Determinants questions
307 published questions with worked solutions.
- Let f(n)= vmatrix n & n+1 & n+2 ^ n P_ n & ^ n+1 P_ n+1 & ^ n+2 P_ n+2 ^ n C_ n & ^ n+1 C_ n+1 & ^ n+2 C_ n+2 vmatrix , where the...
- Let x -1 and let a,b,c be nonzero real numbers. Then the determinant vmatrix a(1+x) & b & c a & b(1+x) & c a & b & c(1+x) vmatrix...
- Let (x)= vmatrix x+a & x+b & x+a-c x+b & x+c & x-1 x+c & x+d & x-b+d vmatrix and _0^2 (x) ,dx=-16, where a,b,c,d are in AP. Then...
- If A+B+C= , e^ i = +i and z= vmatrix e^ 2iA & e^ -iC & e^ -iB e^ -iC & e^ 2iB & e^ -iA e^ -iB & e^ -iA & e^ 2iC vmatrix then
- If vmatrix a+x & a-x & a-x a-x & a+x & a-x a-x & a-x & a+x vmatrix =0 then x is
- The system of equations cases 6x+5y+ z=0 3x-y+4z=0 x+2y-3z=0 cases has
- The rank of the matrix bmatrix -5&3&2 3&2&-5 4&-1&-3 bmatrix is
- The rank of the matrix bmatrix 1&2&3 &2&4 2&-3&1 bmatrix is 3 if
- A second-order determinant is written down at random using the numbers 1, -1 as elements. The probability that the value of the...
- If vmatrix x&4&7&9 0&1&5&8 0&0&2&6 0&0&0&3 vmatrix = the total number of arrangements of 4 different things, taking at least one...
- Let = vmatrix a_ 11 & a_ 12 & a_ 13 a_ 21 & a_ 22 & a_ 23 a_ 31 & a_ 32 & a_ 33 vmatrix and a_ pq = i^ p+q where i = -1 . The...
- If the system of linear equations cases x+2ay+az=0 +3by+bz=0 +4cy+cz=0 cases has a nonzero solution then a,b,c
- If in a ABC, vmatrix A & B & C B & C & A C & A & B vmatrix = 0 then
- If a, b, c are three consecutive integers then the determinant vmatrix -a^2 & ab & ac ab & -b^2 & bc ac & bc & -c^2 vmatrix is...
- If a_1,a_2,a_3, ,a_n, are in GP then the determinant = vmatrix a_n& a_ n+1 & a_ n+2 a_ n+3 & a_ n+4 & a_ n+5 a_ n+6 & a_ n+7 & a_...
- The system of equations x+y+z= -1, x+ y+z= -1, x+y+ z= -1 has no solution if is
- If a^2+b^2+c^2+2=0 and f(x)= vmatrix 1+a^2x & (1+b^2)x & (1+c^2)x (1+a^2)x & 1+b^2x & (1+c^2)x (1+a^2)x & (1+b^2)x & 1+c^2x...
- If _r = vmatrix 2^n + 1 & 2^ n+1 & n(n+2) 1 & 1 & -1 ^ n C_ r & 2^r & 2r + 1 vmatrix then the value of _ r=0 ^ n _r is
- If > 0 such that the system of equations cases x + y - 2z = 0, x - 2y + z = 0, x + 3y - z = 0 cases has infinite number of...
- The number of distinct real roots of vmatrix x & x & x x & x & x x & x & x vmatrix = 0 in the interval - 4 x 4 is
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