JEE Advanced questions
3844 published questions with worked solutions.
- If x+y and y+3x are two factors of the expression x^3- x^2y+xy^2+y^3 then the third factor is
- If a R , b R then the factors of the expression a(x^2-y^2)-bxy are
- If a, b, c are in HP then the expression a(b-c)x^2+b(c-a)x+c(a-b)
- The number of positive integral values of k for which (16x^2+12x+39)+k(9x^2-2x+11) is a perfect square is
- If x^2-bx+c=0 has equal integral roots then
- Let A, G and H be the AM, GM and HM of two positive numbers a and b. The quadratic equation whose roots are A and H is
- Let A, G and H are the AM, GM and HM respectively of two unequal positive integers. Then the equation Ax^2-|G|x-H=0 has
- Let x^2-px+q=0, where p R , q R , have the roots , such that +2 =0 then
- The cubic equation whose roots are the AM, GM and HM of the roots of x^2-2px+q^2=0 is
- If x^2+ax+b=0 and x^2+bx+a=0, a b, have a common root then
- The line y+14=0 cuts the curve whose equation is x(x^2+x+1)+y=0 at
- If a, b, c are in GP, where a, c are positive, then the equation ax^2+bx+c=0 has
- If , are the roots of the equation x^2+x+3=0 then the equation 3x^2+5x+3=0 has a root
- If , are the roots of x^2-2ax+b^2=0 and , are the roots of x^2-2bx+a^2=0 then
- If x, y, z are three consecutive terms of a GP, where x>0 and the common ratio is r, then the inequality z+3x>4y holds for
- The equation ||x-1|+a |=4 can have real solutions for x if a belongs to the interval
- The equation |x+1| ,|x-1|=a^2-2a-3 can have real solutions for x if a belongs to
- The common roots of the equations x^3+2x^2+2x+1=0 and 1+x^ 130 +x^ 1988 =0 are (where is a nonreal cube root of unity)
- For the equation 2x^2+6 2 ,x+1=0
- The equation x^ 34( _2x)^2+ _2x- 54 = 2 has