IIT JAM 2024
IIT MADRAS
Hello student today i want to tell iit jam 2024 exam,
This year IIT MADRAS conduct this exam. I give you some question if you complete this you absolute selected in iit jam 2024.
There are we provided some basic question for your prectise because the question prectise is very important in iit jam level exam. This exam not tough but high level of greduation level exam .
so there we provided some question for iit jam mathematics-
1-Find the derivative of the function f(x)=sin 2(x)cos(x) with respect to x.
2-Which of the following is NOT an axiom for a vector space?
a) Closure under addition
b) Closure under scalar multiplication
c) Existence of additive identity
d) Existence of a multiplicative identity
3-If a set of vectors is linearly independent, what is the maximum number of vectors it can have in a vector space of dimension n?
a) n
b) n + 1
c) n - 1
d) 2n
4-Which of the following is a subspace of the vector space R^3?
a) {(x, y, z) | x + y = 1}
b) {(x, y, z) | x + y + z = 0}
c) {(x, y, z) | x^2 + y^2 + z^2 = 1}
d) {(x, y, z) | x = 2y}
5-The dimension of a vector space is equal to:
a) The number of vectors in the basis of the vector space
b) The number of linearly independent vectors in the vector space
c) The number of vectors in the vector space
d) The number of vectors in the subspace of the vector space
6-Which of the following matrices is not invertible?
a) [[1, 0], [0, 1]]
b) [[2, 1], [0, 2]]
c) [[1, 2], [2, 4]]
d) [[0, 0], [0, 0]]
7-If the determinant of a 3x3 matrix A is zero, what can be said about the vectors formed by its rows?
a) They are linearly independent.
b) They are linearly dependent.
c) They form a basis for R^3.
d) They are orthogonal.
8-If the column vectors of a matrix A are linearly independent, what can be said about the matrix A?
a) A is invertible.
b) A has a determinant of zero.
c) A is a square matrix.
d) A is singular.
9-Which of the following is a basis for the vector space of 2x2 symmetric matrices?
a) {{1, 0}, {0, 1}}
b) {{1, 2}, {2, 3}}
c) {{1, 0}, {0, -1}}
d) {{0, 1}, {1, 0}}
10-If two vectors in a vector space have the same span as the standard basis vectors, what can be said about these two vectors?
a) They are linearly independent.
b) They form a basis for the vector space.
c) They are orthogonal to each other.
d) They are scalar multiples of each other.
11-Which of the following is NOT a property of the cross product of two vectors in R^3?
a) Commutativity: A × B = B × A
b) Distributivity over scalar multiplication: a(A × B) = (aA) × B = A × (aB)
c) Associativity: (A × B) × C = A × (B × C)
d) Cross product is zero if and only if the vectors are parallel.
Here are the Answers:
2-d) Existence of a multiplicative identity
3-a) n
4-b) {(x, y, z) | x + y + z = 0}
5-b) The number of linearly independent vectors in the vector space
6-d) [[0, 0], [0, 0]]
7-b) They are linearly dependent.
8-a) A is invertible.
9-b) {{1, 2}, {2, 3}}
10-b) They form a basis for the vector space.
11-a) Commutativity: A × B = B × A
Join US