Q. How many ways can 5 different letters be selected from the alphabet?
A.
26
B.
3003
C.
156
D.
120
Show solution
Solution
The number of ways to choose 5 letters from 26 is C(26, 5) = 65780.
Correct Answer:
B
— 3003
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Q. How many ways can 5 different prizes be awarded to 3 students?
A.
60
B.
100
C.
150
D.
200
Show solution
Solution
The number of ways to award 5 different prizes to 3 students is 3^5 = 243.
Correct Answer:
C
— 150
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Q. How many ways can 6 different books be arranged on a shelf if 2 specific books must be together?
A.
120
B.
720
C.
240
D.
480
Show solution
Solution
Treat the 2 specific books as one unit. Then we have 5 units to arrange: 5! * 2! = 240.
Correct Answer:
C
— 240
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Q. How many ways can 6 people be arranged in a circle?
A.
720
B.
120
C.
60
D.
30
Show solution
Solution
The number of arrangements in a circle is (n-1)! = (6-1)! = 5! = 120.
Correct Answer:
A
— 720
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Q. How many ways can 6 people be divided into 2 groups of 3?
Show solution
Solution
The number of ways to divide 6 people into 2 groups of 3 is (6! / (3!3!)) / 2 = 20.
Correct Answer:
A
— 20
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Q. How many ways can a committee of 3 be formed from 5 people?
Show solution
Solution
The number of ways to choose 3 from 5 is C(5,3) = 10.
Correct Answer:
A
— 10
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Q. How many ways can you arrange the letters of the word 'BANANA'?
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Solution
The word 'BANANA' has 6 letters with 'A' repeating 3 times and 'N' repeating 2 times. The arrangements are 6!/(3!2!) = 60.
Correct Answer:
B
— 30
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Q. How many ways can you choose 3 fruits from a basket of 5 different fruits?
Show solution
Solution
The number of ways to choose 3 fruits from 5 is given by 5C3 = 10.
Correct Answer:
A
— 10
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Q. How many ways can you form a committee of 3 from a group of 10 people?
A.
120
B.
90
C.
80
D.
100
Show solution
Solution
The number of ways to form a committee of 3 from 10 is given by 10C3 = 120.
Correct Answer:
A
— 120
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Q. How many ways can you select 2 fruits from 5 different fruits?
Show solution
Solution
The number of ways to choose 2 from 5 is given by 5C2 = 10.
Correct Answer:
A
— 10
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Q. How many ways can you select 2 students from a group of 8?
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Solution
The number of ways to select 2 students from 8 is given by 8C2 = 28.
Correct Answer:
A
— 28
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Q. Identify the family of curves represented by the equation x^2 + y^2 = r^2.
A.
Straight lines
B.
Ellipses
C.
Circles
D.
Hyperbolas
Show solution
Solution
The equation x^2 + y^2 = r^2 represents a family of circles with varying radii 'r'.
Correct Answer:
C
— Circles
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Q. Identify the family of curves represented by the equation y = a(x - h)^2 + k.
A.
Parabolas
B.
Circles
C.
Ellipses
D.
Hyperbolas
Show solution
Solution
The equation y = a(x - h)^2 + k represents a family of parabolas that open upwards or downwards.
Correct Answer:
A
— Parabolas
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Q. Identify the family of curves represented by the equation y = ax^2 + bx + c.
A.
Linear functions
B.
Quadratic functions
C.
Cubic functions
D.
Exponential functions
Show solution
Solution
The equation y = ax^2 + bx + c represents a family of quadratic functions with varying coefficients (a, b, c).
Correct Answer:
B
— Quadratic functions
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Q. Identify the family of curves represented by the equation y = a^x.
A.
Exponential functions
B.
Logarithmic functions
C.
Polynomial functions
D.
Trigonometric functions
Show solution
Solution
The equation y = a^x represents a family of exponential functions where a is a positive constant.
Correct Answer:
A
— Exponential functions
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Q. Identify the family of curves represented by the equation y = c/x, where c is a constant.
A.
Linear functions
B.
Hyperbolas
C.
Parabolas
D.
Circles
Show solution
Solution
The equation y = c/x represents a family of hyperbolas with varying asymptotes.
Correct Answer:
B
— Hyperbolas
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Q. Identify the family of curves represented by the equation y = e^(kx), where k is a constant.
A.
Linear functions
B.
Exponential functions
C.
Logarithmic functions
D.
Polynomial functions
Show solution
Solution
The equation y = e^(kx) represents a family of exponential functions with varying growth rates determined by k.
Correct Answer:
B
— Exponential functions
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Q. Identify the family of curves represented by the equation y = e^(kx).
A.
Linear functions
B.
Exponential functions
C.
Logarithmic functions
D.
Polynomial functions
Show solution
Solution
The equation y = e^(kx) represents a family of exponential functions with varying growth rates determined by 'k'.
Correct Answer:
B
— Exponential functions
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Q. Identify the family of curves represented by the equation y = mx^3 + c.
A.
Cubic functions
B.
Quadratic functions
C.
Linear functions
D.
Exponential functions
Show solution
Solution
The equation y = mx^3 + c represents a family of cubic functions with varying coefficients m and c.
Correct Answer:
A
— Cubic functions
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Q. Identify the family of curves represented by the equation y = sin(kx) for varying k.
A.
Sine waves
B.
Cosine waves
C.
Straight lines
D.
Parabolas
Show solution
Solution
The equation y = sin(kx) represents a family of sine waves with varying frequencies determined by k.
Correct Answer:
A
— Sine waves
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Q. Identify the family of curves represented by the equation y^2 = 4ax.
A.
Parabolas
B.
Hyperbolas
C.
Ellipses
D.
Straight lines
Show solution
Solution
The equation y^2 = 4ax represents a family of parabolas that open to the right with varying values of 'a'.
Correct Answer:
A
— Parabolas
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Q. If 2x + 3y = 12 and x + 2y = 10, what is the value of x?
Show solution
Solution
From the second equation, x = 10 - 2y. Substituting into the first gives 2(10 - 2y) + 3y = 12, solving gives y = 2, x = 6.
Correct Answer:
C
— 4
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Q. If 5x - 7 < 3, what is the range of x?
A.
x < 2
B.
x > 2
C.
x < 1
D.
x > 1
Show solution
Solution
5x - 7 < 3 => 5x < 10 => x < 2
Correct Answer:
A
— x < 2
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Q. If 5x - 7 < 3, what is the value of x?
A.
x < 2
B.
x > 2
C.
x < 1
D.
x > 1
Show solution
Solution
5x - 7 < 3 => 5x < 10 => x < 2
Correct Answer:
A
— x < 2
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Q. If 5x - 7 < 3x + 1, what is the range of x?
A.
x < 4
B.
x > 4
C.
x < 2
D.
x > 2
Show solution
Solution
5x - 7 < 3x + 1 => 2x < 8 => x < 4.
Correct Answer:
A
— x < 4
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Q. If 6x + 4 > 10, what is the value of x?
A.
x < 1
B.
x > 1
C.
x < 2
D.
x > 2
Show solution
Solution
6x + 4 > 10 => 6x > 6 => x > 1.
Correct Answer:
B
— x > 1
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Q. If 7 - 2x > 3, what is the value of x?
A.
x < 2
B.
x > 2
C.
x ≤ 2
D.
x ≥ 2
Show solution
Solution
7 - 2x > 3 => -2x > -4 => x < 2.
Correct Answer:
B
— x > 2
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Q. If 7 - 2x ≥ 1, what is the range of x?
A.
x ≤ 3
B.
x ≥ 3
C.
x < 3
D.
x > 3
Show solution
Solution
7 - 2x ≥ 1 => -2x ≥ -6 => x ≤ 3
Correct Answer:
B
— x ≥ 3
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Q. If 7 - 2x ≥ 3, what is the value of x?
A.
x ≤ 2
B.
x ≥ 2
C.
x < 2
D.
x > 2
Show solution
Solution
7 - 2x ≥ 3 => -2x ≥ -4 => x ≤ 2.
Correct Answer:
B
— x ≥ 2
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Q. If 7 - 3x ≤ 1, what is the value of x?
A.
x ≤ 2
B.
x ≥ 2
C.
x < 2
D.
x > 2
Show solution
Solution
7 - 3x ≤ 1 => -3x ≤ -6 => x ≥ 2.
Correct Answer:
B
— x ≥ 2
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Showing 991 to 1020 of 2847 (95 Pages)
Mathematics Syllabus (JEE Main) MCQ & Objective Questions
The Mathematics Syllabus for JEE Main is crucial for students aiming to excel in competitive exams. Understanding this syllabus not only helps in grasping key concepts but also enhances your ability to tackle objective questions effectively. Practicing MCQs and important questions from this syllabus is essential for solid exam preparation, ensuring you are well-equipped to score better in your exams.
What You Will Practise Here
Sets, Relations, and Functions
Complex Numbers and Quadratic Equations
Permutations and Combinations
Binomial Theorem
Sequences and Series
Limits and Derivatives
Statistics and Probability
Exam Relevance
The Mathematics Syllabus (JEE Main) is not only relevant for JEE but also appears in CBSE and State Board examinations. Students can expect a variety of question patterns, including direct MCQs, numerical problems, and conceptual questions. Mastery of this syllabus will prepare you for similar topics in NEET and other competitive exams, making it vital for your overall academic success.
Common Mistakes Students Make
Misinterpreting the questions, especially in word problems.
Overlooking the importance of units and dimensions in problems.
Confusing formulas related to sequences and series.
Neglecting to practice derivations, leading to errors in calculus.
Failing to apply the correct methods for solving probability questions.
FAQs
Question: What are the key topics in the Mathematics Syllabus for JEE Main? Answer: Key topics include Sets, Complex Numbers, Permutations, Binomial Theorem, and Calculus.
Question: How can I improve my performance in Mathematics MCQs? Answer: Regular practice of MCQs and understanding the underlying concepts are essential for improvement.
Now is the time to take charge of your exam preparation! Dive into solving practice MCQs and test your understanding of the Mathematics Syllabus (JEE Main). Your success is just a question away!
