JEE Advanced questions
3844 published questions with worked solutions.
- If a, b, c are rational and no two of them are equal then the equations (b-c)x^2+(c-a)x+a-b=0 and a(b-c)x^2+b(c-a)x+c(a-b)=0
- The equations x^2+b^2=1-2bx and x^2+a^2=1-2ax have one and only one root common. Then
- If px^2+qx+r=0 has no real roots and p, q, r are real such that p+r>0 then
- Let p and q be roots of the equation x^2-2x+A=0, and let r and s be the roots of the equation x^2-18x+B=0. If p<q<r<s are in...
- The quadratic equation x^2-2x- =0, 0,
- A quadratic equation whose roots are ( )^2 and ( )^2, where , , are the roots of x^3+27=0, is
- The graph of the curve x^2=3x-y-2 is
- a(x^2-y^2)+ x(y+1)+1 can be resolved into linear rational factors. Then
- x^2-4 is a factor of f(x)=(a_1x^2+b_1x+c_1) (a_2x^2+b_2x+c_2) if
- If a, b are the real roots of x^2+px+1=0 and c, d are the real roots of x^2+qx+1=0 then (a-c)(b-c)(a+d)(b+d) is divisible by
- If x [2,4] then for the expression x^2-6x+5
- If 0<a<5, 0<b<5 and x^2+5 2 =x-2 (a+bx) is satisfied for at least one real x then the greatest value of a+b is
- Let f(x)=x^2(x+2)+x+3. Then
- If a < 0, b > 0 then a b is equal to
- If n_1, n_2 are positive integers then (1+i)^ n_1 + (1+i^3)^ n_1 + (1+i^5)^ n_2 + (1+i^7)^ n_2 is a real number if and only if
- The complex number 2^ n (1+i)^ 2n + (1+i)^ 2n 2^ n , n Z , is equal to
- The smallest positive integral value of n for which ( 1-i 1+i )^ n is purely imaginary with positive imaginary part, is
- If (a+ib)^5 = + i then (b+ia)^5 is equal to
- If i= -1 , the number of values of i^ n + i^ -n for different n Z is
- Im (z) is equal to