Exams › JEE Main › Maths
Evaluate the determinant | cos(theta+phi) -sin(theta+phi) cos 2phi | | sin theta cos theta sin phi | | -cos theta sin theta cos phi | Which statement best describes it?
- equals 0
- is independent of theta
- is independent of phi
- is independent of both theta and phi
Correct answer: is independent of theta
Solution
Expanding and using angle-sum identities cancels all theta terms, leaving an expression that depends only on phi; hence the determinant is independent of theta.
Related JEE Main Maths questions
- If [ ] represents the greatest integer less than or equal to the given real number, and -1 ≤ x < 0, 0 ≤ y < 1, 1 ≤ z < 2, then the determinant
[x] [y] [z]
[x+1] [y+1] [z]
[x] [y] [z]+1
is equal to:
- Let x, y and z be complex numbers. If Δ denotes the determinant of the matrix
[0, -y, -z; y, 0, -x; z, x, 0],
then Δ is
- For the linear system
x1 + 2x2 + 3x3 = 6
x1 + 3x2 + 5x3 = 9
2x1 + 5x2 + ax3 = b
if it is consistent and admits infinitely many solutions, then which statement must be true?
- For which value(s) of x does the determinant of the matrix
| 1 (x−3) (x−3)² |
| 1 (x−4) (x−4)² |
| 1 (x−5) (x−5)² |
become zero?
- Let Δ_r denote the determinant
[2r-1, {^mC_r}, 1; m²-1, 2^m, m+1; sin²(m²), sin²(m), sin²(m+1)].
Then the value of ∑_(r=0)^(m) Δ_r is
- If the determinant expression [a, b, ax+by; b, c, bx+cy; ax+by, bx+cy, 0] is considered under the conditions b²-ac<0 and a<0, what is its sign?
⚔️ Practice JEE Main Maths free + battle 1v1 →