Mathematics questions
18011 published questions with worked solutions.
- Let |z| 1. If m and n represent max. |z-3| and min. |z-3| respectively, then find m^2-n^2.
- If -7-24i =x+iy, then find x^2+y^2.
- ABCD is a rhombus such that its diagonals AC and BD intersect at point M and satisfy BD=2AC. If points D and M represent the...
- If x+iy= 1 1+ +i , then find 4x^2.
- Let p,q R and (1- 3i )^ 200 =2^ 199 (p+iq), i= -1 . Then p+q+q^2 and p-q+q^2 are roots of the equation
- Let , , be the three roots of the equation x^3+bx+c=0. If =1=- , then b^3+2c^3-3 ^3-6 ^3-8 ^3 is equal to
- The sum of all the roots of the equation |x^2-8x+15 |-2x+7=0 is
- The number of real roots of the equation x|x|-5|x+2|+6=0, is
- For a C, let A= z C: Re (a+ z)> Im ( a+z) and B= z C: Re (a+ z)< Im ( a+z) . The among the two statements: (S1): If Re (a), Im...
- Let the complex number z=x+iy be such that 2z-3i 2z+i is purely imaginary. If x+y^2=0, then y^4+y^2-y is equal to
- Let A= (0,2 ): 1+2i 1-i is purely imaginary . Then the sum of the elements in A is
- If for z= +i , |z+2|=z+4(1+i), then + and are the roots of the equation
- If and are the roots of the equation x^2-x+1=0, then ^ 101 + ^ 107 is equal to
- Let for a a_1 0, f(x)=ax^2+bx+c, g(x)=a_1x^2+b_1x+c_1 and p(x)=f(x)-g(x). If p(x)=0 only for x=-1 and p(-2)=2, then the value of...
- Sachin and Rahul attempted to solve a quadratic equation. Sachin made a mistake in writing down the constant term and ended up in...
- If both the roots of the quadratic equation x^2-mx+4=0 are real and distinct and they lie in the interval [1,5] then m lies in...
- The number of all possible positive integral values of for which the roots of the quadratic equation, 6x^2-11x+ =0 are rational...
- Consider the quadratic equation (c-5)x^2-2cx+(c-4)=0, c 5. Let S be the set of all integral values of c for which one root of the...
- The value of such that sum of the squares of the roots of the quadratic equation, x^2+(3- )x+2= has the least value is
- If one real root of the quadratic equation 81x^2+kx+256=0 is cube of the other root, then a value of k is