Determinants questions
307 published questions with worked solutions.
- Let for i = 1, 2, 3, p_i(x) be a polynomial of degree 2 in x, p'_i(x) and p''_i(x) be the first and second order derivatives of...
- If vmatrix a^2 & b^2 & c^2 (a+ )^2 & (b+ )^2 & (c+ )^2 (a- )^2 & (b- )^2 & (c- )^2 vmatrix = k vmatrix a^2 & b^2 & c^2 & b & c 1...
- If _r = vmatrix r & 2r-1 & 3r-2 n2 & n-1 & a 12n(n-1) & (n-1)^2 & 12(n-1)(3n+4) vmatrix , then the value of _ r=1 ^ n-1 _r
- If vmatrix a+x & a & x a-x & a & x a-x & a & -x vmatrix =0 then x is
- vmatrix 0 & p-q & p-r q-p & 0 & q-r r-p & r-q & 0 vmatrix is equal to
- If a b c such that vmatrix a^3-1 & b^3-1 & c^3-1 a & b & c a^2 & b^2 & c^2 vmatrix =0 then
- vmatrix 1+x & 1 & 1 1 & 1+x & 1 1 & 1 & 1+x vmatrix is equal to
- If vmatrix 6i & -3i & 1 4 & 3i & -1 20 & 3 & i vmatrix = x+iy then
- The determinant vmatrix xp+y & x & y yp+z & y & z 0 & xp+y & yp+z vmatrix =0 for all p R if
- The determinant vmatrix a & a+d & a+2d a^2 & (a+d)^2 & (a+2d)^2 2a+3d & 2(a+d) & 2a+d vmatrix =0. Then
- The value of the determinant vmatrix bc & ca & ab p & q & r 1 & 1 & 1 vmatrix , where a, b, c are the pth, qth and rth terms of a...
- The sum of two nonintegral roots of vmatrix x & 2 & 5 3 & x & 3 5 & 4 & x vmatrix =0 is
- If x, y, z are integers in AP, lying between 1 and 9, and x51, y41 and z31 are three-digit numbers then the value of vmatrix 5 &...
- If _1 = vmatrix 1 & 1 & 1 a & b & c a^2 & b^2 & c^2 vmatrix , _2 = vmatrix 1 & bc & a 1 & ca & b 1 & ab & c vmatrix then
- The value of vmatrix a_1x+b_1y & a_2x+b_2y & a_3x+b_3y b_1x+a_1y & b_2x+a_2y & b_3x+a_3y b_1x+a_1 & b_2x+a_2 & b_3x+a_3 vmatrix...
- If , are nonreal numbers satisfying x^3 - 1 = 0 then the value of vmatrix +1 & & & + & 1 & 1 & + vmatrix is equal to
- The value of vmatrix ^ 10 C_4 & ^ 10 C_5 & ^ 11 C_m ^ 11 C_6 & ^ 11 C_7 & ^ 12 C_ m+2 ^ 12 C_8 & ^ 12 C_9 & ^ 13 C_ m+4 vmatrix...
- If x > 0 and 1, y > 0 and 1, z > 0 and 1 then the value of vmatrix 1 & _x y & _x z _y x & 1 & _y z _z x & _z y & 1 vmatrix is
- The value of the determinant vmatrix ^ 5 C_0 & ^ 5 C_3 & 14 ^ 5 C_1 & ^ 5 C_4 & 1 ^ 5 C_2 & ^ 5 C_5 & 1 vmatrix is
- The value of vmatrix x & x^2-yz & 1 y & y^2-zx & 1 z & z^2-xy & 1 vmatrix is
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