JEE Advanced questions
3844 published questions with worked solutions.
- 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 vmatrix x_1 & y_1 & 1 x_2 & y_2 & 1 x_3 & y_3 & 1 vmatrix = vmatrix 1 & 1 & 1 b_1 & b_2 & b_3 a_1 & a_2 & a_3 vmatrix then the...
- 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 vmatrix 1 & 1 & 1 (2^x+2^ -x )^2 & (3^x+3^ -x )^2 & (5^x+5^ -x )^2 (2^x-2^ -x )^2 & (3^x-3^ -x )^2 & (5^x-5^ -x )^2...
- 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
- If -1 = i, and is a nonreal cube root of unity then the value of vmatrix 1 & ^2 & 1+i+ ^2 -i & -1 & -1-i+ 1-i & ^2-1 & -1 vmatrix...
- If f(x) = vmatrix 1 & x & x+1 2x & x(x-1) & x(x+1) 3x(x-1) & x(x-1)(x-2) & x(x^2-1) vmatrix then f(100) is equal to
- The value of vmatrix i^m & i^ m+1 & i^ m+2 i^ m+5 & i^ m+4 & i^ m+3 i^ m+6 & i^ m+7 & i^ m+8 vmatrix , where i = -1 , is
- If _1 = vmatrix 7 & x & 2 -5 & x+1 & 3 4 & x & 7 vmatrix , _2 = vmatrix x & 2 & 7 x+1 & 3 & -5 x & 7 & 4 vmatrix then _1 - _2 = 0...
- If _1 = vmatrix 10 & 4 & 3 17 & 7 & 4 4 & -5 & 7 vmatrix , _2 = vmatrix 4 & x+5 & 3 7 & x+12 & 4 -5 & x-1 & 7 vmatrix such that...
- Let vmatrix ^2+3 & -1 & +3 +1 & -2 & -4 -3 & +4 & 3 vmatrix = p ^4 + q ^3 + r ^2 + s + t be an identity in , where p, q, r, s, t...
- Let vmatrix 1+x & x & x^2 x & 1+x & x^2 x^2 & x & 1+x vmatrix = ax^5+bx^4+cx^3+dx^2+ x+ be an identity in x, where a, b, c, d, ,...
- Using the factor theorem it is found that b+c, c+a and a+b are three factors of the determinant vmatrix -2a & a+b & a+c b+a & -2b...
- If the determinant vmatrix 2x & ^2 x & 4x ^2 x & 2x & ^2 x 4x & ^2 x & 2x vmatrix is expanded in powers of x then the constant...
- If (x)= vmatrix 1 & x & 1- x 1+ x & x & 1+ x- x x & x & 1 vmatrix then _0^ /2 (x) ,dx is equal to
- If i= -1 and [4] 1 = , , , then vmatrix & & & & & & & & & & & & vmatrix is equal to