Determinants questions
307 published questions with worked solutions.
- Consider the system of equations x - 2y + 3z = -1, -x + y - 2z = k, x - 3y + 4z = 1. STATEMENT-1: The system of equations has no...
- Consider the system of equations ax + by = 0, cx + dy = 0, where a, b, c, d 0, 1 . STATEMENT-1: The probability that the system...
- The number of values of k, for which the system of equation : (k + 1) x + 8y = 4k, kx + (k + 3) y = 3k –1, has no solution, is -
- If the system of equations 3x + y + 4z = 3 2x + y - z = -3 x + 2y + z = 4 has no solution, then the value of is equal to:
- Let n be the number obtained on rolling a fair die. If the probability that the system x - ny + z = 6 x + (n-2)y + (n+1)z = 8...
- Among the statements : I : If vmatrix 1 & & & 1 & & & 1 vmatrix = vmatrix 0 & & & 0 & & & 0 vmatrix , then ^2 + ^2 + ^2 = 3 2 ,...
- The system of linear equations x+y+z=6 2x+5y+az=36 x+2y+3z=b has
- Let P=[p_ ij ] and Q=[q_ ij ] be two square matrices of order 3 such that q_ ij = 2^ (i+j-1) p_ ij and (Q) = 2^ 10 . Then the...
- Let A be a square matrix of order 3 such that det(A) = –2 and det(3adj(–6adj(3A))) = 2^ m+n .3^ mn , m > n. Then 4m + 2n is equal...
- The system of equations x + y + z = 6, x + 2y + 5z = 9, x + 5y + = , has no solution if
- If the system of equations (λ – 1)x + (λ – 4)y + λz = 5 λx + (λ – 1)y + (λ –4)z = 7 (λ + 1)x + (λ + 2)y – (λ + 2)z = 9 has...
- For some a, b, let f(x) = vmatrix a+ x x & 1 & b a & 1+ x x & b a & 1 & b+ x x vmatrix , x 0, _ x 0 f(x) = + a + b. Then ( + +...
- Let M and m respectively be the maximum and the minimum values of f(x) = vmatrix 1+ ^2 x & ^2 x & 4 4x ^2 x & 1+ ^2 x & 4 4x ^2 x...
- Let A = [a_ ij ] = bmatrix _5 128 & _4 5 _5 8 & _4 25 bmatrix . If A_ ij is the co-factor of a_ ij , C_ ij = _ k=1 ^ 2 a_ ik A_...
- Let A = [a_ ij ] be a 2 × 2 matrix such that a_ ij 0, 1 for all i and j. Let the random variable X denote the possible values of...
- If the system of equations 2x + λy + 3z = 5 3x + 2y – z = 7 4x + 5y + μz = 9 has infinitely many solutions, then ( ^2 + ^2) is...
- If y(x) = vmatrix x & x & x+ x+1 27&28&27 1&1&1 vmatrix , x R, then d^2y dx^2 +y is equal to
- Consider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of A consisting of all...
- If in a ABC, ^3A+ ^3B+ ^3C=3 A B C, then vmatrix a&b&c &c&a &a&b vmatrix =
- If , 0, and f(n) = ^n + ^n and vmatrix 3 & 1 + f(1) & 1 + f(2) 1 + f(1) & 1 + f(2) & 1 + f(3) 1 + f(2) & 1 + f(3) & 1 + f(4)...
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