
0.1 V
C.
0.5 V
D.
0.0 V
Show solution
Solution
Maximum possible error is equal to the uncertainty, which is ±0.2 V.
Correct Answer:
A
— 0.2 V
Learn More →
Q. In an experiment, the voltage is measured as 12.0 V with an uncertainty of ±0.3 V. What is the absolute error in the voltage measurement?
A.
0.3 V
B.
0.25 V
C.
0.5 V
D.
0.1 V
Show solution
Solution
The absolute error is given as ±0.3 V.
Correct Answer:
A
— 0.3 V
Learn More →
Q. In an experiment, the voltage is measured as 12.0 V with an uncertainty of ±0.5 V. What is the maximum possible error in the voltage measurement?
A.
0.5 V
B.
0.25 V
C.
1 V
D.
0.1 V
Show solution
Solution
The maximum possible error is the absolute uncertainty, which is ±0.5 V.
Correct Answer:
A
— 0.5 V
Learn More →
Q. In an experiment, the voltage is measured as 12.0 V with an uncertainty of ±0.5 V. What is the absolute error in the voltage measurement?
A.
0.5 V
B.
0.05 V
C.
5 V
D.
1 V
Show solution
Solution
The absolute error is given directly as ±0.5 V.
Correct Answer:
A
— 0.5 V
Learn More →
Showing 15241 to 15270 of 31669 (1056 Pages)
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!