Mathematics questions
18011 published questions with worked solutions.
- All the values of m for which both roots of the equation x^2-2mx+m^2-1=0 are greater than -2 but less than 4 lie in the interval
- Let a,b,c be real. If ax^2+bx+c=0 has two real roots and , where <-1 and >1, then 1+ ca+ | ba | is
- If ax^2+bx+c=0 and 2x^2+3x+4=0 have a common root where a,b,c N (set of natural numbers), the least value of a+b+c is
- If x is real, then x^2-2x+4 x^2+2x+4 takes values in the interval
- If x is real, the expression x^2+34x-71 x^2+2x-7 takes all values except those which lie in the interval (a,b) where
- If (x^2-3x+2 ) is a factor of x^4-px^2+q=0, then the values of p and q are
- If x is real, then the minimum value of x^2-x+1 x^2+x+1 , is
- If the roots of the equation bx^2+cx+a=0 be imaginary, then for all real values of x, the expression 3b^2x^2+6bcx+2c^2 is
- If x is real, then the value of x+2 2x^2+3x+6 lies in
- The values of k for which the equations x^2-kx-21=0 and x^2-3kx+35=0 will have a common roots are
- If x^2+x+1 x^2+2x+1 =A+ B x+1 + C (x+1)^2 , then A-B is equal to
- If x^3 (2x-1)(x+2)(x-3) =A+ B 2x-1 + C x+2 + D x-3 , then A is equal to
- The partial fraction of 3x^3-8x^2+10 (x-1)^4 is
- If 3x (x-a)(x-b) = 2 x-a + 1 x-b , then a:b is equal to
- If x-4 x^2-5x+6 can be expanded in the ascending powers of x, then the coefficient of x^3 is
- If a real valued function f of a real variable x such that 1 (1+x) (1+x^2 ) = A 1+x + f(x) 1+x^2 , then f(x) is equal to
- Let a,b and c be such that 1 (1-x)(1-2x)(1-3x) = a 1-x + b 1-2x + c 1-3x , then a1+ b3+ c5 is equal to
- If x+1 (2x-1)(3x+1) = A 2x-1 + B 3x+1 , then 16A+9B is equal to
- If 3x+2 (x+1) (2x^2+3 ) = A x+1 + Bx+C 2x^2+3 , then A+C-B is equal to
- If is a cube root of unit and is not real, then ^ 3n+1 + ^ 3n+3 + ^ 3n+5 has the value