Mathematics questions
18011 published questions with worked solutions.
- Let S = z ℂ : |z − 3| 1 and z(4 + 3i) + z̄(4 − 3i) 24 . If + i is the point in S which is closest to 4i, then 25( + ) is equal to...
- The number of 7-digit numbers which are multiples of 11 and are formed using all the digits 1, 2, 3, 4, 5, 7 and 9 is _____.
- The remainder on dividing 1 + 3 + 3^ 2 + 3^ 3 + … + 3^ 2021 by 50 is _____.
- The area (in sq. units) of the region enclosed between the parabola y^ 2 = 2x and the line x + y = 4 is _____.
- Let a circle C : (x - h)^ 2 + (y - k)^ 2 = r^ 2 , k > 0, touch the x-axis at (1, 0). If the line x + y = 0 intersects the circle...
- Let the hyperbola H : x^ 2 /a^ 2 - y^ 2 = 1 and the ellipse E : 3x^ 2 + 4y^ 2 = 12 be such that the length of latus rectum of H...
- The sum of slopes of lines 3x^2+5xy-2y^2=0 is
- The equation y= 3x, y=1 are the sides of
- The equation 12x^2+7xy+ay^2+13x+9y+3=0 represents a pair of perpendicular lines. Then, the value of 'a' is
- The polar equation +7 = 1r represents a
- If the equation 4x^2+hxy+y^2=0 represent coincident lines, then h is equal to
- The equation of the straight line perpendicular to 5x-2y=7 and passing through the point of intersection of the lines 2x+3y=1 and...
- A square of side a lies above the x-axis and has one vertex at origin. The side passing through the origin makes an angle (0< < 4...
- The points (1,1), (-5,5) and (13, ) lie on the same straight line, if is equal to
- The equation to a pair of opposite sides of a parallelogram are x^2-5x+6=0 and y^2-6y+5=0, the equation to its diagonals are
- The equation of the pair of straight lines perpendicular to the pair 2x^2+3xy+2y^2+10x+5y=0 and passing through the origin, is
- Given four lines with equations x+2y-3=0, 2x+3y-4=0, 3x+4y-5=0, 4x+5y-6=0 These lines are
- The pairs of straight lines x^2-3xy+2y^2=0 and x^2-3xy+2y^2+x-2=0 form a
- The equation of the sides of a triangle are x-3y=0, 4x+3y=5 and 3x+y=0. The line 3x-4y=0 passes through
- The equation of straight line through the intersection of the lines x-2y=1 and x+3y=2 and parallel to 3x+4y=0, is