Practice questions
88551 published questions with worked solutions.
- If a,b,c are real and x^3-3b^2x+2c^3 is divisible by x-a and x-b, then
- If the roots of a_1x^2+b_1x+c_1=0 are _1, _1 and those of a_2x^2+b_2x+c_2=0 are _2, _2 such that _1 _2= _1 _2=1, then
- If p and q are the roots of the equation x^2+px+q=0, then
- The equation formed by decreasing each root of ax^2+bx+c=0 by 1 is 2x^2+8x+2=0, then
- If a,b,c R and a+b+c=0, then the quadratic equation 4ax^2+3bx+2c=0 has
- The condition that one root of the equation ax^2+bx+c=0 may be double of the other, is
- If a<c<b, then the roots of the equation (a-b)^2x^2+2(a+b-2c)x+1=0 are
- If f(x)= _ k=2 ^n (x- 1 k-1 ) (x- 1k ), then the product of roots of f(x)=0 as n , is
- The number of solutions of the equation 2 (e^x )=5^x+5^ -x , isNot in JEE Main syllabus
- If one root of the equation (a-b)x^2+ax+1=0 be double the other and if a R, then the greatest value of b is
- If the difference between the roots of x^2+ax+b=0 and x^2+bx+a=0 is same and a b, then
- If , are the roots of x^2+px+q=0 and also of x^ 2n +p^nx^n+q^n=0 and if , are the roots of x^n+1+(x+1)^n=0, then n is
- If is a root of the equation 2x(2x+1)=1, then the other root is
- If a(p+q)^2+2bpq+c=0 and a(p+r)^2+2bpr+c=0, then qr=
- p,q,r and s are integers. If the A.M. of the roots of x^2-px+q^2=0 and G.M. of the roots of x^2-rx+s^2=0 are equal, then
- If one root of the equation 8x^2-6x-a-3=0 is the square of the other, then the values of a are
- The sum of the real roots of the equation |x-2|^2+|x-2|-2=0, is
- The number of values of a for which (a^2-3a+2 )x^2+ (a^2-5a+6 )x+a^2-4=0 is an identity in x, is
- If a,b,c are in G.P., then the equations ax^2+2bx+c=0 and dx^2+2ex+f=0 have a common root if da, eb, fc are in
- Let , be the roots of ax^2+bx+c=0, and let ^n+ ^n=S_n for n 1. Then the value of the determinant vmatrix 3&1+S_1&1+S_2...