JEE Advanced questions
3844 published questions with worked solutions.
- If 1 4-3i is a root of ax^2+bx+1=0, where a,b are real, then
- If , , be the roots of the equation x(1+x^2)+x^2(6+x)+2=0 then the value of ^ -1 + ^ -1 + ^ -1 is
- The roots of the equation x^3+14x^2-84x-216=0 are in
- If z_0= +i , i= -1 , then the roots of the cubic equation x^3-2(1+ )x^2+(4 + ^2+ ^2)x-2( ^2+ ^2)=0 are
- If 3 and 1+ 2 are two roots of a cubic equation with rational coefficients then the equation is
- Let a,b,c be three real numbers such that 2a+3b+6c=0. Then the quadratic equation ax^2+bx+c=0 has
- The quadratic equations x^2+(a^2-2)x-2a^2=0 and x^2-3x+2=0 have
- If the equations x^2+ix+a=0, x^2-2x+ia=0, a 0 have a common root then
- If x^2-2r p_rx+r=0; r=1,2,3 are three quadratic equations of which each pair has exactly one root common then the number of...
- If ( ^2+ -2)x^2+( +2)x<1 for all x R then belongs to the interval
- The least integral value of k for which (k-2)x^2+8x+k+4>0 for all x R , is
- The set of possible values of x such that 5^x+(2 3)^ 2x -169 is always positive is
- If all real values of x obtained from the equation 4^x-(a-3)2^x+a-4=0 are nonpositive then
- The set of possible values of for which x^2-( ^2-5 +5)x+(2 ^2-3 -4)=0 has roots whose sum and product are both less than 1 is
- If _ 10 x+ _ 10 y 2 then the smallest possible value of x+y is
- If f(x)= x^2-1 x^2+1 for every real number x then the minimum value of f
- If ax^2+bx+6=0 does not have two distinct real roots, where a R , b R , then the least value of 3a+b is
- If ab=2a+3b, a>0, b>0 then the minimum value of ab is
- If x^2-1 is a factor of x^4+ax^3+3x-b then
- If x+ y-2 and x- y+1 are factors of the expression 6x^2-xy-y^2-6x+8y-12 then