JEE Advanced questions
3844 published questions with worked solutions.
- The roots of vmatrix x & a & b & 1 & x & b & 1 & & x & 1 & & & 1 vmatrix =0 are independent of
- The value of vmatrix 1&0&0&0&0 2&2&0&0&0 4&4&3&0&0 5&5&5&4&0 6&6&6&6&5 vmatrix is
- If vmatrix b^2+c^2 & ab & ac ba & c^2+a^2 & bc ca & cb & a^2+b^2 vmatrix is the square of a determinant of the third order then...
- The system of equations ax+4y+z=0, bx+3y+z=0, cx+2y+z=0 has nontrivial solutions if a, b, c are in
- If the equations a(y+z)=x, b(z+x)=y and c(x+y)=z, where a -1, b -1, c -1, admit of nontrivial solutions then (1+a)^ -1 +(1+b)^ -1...
- The system of equations cases 2x-y+z=0 x-2y+z=0 x-y+2z=0 cases has infinite number of nontrivial solutions for
- The equations x+y+z=6, x+2y+3z=10, x+2y+mz=n give infinite number of values of the triplet (x,y,z) if
- The system of equations 2x+3y=8, 7x-5y+3=0, 4x-6y+ =0 is solvable if is
- If the system of equations cases ax+by+c=0 bx+cy+a=0 cx+ay+b=0 cases has a solution then the system of equations cases...
- Let _1, _2, _3, , _k be the set of third-order determinants that can be made with the distinct nonzero real numbers a_1,a_2,a_3,...
- vmatrix x^2 & (y+z)^2 & yz y^2 & (z+x)^2 & zx z^2 & (x+y)^2 & xy vmatrix is divisible by
- The equation vmatrix 1&x&x^2 ^2&1&x &x^2&1 vmatrix =0 has
- 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...
- The arbitrary constant on which the value of the determinant vmatrix 1 & & ^2 (p-d)a & pa & (p-d)a (p-d)a & pa & (p-d)a 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
- Eliminating a,b,c from x= a b-c , y= b c-a , z= c a-b we get
- The system of equations cases 6x+5y+ z=0 3x-y+4z=0 x+2y-3z=0 cases has