JEE Advanced · Mathematics
Algebra, calculus and vectors
42 practice questions, each with the answer and an explanation.
Practise Algebra, calculus and vectors now
Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.
All 42 questions
- What are the eigenvalues of the matrix with rows (6, 2) and (0, 2)?
- The curve has two stationary points. Find the difference between their -coordinates (larger minus smaller).
- If and are the roots of , find .
- If and , find the real part of .
- Find for and .
- Two independent events have probabilities 0.5 and 0.4. What is the probability that at least one occurs?
- The Taylor series of e^(5x) about x = 0 has the coefficient of x³ equal to
- How many functions are there from a set of 4 elements to a set of 5 elements?
- Find the determinant of the 3×3 matrix with rows (4, 4, 4); (5, -2, -1); (-3, -1, 4).
- Find a × b for a = 4i − 3j + 2k and b = 0i + 4j − 1k.
- Find the eccentricity of the hyperbola x²/144 − y²/25 = 1.
- Find the area under the curve between and .
- Evaluate .
- If and are the roots of , find .
- Find the value of .
- A random variable takes the values 1, 5 and 4 with probabilities 1/2, 1/3 and 1/6 respectively. What is its expected value?
- What is the limit of (sin 3x)/x as x tends to 0?
- Find the determinant of the 3×3 matrix with rows (1, -2, 3); (-1, 0, -2); (4, 4, 1).
- Find a × b for a = -3i − 3j + 0k and b = 0i + 3j − 2k.
- What are the eigenvalues of the matrix with rows (1, 1) and (0, 5)?
- Find the area under the curve between and .
- Evaluate .
- Find the term independent of in the expansion of .
- If and , find the real part of .
- A random variable takes the values 6, 1 and 3 with probabilities 1/2, 1/3 and 1/6 respectively. What is its expected value?
- What is the limit of (sin 6x)/x as x tends to 0?
- How many relations are there on a set with 3 elements?
- Find the determinant of the 3×3 matrix with rows (2, -2, -3); (1, -1, 1); (5, -2, 4).
- Find a × b for a = -3i + 4j + 2k and b = 3i + 1j + 2k.
- What are the eigenvalues of the matrix with rows (5, -4) and (0, 1)?
- Find the area enclosed between the curve and the line .
- If and are the roots of , find .
- How many reflexive relations are there on a set with 5 elements?
- Find the determinant of the 3×3 matrix with rows (4, 4, 3); (0, 0, 4); (-1, 4, 1).
- Find a × b for a = 4i + 0j + 1k and b = 1i + 1j + 1k.
- Evaluate the integral of 2x(x² + 1)^5 from x = 0 to x = 1.
- What are the eigenvalues of the matrix with rows (6, 2) and (0, 4)?
- Find the modulus of .
- Two independent events have probabilities 0.5 and 0.25. What is the probability that at least one occurs?
- Find the determinant of the 3×3 matrix with rows (-1, 4, 4); (5, 4, 4); (3, -3, 5).
- What are the eigenvalues of the matrix with rows (1, 2) and (0, 6)?
- Find the area under the curve between and .