Mathematics questions
18011 published questions with worked solutions.
- Let S denote the set of all real values of a for which the roots of the equation x^2-2ax+a^2-1=0 lie between 5 and 10, then S...
- The set of values of a' for which x^2+ax+ ^ -1 (x^2-4x+5 )+ ^ -1 (x^2-4x+5 )=0 has at least one real root is given by
- If the equation 2x^2-7x+1=0 and ax^2+bx+2=0 have a common root, then
- The equation (x-b)(x-c)+(x-a)(x-b)+(x-a)(x-c)=0 has all its roots
- If a+b+c=0 and a c then the roots of the equation (b+c-a)x^2+(c+a-b)x+(a+b-c)=0, are
- The number of real roots of the equation |x|^2-3|x|+2=0 is
- If x+1 is a factor of x^4+(p-3)x^3-(3p-5)x^2+(2p-9)x+6, then p is
- If is a root of 25x^2+5x-12=0, -1<x<0. Then the value of 2 is
- If , are the roots of the equation x^2+px+q=0 and ^4, ^4 are the roots of x^2-rx+s=0, then the equation x^2-4qx+2q^2-r=0 has...
- 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