Q. What is the derivative of f(x) = x^5 + 2x^3 - x?
A.
5x^4 + 6x^2 - 1
B.
5x^4 + 6x^3 - 1
C.
5x^4 + 2x^2 - 1
D.
5x^4 + 2x^3
Show solution
Solution
The derivative f'(x) = d/dx(x^5 + 2x^3 - x) = 5x^4 + 6x^2 - 1.
Correct Answer:
A
— 5x^4 + 6x^2 - 1
Learn More →
Q. What is the derivative of f(x) = x^5?
A.
5x^4
B.
4x^5
C.
x^4
D.
5x^3
Show solution
Solution
The derivative f'(x) = d/dx(x^5) = 5x^4.
Correct Answer:
A
— 5x^4
Learn More →
Q. What is the derivative of f(x) = |x| at x = 0?
A.
0
B.
1
C.
-1
D.
Undefined
Show solution
Solution
The left-hand derivative is -1 and the right-hand derivative is 1, hence the derivative at x = 0 is undefined.
Correct Answer:
D
— Undefined
Learn More →
Q. What is the derivative of f(x) = √x?
A.
1/(2√x)
B.
2√x
C.
1/x
D.
√x/2
Show solution
Solution
f'(x) = 1/(2√x).
Correct Answer:
A
— 1/(2√x)
Learn More →
Q. What is the derivative of sin^(-1)(x)?
A.
1/√(1-x^2)
B.
-1/√(1-x^2)
C.
1/x
D.
0
Show solution
Solution
The derivative of sin^(-1)(x) is 1/√(1-x^2)
Correct Answer:
A
— 1/√(1-x^2)
Learn More →
Q. What is the derivative of y = sin^(-1)(x)?
A.
1/√(1-x^2)
B.
1/(1+x^2)
C.
1/(1-x^2)
D.
√(1-x^2)
Show solution
Solution
The derivative of y = sin^(-1)(x) is 1/√(1-x^2)
Correct Answer:
A
— 1/√(1-x^2)
Learn More →
Q. What is the derivative of \( y = \tan^{-1}(x) \)?
A.
\( \frac{1}{1+x^2} \)
B.
\( \frac{1}{x^2+1} \)
C.
\( \frac{1}{x} \)
D.
0
Show solution
Solution
The derivative of \( y = \tan^{-1}(x) \) is \( \frac{1}{1+x^2} \).
Correct Answer:
A
— \( \frac{1}{1+x^2} \)
Learn More →
Q. What is the determinant of the matrix [[0, 1], [1, 0]]?
Show solution
Solution
The determinant is calculated as (0*0) - (1*1) = 0 - 1 = -1.
Correct Answer:
C
— -1
Learn More →
Q. What is the determinant of the matrix \( E = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \)?
Show solution
Solution
The determinant is calculated as \( 1*4 - 2*3 = 4 - 6 = -2 \).
Correct Answer:
A
— -2
Learn More →
Q. What is the determinant of the matrix \( H = \begin{pmatrix} 1 & 2 \\ 2 & 4 \end{pmatrix} \)?
Show solution
Solution
The determinant is 0 because the rows are linearly dependent.
Correct Answer:
A
— 0
Learn More →
Q. What is the determinant of the matrix \( \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \)?
Show solution
Solution
The determinant of the identity matrix is 1.
Correct Answer:
B
— 1
Learn More →
Q. What is the determinant of the matrix \( \begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix} \)?
Show solution
Solution
The determinant is calculated as (1*1) - (1*1) = 1 - 1 = 0.
Correct Answer:
A
— 0
Learn More →
Q. What is the determinant of the matrix \( \begin{pmatrix} 1 & 2 & 1 \\ 0 & 1 & 0 \\ 2 & 3 & 1 \end{pmatrix} \)?
Show solution
Solution
The determinant is calculated as \( 1(1*1 - 0*3) - 2(0*1 - 0*2) + 1(0*3 - 1*2) = 1 - 0 - 2 = -1 \).
Correct Answer:
B
— 1
Learn More →
Q. What is the determinant of the matrix \( \begin{pmatrix} 1 & 2 \\ 2 & 4 \end{pmatrix} \)?
Show solution
Solution
The determinant is 0 because the rows are linearly dependent.
Correct Answer:
A
— 0
Learn More →
Q. What is the determinant of the matrix \( \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \)?
Show solution
Solution
The determinant is calculated as \( 1*4 - 2*3 = 4 - 6 = -2 \).
Correct Answer:
A
— -2
Learn More →
Q. What is the determinant of the matrix \( \begin{pmatrix} 1 & 2 \\ 3 & 5 \end{pmatrix} \)?
Show solution
Solution
The determinant is calculated as \( 1*5 - 2*3 = 5 - 6 = -1 \).
Correct Answer:
B
— 1
Learn More →
Q. What is the determinant of the matrix \( \begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix} \)?
Show solution
Solution
The determinant is calculated as (3*4) - (2*1) = 12 - 2 = 10.
Correct Answer:
A
— 10
Learn More →
Q. What is the determinant of the matrix \( \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix} \)?
Show solution
Solution
The determinant is calculated as \( 5*8 - 6*7 = 40 - 42 = -2 \).
Correct Answer:
A
— -2
Learn More →
Q. What is the determinant of the matrix: | 1 2 3 | | 4 5 6 | | 7 8 10 |?
Show solution
Solution
Calculating gives a determinant of -3.
Correct Answer:
A
— -3
Learn More →
Q. What is the directrix of the parabola given by the equation y^2 = 8x?
A.
x = -2
B.
x = 2
C.
y = -4
D.
y = 4
Show solution
Solution
The standard form of a parabola is (y - k)^2 = 4p(x - h). Here, p = 2, so the directrix is x = -2.
Correct Answer:
A
— x = -2
Learn More →
Q. What is the directrix of the parabola y^2 = 8x?
A.
x = -2
B.
x = 2
C.
y = -4
D.
y = 4
Show solution
Solution
For the parabola y^2 = 4px, here 4p = 8, so p = 2. The directrix is x = -p = -2.
Correct Answer:
A
— x = -2
Learn More →
Q. What is the distance between the centers of two circles with equations (x - 1)² + (y - 2)² = 9 and (x + 3)² + (y + 4)² = 16?
Show solution
Solution
The distance between centers (1, 2) and (-3, -4) is calculated using the distance formula.
Correct Answer:
D
— 6
Learn More →
Q. What is the distance between the foci of the ellipse given by the equation 4x^2 + 9y^2 = 36?
Show solution
Solution
The distance between the foci is 6, calculated using the formula 2c where c = √(a^2 - b^2).
Correct Answer:
A
— 6
Learn More →
Q. What is the distance between the foci of the ellipse x^2/25 + y^2/16 = 1?
Show solution
Solution
The distance between the foci is given by 2c, where c = √(a^2 - b^2) = √(25 - 16) = 3, so the total distance is 2c = 6.
Correct Answer:
A
— 7
Learn More →
Q. What is the distance between the points (1, 2) and (4, 6)?
Show solution
Solution
Distance = √[(4-1)² + (6-2)²] = √[9 + 16] = √25 = 5.
Correct Answer:
A
— 5
Learn More →
Q. What is the distance between the points (3, 4) and (7, 1)?
Show solution
Solution
Distance = √[(7-3)² + (1-4)²] = √[16 + 9] = √25 = 5.
Correct Answer:
A
— 5
Learn More →
Q. What is the distance between the points P(1, 2, 3) and Q(4, 5, 6)?
Show solution
Solution
Distance = √((4-1)² + (5-2)² + (6-3)²) = √(9 + 9 + 9) = 3√3.
Correct Answer:
A
— 3√3
Learn More →
Q. What is the distance from the point (1, 2) to the line 3x + 4y - 10 = 0?
Show solution
Solution
Distance = |3(1) + 4(2) - 10| / √(3² + 4²) = |3 + 8 - 10| / 5 = 1.
Correct Answer:
B
— 2
Learn More →
Q. What is the distance from the point (3, 4) to the line 2x + 3y - 6 = 0?
Show solution
Solution
Distance = |2(3) + 3(4) - 6| / √(2² + 3²) = |6 + 12 - 6| / √13 = 12/√13.
Correct Answer:
A
— 1
Learn More →
Q. What is the domain of the function f(x) = 1/(x - 2)?
A.
x ≠ 2
B.
x > 2
C.
x < 2
D.
All real numbers
Show solution
Solution
The function is undefined at x = 2, so the domain is all real numbers except 2.
Correct Answer:
A
— x ≠ 2
Learn More →
Showing 2281 to 2310 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!
