Q. What type of curves does the equation (x^2/a^2) + (y^2/b^2) = 1 represent?
A.
Ellipses
B.
Circles
C.
Parabolas
D.
Hyperbolas
Show solution
Solution
The equation (x^2/a^2) + (y^2/b^2) = 1 represents a family of ellipses with varying semi-major (a) and semi-minor (b) axes.
Correct Answer:
A
— Ellipses
Learn More →
Q. What type of curves does the equation y = a + b cos(x) represent?
A.
Linear functions
B.
Cosine waves with varying amplitudes
C.
Parabolas
D.
Exponential functions
Show solution
Solution
The equation y = a + b cos(x) represents cosine waves with varying amplitudes 'b' and vertical shifts 'a'.
Correct Answer:
B
— Cosine waves with varying amplitudes
Learn More →
Q. What type of curves does the equation y = a e^(bx) represent?
A.
Linear functions
B.
Exponential functions
C.
Trigonometric functions
D.
Polynomial functions
Show solution
Solution
The equation y = a e^(bx) represents a family of exponential functions with varying growth rates.
Correct Answer:
B
— Exponential functions
Learn More →
Q. What type of curves does the equation y = a sin(bx + c) represent?
A.
Linear functions
B.
Exponential functions
C.
Trigonometric functions
D.
Polynomial functions
Show solution
Solution
The equation y = a sin(bx + c) represents a family of trigonometric functions (sine waves) with varying amplitude (a) and frequency (b).
Correct Answer:
C
— Trigonometric functions
Learn More →
Q. What type of curves does the equation y = a(x - h)^2 + k represent?
A.
Linear functions
B.
Parabolas
C.
Circles
D.
Ellipses
Show solution
Solution
The equation y = a(x - h)^2 + k represents a family of parabolas with vertex at (h, k) and varying 'a' determining the direction and width.
Correct Answer:
B
— Parabolas
Learn More →
Q. What type of curves does the equation y = e^(kx) represent?
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 (k).
Correct Answer:
B
— Exponential functions
Learn More →
Q. What type of curves does the equation y = k/x represent?
A.
Hyperbolas
B.
Parabolas
C.
Circles
D.
Ellipses
Show solution
Solution
The equation y = k/x represents a family of hyperbolas where k is a constant.
Correct Answer:
A
— Hyperbolas
Learn More →
Q. What type of curves does the equation y = kx^2 represent?
A.
Straight lines
B.
Parabolas with varying widths
C.
Circles
D.
Ellipses
Show solution
Solution
The equation y = kx^2 represents a family of parabolas that open upwards or downwards depending on the sign of 'k'.
Correct Answer:
B
— Parabolas with varying widths
Learn More →
Q. What type of curves does the equation y = mx^3 + bx + c represent?
A.
Linear functions
B.
Cubic functions
C.
Quadratic functions
D.
Exponential functions
Show solution
Solution
The equation y = mx^3 + bx + c represents a family of cubic functions with varying coefficients.
Correct Answer:
B
— Cubic functions
Learn More →
Q. What type of curves does the equation y = mx^3 + bx^2 + cx + d represent?
A.
Linear functions
B.
Quadratic functions
C.
Cubic functions
D.
Quartic functions
Show solution
Solution
The equation y = mx^3 + bx^2 + cx + d represents a family of cubic functions with varying coefficients.
Correct Answer:
C
— Cubic functions
Learn More →
Q. What type of curves does the equation y = mx^3 + c represent?
A.
Linear functions
B.
Cubic functions
C.
Quadratic functions
D.
Exponential functions
Show solution
Solution
The equation y = mx^3 + c represents a family of cubic functions where m is the coefficient of x^3.
Correct Answer:
B
— Cubic functions
Learn More →
Q. What value of a makes the function f(x) = { 2x + 1, x < 1; a, x = 1; x^2 + 1, x > 1 continuous at x = 1?
Show solution
Solution
Setting 2(1) + 1 = a and a = 2 for continuity.
Correct Answer:
B
— 2
Learn More →
Q. What value of a makes the function f(x) = { 2x + a, x < 3; 5, x = 3; x^2 - 1, x > 3 continuous at x = 3?
Show solution
Solution
Setting 2(3) + a = 5 gives a = -1.
Correct Answer:
C
— 2
Learn More →
Q. What value of a makes the function f(x) = { 4 - x^2, x < 0; ax + 2, x = 0; x + 1, x > 0 continuous at x = 0?
Show solution
Solution
Setting 4 = 2 gives a = 1 for continuity.
Correct Answer:
B
— 0
Learn More →
Q. What value of k makes the function f(x) = { kx, x < 1; 2, x = 1; x + 1, x > 1 continuous at x = 1?
Show solution
Solution
Setting the left limit (k(1) = k) equal to the right limit (1 + 1 = 2), we find k = 2.
Correct Answer:
B
— 1
Learn More →
Q. What value of m makes the function f(x) = { 3x + 1, x < 2; mx + 4, x = 2; x^2 - 1, x > 2 continuous at x = 2?
Show solution
Solution
Setting the left limit (3(2) + 1 = 7) equal to the right limit (2^2 - 1 = 3), we find m = 3.
Correct Answer:
D
— 4
Learn More →
Q. Which measure of dispersion is affected by extreme values?
A.
Range
B.
Variance
C.
Standard Deviation
D.
All of the above
Show solution
Solution
All of these measures are affected by extreme values in the data set.
Correct Answer:
D
— All of the above
Learn More →
Q. Which measure of dispersion is not affected by extreme values?
A.
Range
B.
Variance
C.
Standard Deviation
D.
Interquartile Range
Show solution
Solution
Interquartile Range is not affected by extreme values.
Correct Answer:
D
— Interquartile Range
Learn More →
Q. Which of the following equations has no real roots?
A.
x^2 + 2x + 1 = 0
B.
x^2 - 4 = 0
C.
x^2 + 4x + 5 = 0
D.
x^2 - 1 = 0
Show solution
Solution
The discriminant for x^2 + 4x + 5 is negative (16 - 20 < 0), indicating no real roots.
Correct Answer:
C
— x^2 + 4x + 5 = 0
Learn More →
Q. Which of the following functions is an even function?
A.
f(x) = x^3
B.
f(x) = x^2
C.
f(x) = x + 1
D.
f(x) = sin(x)
Show solution
Solution
An even function satisfies f(-x) = f(x). Here, f(x) = x^2 is even.
Correct Answer:
B
— f(x) = x^2
Learn More →
Q. Which of the following functions is continuous at x = 2?
A.
f(x) = 1/x
B.
f(x) = x^2 - 4
C.
f(x) = sin(1/x)
D.
f(x) =
.
x
.
Show solution
Solution
f(x) = x^2 - 4 is a polynomial function and is continuous everywhere, including at x = 2.
Correct Answer:
B
— f(x) = x^2 - 4
Learn More →
Q. Which of the following functions is continuous at x = 2? f(x) = { x^2 - 4, x < 2; 3x - 6, x >= 2 }
A.
Continuous
B.
Not continuous
C.
Depends on k
D.
None of the above
Show solution
Solution
At x = 2, f(2) = 0 and limit from left is 0, limit from right is also 0. Hence, it is continuous.
Correct Answer:
A
— Continuous
Learn More →
Q. Which of the following functions is continuous at x = 2? f(x) = { x^2, x < 2; 4, x = 2; 2x, x > 2 }
A.
Continuous
B.
Not continuous
C.
Depends on k
D.
None of the above
Show solution
Solution
To check continuity at x = 2, we find the left limit (4), right limit (4), and f(2) (4). All are equal, so f(x) is continuous.
Correct Answer:
A
— Continuous
Learn More →
Q. Which of the following functions is continuous everywhere?
A.
f(x) = 1/x
B.
f(x) = x^2
C.
f(x) = sin(x)
D.
f(x) =
.
x
.
Show solution
Solution
f(x) = x^2 is a polynomial function and is continuous everywhere.
Correct Answer:
B
— f(x) = x^2
Learn More →
Q. Which of the following functions is differentiable at x = 1? f(x) = { x^2, x < 1; 2x - 1, x >= 1 }
A.
f(1) = 1
B.
f(1) = 0
C.
f(1) = 2
D.
f(1) = 3
Show solution
Solution
Check continuity and differentiability at x = 1 by equating left and right derivatives.
Correct Answer:
A
— f(1) = 1
Learn More →
Q. Which of the following functions is differentiable everywhere?
A.
f(x) =
B.
x
C.
D.
f(x) = x^2
.
f(x) = sqrt(x)
.
f(x) = 1/x
Show solution
Solution
f(x) = x^2 is a polynomial and differentiable everywhere.
Correct Answer:
B
— x
Learn More →
Q. Which of the following functions is even?
A.
f(x) = x^3
B.
f(x) = x^2
C.
f(x) = x + 1
D.
f(x) = sin(x)
Show solution
Solution
A function is even if f(-x) = f(x). Here, f(x) = x^2 is even.
Correct Answer:
B
— f(x) = x^2
Learn More →
Q. Which of the following functions is not a polynomial function?
A.
f(x) = x^2 + 3x + 1
B.
g(x) = 2x^3 - 4
C.
h(x) = sqrt(x)
D.
k(x) = 5
Show solution
Solution
h(x) = sqrt(x) is not a polynomial function.
Correct Answer:
C
— h(x) = sqrt(x)
Learn More →
Q. Which of the following functions is not a polynomial?
A.
f(x) = x^3 + 2x^2 - 5
B.
g(x) = 1/x
C.
h(x) = 4x - 7
D.
k(x) = 2
Show solution
Solution
g(x) = 1/x is not a polynomial because it has a negative exponent.
Correct Answer:
B
— g(x) = 1/x
Learn More →
Q. Which of the following functions is not continuous at x = 0?
A.
f(x) = x^3
B.
f(x) = e^x
C.
f(x) = 1/x
D.
f(x) = ln(x)
Show solution
Solution
The function f(x) = 1/x is not defined at x = 0, hence it is not continuous there.
Correct Answer:
C
— f(x) = 1/x
Learn More →
Showing 2761 to 2790 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!
