Exams › JEE Advanced › Maths
If px⁴ + qx³ + rx² + sx + t equals the 3x3 determinant with rows (x²+3x, x-1, x+3), (x+1, 2-x, x-3), (x-3, x+4, 3x), then the value of t is:
- 33
- 0
- 21
- none
Correct answer: 21
Solution
Putting x = 0 gives the determinant of rows (0,-1,3), (1,2,-3), (-3,4,0), which evaluates to 21; hence t = 21.
Related JEE Advanced Maths questions
- What is the nature of the solution for the equations x + y + z = 3, 2x + y + 2z = 5, and x − y + 3z = 3?
- What is the nature of the solutions for the equations x + y + z = 3, 2x + 2y + 2z = 7, and x − y + 3z = 3?
- Consider the matrix M = [0 1 a; 1 2 3; 3 b 1] and its adjugate adj M = [-1 1 -1; 8 -6 2; -5 3 -1], where a and b are real numbers. Which of the following statements is/are true?
- Given that the 3x3 determinant |x, 2, x; x², x, 6; x, 1, x| equals Ax⁴ + Bx³ + Cx² + Dx + E, find the sum of the digits of the square of (5A + 4B + 3C + 2D + E).
- The determinant with rows (x², (y+z)², yz), (y², (x+z)², zx), (z², (x+y)², xy) is divisible by which of the following?
- Consider the determinant equation: det([[a1 + b1*x, a1*x + b1, c1], [a2 + b2*x, a2*x + b2, c2], [a3 + b3*x, a3*x + b3, c3]]) = 0. Which of the following are possible conditions that guarantee this holds for all choices of ai, bi, ci?
⚔️ Practice JEE Advanced Maths free + battle 1v1 →