Mathematics questions
18011 published questions with worked solutions.
- If z any complex number satisfying |z-3-2i| 2, then the minimum value of |2z-6+5i| is
- For an integer k, let _k= [ k 7 ]+i [ k 7 ], where i= -1 . The value of the expression _ k=1 ^ 12 | _ k+1 - _k| _ k=1 ^3| _ 4k-1...
- Let =e^ i /3 and a,b,c,x,y,z be non-zero complex numbers such that (relations not printed in the source). Then, the value of...
- The smallest value of k, for which both the roots of the equation x^2-8kx+16 (k^2-k+1 )=0 are real, distinct and have values at...
- For a positive integer n, if the quadratic equation x(x+1)+(x+1)(x+2)+ +(x+n-1)(x+n)=10n has two consecutive integral solutions,...
- Let - 6< <- 12 . Suppose _1 and _1 are the roots of the equation x^2-2x +1=0, and _2 and _2 are the roots of the equation x^2+2x...
- Let and be the roots of equation x^2-6x-2=0. If a_n= ^n- ^n for n 1, then the value of a_ 10 -2a_8 2a_9 is
- The quadratic equation p(x)=0 with real coefficients has purely imaginary roots. Then the equation p(p(x))=0 has
- Let and be the roots of equation px^2+qx+r=0, p 0. If p,q and r are in A.P. and 1 + 1 =4, then the value of | - | is
- The set of all real numbers x for which x^2-|x+2|+x>0 is
- The number of solutions of _4(x-1)= _2(x-3) is
- If the equations x^2+2x+3=0 and ax^2+bx+c=0, a,b,c R have a common root, then a:b:c is
- A value of b for which the equations x^2+bx-1=0 and x^2+x+b=0 have one root in common is
- Let , be the roots of the equation (x-a)(x-b)=c, c 0. Then the roots of the equation (x- )(x- )+c=0 are
- If a R and the equation -3 (x-[x] )^2+2 (x-[x] )+a^2=0 (where [x] denotes the greatest integer x) has no integral solution, then...
- The real number k for which the equation 2x^3+3x+k=0 has two distinct real roots in [0,1]
- Let a,b,c be non-zero real numbers such that _0^1 (1+ ^8x ) (ax^2+bx+c )dx= _0^2 (1+ ^8x ) (ax^2+bx+c )dx. Then the quadratic...
- If and are the roots of the equation x^2-5x+1=0, then find the value of 1 ( -5)^2 + 1 ( -5)^2 .
- Find the sum of the roots of the equation 2 (x^2+ 1 x^2 )-9 (x+ 1x )+14=0, x R.
- Find the number of all possible positive integral values of for which the roots of 7x^2-15x+ =0 are rational numbers.