Mathematics questions
18011 published questions with worked solutions.
- If for the complex numbers z satisfying |z-2-2i| 1, the maximum value of |3iz+6| is attained at a + ib, then a + b is equal to...
- Let the points of intersections of the lines x – y + 1 = 0, x – 2y + 3 = 0 and 2x – 5y + 11 = 0 are the mid points of the sides...
- All the arrangements, with or without meaning, of the word FARMER are written excluding any word that has two R appearing...
- If the sum of the coefficients in the expansion of (x+y)^n is 4096, then the greatest coefficient in the expansion is _________.
- Let a =2 i - j +2 k and b = i +2 j - k .r Let a vector v be in the plane containing a and b . If v is perpendicular to the vector...
- Let [t] denote the greatest integer t. The number of points where the function f(x)=[x]|x^2-1|+ ( [x]+3 )-[x+1], x (–2,2) is not...
- The maximum value of f(x)= vmatrix ^2x&1+ ^2x& 2x 1+ ^2x& ^2x& 2x ^2x& ^2x& 2x vmatrix , x is:
- Let A denote the event that a 6-digit integer formed by 0, 1, 2, 3, 4, 5, 6 without repetitions, be divisible by 3. Then...
- Let R be such that the function f(x)= cases ^ -1 (1- x ^2) ^ -1 (1- x ) x - x ^3 , & x 0 , & x=0 cases is continuous at x = 0,...
- If (x, y, z) be an arbitrary point lying on a plane P which passes through the point (42, 0, 0), (0, 42, 0) and (0, 0, 42), then...
- Let C be the locus of the mirror image of a point on the parabola y^2=4x with respect to the line y = x. Then the equation of...
- If y = y(x) is the solution of the differential equation dy dx +( x)y= x, 0 x 3 , with y(0) = 0, then y ( 4 ) equal to:
- Let A = 2, 3, 4, 5, ...., 30 and ' ' be an equivalence relation on A × A, defined by (a, b) (c, d), if and only if ad = bc. Then...
- Let the lengths of intercepts on x-axis and y-axis made by the circle x^2+y^2+ax+2ay+c=0, (a < 0) be 2 2 and 2 5, respectively....
- The least value of |z| where z is complex number which satisfies the inequality ( (|z|+3)(|z|-1) |z|+1| _e2 ) _ 2 |5 7+9i|, i= -1...
- Consider a rectangle ABCD having 5, 7, 6, 9 points on the line segments AB, CD, BC, DA respectively. Let be the number of...
- If the point of intersections of the ellipse x^2 16 + y^2 b^2 =1 and the circle x^2+y^2=4b, b > 4 lie on the curve y^2=3x^2, then...
- Given that the inverse trigonometric functions take principal values only. Then, the number of real values of x which satisfy ^...
- Let A(–1, 1), B(3, 4) and C(2, 0) be given three points. A line y = mx, m > 0, intersects lines AC and BC at point P and Q...
- Let f be a real valued function, defined on R – –1, 1 & given by f(x)=3 _e | x-1 x+1 |- 2 x-1 . Then in which of the following...