JEE Main questions
34495 published questions with worked solutions.
- If at least one root of 2x^2+3x+5=0 and ax^2+bx+c=0, a,b,c N is common, then the maximum value of a+b+c is
- Let , be the roots of the equation ax^2+2bx+c=0 and , be the roots of the equation px^2+2qx+r=0. If , , , are in GP, then
- Let a,b,c,p,q be real numbers. Suppose , are the roots of the equation x^2+2px+q=0 and , 1 are the roots of the equation...
- Let |z|=2 and w= z+1 z-1 where z,w C (where C is the set of complex numbers). Then product of least and greatest value of modulus...
- If the expression (1+ir)^3 is of the form s(1+i) where real s where r is also real and, then the sum of all possible values of r...
- If x=a+bi is a complex number such that x^2=3+4i and x^3=2+11i where i= -1 , then (a+b) equal to
- If complex number z(z 2) satisfies the equation z^2=4z+|z|^2+ 16 |z|^3 then the value of |z|^4 is
- Let z=9+bi where b is non zero real and i^2=-1. If the imaginary part of z^2 and z^3 are equal, then b/3 is
- If z be a complex number satisfying z^4+z^3+2z^2+z+1=0, then |z| is equal to
- Modulus of non zero complex number z, satisfying z+z=0 and |z|^2-4zi=z^2 is
- Let A= a R the equation (1+2i)x^3-2(3+i)x^2+(5-4i)x+2a^2=0 has at least one real root . Then the value of a^2 2 is
- The minimum value of the expression E=|z|^2+|z-3|^2+|z-6i|^2 is m then the value of m/5 is
- If the complex numbers x and y satisfy x^3-y^3=98i and x-y=7i then x=a+ib where a,b R. The value of (a+b)/3 equals
- Suppose that z is a complex number that satisfies |z-2-2i| 1. The maximum value of |2iz+4| is equal to
- Let Z_1=(8+i) +(7+4i) and Z_2=(1+8i) +(4+7i) are two complex numbers. If Z_1 Z_2=a+ib where a,b R. If M is the greatest value of...
- Let 1,w,w^2 be the cube root of unity. The least possible degree of a polynomial with real coefficients having roots 2w,(2+3w),...
- If is the imaginary cube root of unity, then find the number of pairs of integers (a,b) such that |a +b|=1
- If [ 1+ +i +i(1+ ) ]^4= n +i n , then n is
- If |z+2-i|=5 and maximum value of |3z+9-7i| is M then the value of M/4 is
- If x= - ^2-2, then the value of x^4+3x^3+2x^2-11x-6 is (where is cube root of unity)