Q. If a sequence is defined as a_n = 3n + 1, what is the value of a_7? (2023)
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Solution
Substituting n = 7 into the formula gives a_7 = 3(7) + 1 = 21 + 1 = 22.
Correct Answer:
A
— 22
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Q. If a sequence is defined as a_n = 3n + 2, what is the value of a_5?
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Solution
Substituting n = 5 into the equation gives a_5 = 3(5) + 2 = 15 + 2 = 17.
Correct Answer:
B
— 17
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Q. If a sequence is defined by the formula a_n = 3n + 2, what is the value of a_7? (2023)
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Solution
Substituting n = 7 into the formula gives a_7 = 3(7) + 2 = 21 + 2 = 23.
Correct Answer:
A
— 23
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Q. If a student can choose 2 subjects from 5 available subjects, how many different combinations can be made?
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Solution
The number of ways to choose 2 subjects from 5 is given by 5C2 = 10.
Correct Answer:
A
— 10
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Q. If a student can choose 2 subjects from 5 available subjects, how many different combinations of subjects can be chosen?
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Solution
The number of ways to choose 2 subjects from 5 is 5C2 = 10.
Correct Answer:
A
— 10
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Q. If a team of 4 is to be selected from 10 players, how many different teams can be formed?
A.
210
B.
120
C.
300
D.
150
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Solution
The number of ways to choose 4 players from 10 is given by 10C4 = 210.
Correct Answer:
A
— 210
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Q. If a team of 4 is to be selected from 8 players, how many different teams can be formed?
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Solution
The number of ways to choose 4 players from 8 is given by 8C4 = 70.
Correct Answer:
B
— 56
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Q. If a team of 5 is to be selected from 10 players, how many different teams can be formed?
A.
252
B.
120
C.
210
D.
300
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Solution
The number of ways to choose 5 players from 10 is given by 10C5 = 252.
Correct Answer:
A
— 252
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Q. If set A = {1, 2, 3, 4} and set B = {3, 4, 5, 6}, what is the difference A - B?
A.
{1, 2}
B.
{3, 4}
C.
{5, 6}
D.
{}
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Solution
The difference A - B includes elements in A that are not in B, which are {1, 2}.
Correct Answer:
A
— {1, 2}
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Q. If set A = {1, 2, 3, 4} and set B = {3, 4, 5, 6}, what is the intersection of sets A and B? (2023)
A.
{1, 2}
B.
{3, 4}
C.
{5, 6}
D.
{1, 2, 5, 6}
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Solution
The intersection of sets A and B includes the elements that are common to both sets. Therefore, the intersection is {3, 4}.
Correct Answer:
B
— {3, 4}
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Q. If set A = {1, 2, 3} and set B = {2, 3, 4}, what is A - B? (2023)
A.
{1}
B.
{2, 3}
C.
{3, 4}
D.
{}
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Solution
A - B represents the elements in A that are not in B. Thus, A - B = {1}.
Correct Answer:
A
— {1}
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Q. If set A = {x | x is an even number less than 10} and set B = {x | x is a prime number less than 10}, what is A ∩ B?
A.
{2, 4, 6, 8}
B.
{2}
C.
{2, 3, 5, 7}
D.
{2, 3, 5, 7, 4, 6, 8}
Show solution
Solution
The intersection A ∩ B includes elements that are both even and prime, which is {2}.
Correct Answer:
B
— {2}
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Q. If set A contains the elements {1, 2, 3, 4} and set B contains the elements {3, 4, 5, 6}, what is the intersection of sets A and B?
A.
{1, 2}
B.
{3, 4}
C.
{5, 6}
D.
{1, 2, 3, 4, 5, 6}
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Solution
The intersection of sets A and B is the set of elements that are common to both sets. Therefore, the intersection is {3, 4}.
Correct Answer:
B
— {3, 4}
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Q. If set A contains the numbers {1, 2, 3, 4, 5} and set B contains the numbers {4, 5, 6, 7, 8}, what is the intersection of sets A and B?
A.
{1, 2, 3}
B.
{4, 5}
C.
{6, 7, 8}
D.
{1, 2, 3, 4, 5, 6, 7, 8}
Show solution
Solution
The intersection of sets A and B is the set of elements that are common to both sets, which is {4, 5}.
Correct Answer:
B
— {4, 5}
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Q. If set C = {x | x is a multiple of 3 and less than 30}, how many elements are in set C?
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Solution
The multiples of 3 less than 30 are {3, 6, 9, 12, 15, 18, 21, 24, 27}, totaling 9 elements.
Correct Answer:
B
— 9
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Q. If set P = {1, 2, 3, 4} and set Q = {3, 4, 5, 6}, what is the difference P - Q?
A.
{1, 2}
B.
{3, 4}
C.
{5, 6}
D.
{1, 2, 5, 6}
Show solution
Solution
The difference P - Q includes elements in P that are not in Q, which is {1, 2}.
Correct Answer:
A
— {1, 2}
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Q. If set P = {x | x is an even number less than 10} and set Q = {x | x is a prime number less than 10}, what is the union of sets P and Q?
A.
{2, 3, 4, 5, 6, 8}
B.
{2, 3, 5, 7}
C.
{2, 4, 6, 8}
D.
{2, 3, 4, 5, 7, 8}
Show solution
Solution
Set P = {2, 4, 6, 8} and set Q = {2, 3, 5, 7}. The union is {2, 3, 4, 5, 6, 7, 8}.
Correct Answer:
D
— {2, 3, 4, 5, 7, 8}
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Q. If set P = {x | x is an even number less than 10} and set Q = {x | x is a prime number less than 10}, what is P ∩ Q?
A.
{2, 4, 6, 8}
B.
{2, 3, 5, 7}
C.
{2}
D.
{4, 6, 8}
Show solution
Solution
The intersection P ∩ Q includes only the even prime number, which is {2}.
Correct Answer:
C
— {2}
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Q. If set P = {x | x is an even number less than 10} and set Q = {x | x is a prime number less than 10}, what is the difference P - Q?
A.
{2, 4, 6, 8}
B.
{4, 6, 8}
C.
{2, 6, 8}
D.
{2, 4, 6, 8, 3, 5, 7}
Show solution
Solution
Set P = {2, 4, 6, 8} and set Q = {2, 3, 5, 7}. The difference P - Q = {4, 6, 8}.
Correct Answer:
B
— {4, 6, 8}
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Q. If set P = {x | x is an even number less than 10} and set Q = {x | x is a prime number less than 10}, what is the intersection of sets P and Q?
A.
{2, 4, 6, 8}
B.
{2, 3, 5, 7}
C.
{2}
D.
{4, 6, 8}
Show solution
Solution
The intersection of sets P and Q includes elements that are both even and prime. The only even prime number is 2.
Correct Answer:
C
— {2}
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Q. If set R = {1, 2, 3, 4, 5} and set S = {4, 5, 6, 7}, what is the symmetric difference of sets R and S?
A.
{1, 2, 3, 6, 7}
B.
{4, 5}
C.
{1, 2, 3, 4, 5, 6, 7}
D.
{6, 7}
Show solution
Solution
The symmetric difference of sets R and S includes elements that are in either set but not in both. Thus, it is {1, 2, 3, 6, 7}.
Correct Answer:
A
— {1, 2, 3, 6, 7}
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Q. If set R = {1, 2, 3, 4} and set S = {3, 4, 5, 6}, what is the difference R - S?
A.
{1, 2}
B.
{3, 4}
C.
{5, 6}
D.
{}
Show solution
Solution
The difference R - S includes elements in R that are not in S, which is {1, 2}.
Correct Answer:
A
— {1, 2}
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Q. If set R = {1, 2, 3, 4} and set S = {3, 4, 5, 6}, what is the symmetric difference of sets R and S?
A.
{1, 2, 5, 6}
B.
{3, 4}
C.
{1, 2, 3, 4, 5, 6}
D.
{3, 4, 5}
Show solution
Solution
The symmetric difference is the set of elements in either set R or set S but not in both, which is {1, 2, 5, 6}.
Correct Answer:
A
— {1, 2, 5, 6}
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Q. If set X = {a, b, c} and set Y = {b, c, d}, what is the union of sets X and Y?
A.
{a, b, c, d}
B.
{b, c}
C.
{a, b}
D.
{c, d}
Show solution
Solution
The union of sets X and Y includes all unique elements from both sets. Thus, the union is {a, b, c, d}.
Correct Answer:
A
— {a, b, c, d}
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Q. If the 3rd term of a geometric sequence is 12 and the common ratio is 2, what is the first term? (2023)
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Solution
The 3rd term is given by ar^2. So, 12 = a(2^2) => a = 12/4 = 3.
Correct Answer:
B
— 6
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Q. If the 3rd term of an arithmetic sequence is 12 and the 7th term is 24, what is the common difference? (2023)
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Solution
Let the first term be a and the common difference be d. Then, a + 2d = 12 and a + 6d = 24. Solving these gives d = 3.
Correct Answer:
B
— 3
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Q. If the Binomial Theorem is applied to (x + 1)^n, what is the sum of the coefficients of the expansion?
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Solution
The sum of the coefficients in the expansion of (x + 1)^n is found by substituting x = 1, which gives 2^n.
Correct Answer:
D
— 2^n
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Q. If the Binomial Theorem is applied to (x + 2)^3, what is the coefficient of x^2?
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Solution
The coefficient of x^2 in the expansion of (x + 2)^3 is given by C(3, 2) * 2^1 = 3 * 2 = 6.
Correct Answer:
C
— 12
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Q. If the Binomial Theorem is applied to (x + 2)^4, what is the term containing x^2?
A.
12x^2
B.
24x^2
C.
36x^2
D.
48x^2
Show solution
Solution
The term containing x^2 is C(4,2) * x^2 * 2^2 = 6 * x^2 * 4 = 24x^2.
Correct Answer:
B
— 24x^2
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Q. If the Binomial Theorem is applied to (x + y)^4, what is the term containing x^2y^2?
A.
6x^2y^2
B.
4x^2y^2
C.
8x^2y^2
D.
12x^2y^2
Show solution
Solution
The term containing x^2y^2 in the expansion of (x + y)^4 is given by 4C2 * x^2 * y^2 = 6x^2y^2.
Correct Answer:
A
— 6x^2y^2
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Showing 61 to 90 of 329 (11 Pages)
Modern Math MCQ & Objective Questions
Modern Math is a crucial component of the curriculum for students preparing for school and competitive exams in India. Mastering this subject not only enhances problem-solving skills but also boosts confidence during exams. Practicing MCQs and objective questions is essential for effective exam preparation, as they help identify important questions and clarify key concepts.
What You Will Practise Here
Sets, Relations, and Functions
Probability and Statistics
Linear Equations and Inequalities
Quadratic Equations and Functions
Mathematical Reasoning and Proofs
Sequences and Series
Graphs and their Interpretations
Exam Relevance
Modern Math is frequently tested in various examinations, including CBSE, State Boards, NEET, and JEE. Students can expect questions that assess their understanding of concepts through problem-solving and application. Common question patterns include multiple-choice questions that require students to select the correct answer from given options, as well as numerical problems that test their analytical skills.
Common Mistakes Students Make
Misinterpreting the question stem, leading to incorrect answers.
Overlooking the importance of units in probability and statistics.
Confusing different types of functions and their properties.
Neglecting to check for extraneous solutions in equations.
Failing to apply the correct formulas in problem-solving scenarios.
FAQs
Question: What are some effective strategies for solving Modern Math MCQs?Answer: Focus on understanding the concepts, practice regularly, and review previous years' question papers to familiarize yourself with common patterns.
Question: How can I improve my speed in answering objective questions?Answer: Regular practice with timed quizzes can help enhance your speed and accuracy in answering questions.
Start your journey towards mastering Modern Math today! Solve practice MCQs to test your understanding and reinforce your knowledge. Remember, consistent practice is key to success in your exams!
