Mathematics questions
18011 published questions with worked solutions.
- Let y = y(x) be the solution curve of the differential equation (1 + x^2)dy + (y - ^ -1 x)dx = 0, y(0) = 1. Then the value of...
- The number of strictly increasing functions f from the set 1, 2, 3, 4, 5, 6 to the set 1, 2, 3, , 9 such that f(i) i for 1 i 6,...
- Let f : R (0, ) be a twice differentiable function such that f(3) = 18, f'(3) = 0 and f''(3) = 4. Then _ x 1 ( _e ( f(2+x) f(3)...
- Let the foci of hyperbola coincide with the foci of the ellipse x^2 36 + y^2 16 = 1. If the eccentricity of the hyperbola is 5,...
- The value of _ - /6 ^ /6 ( + 4x^ 11 1 - (|x| + /6) )dx is equal to
- If the coefficient of x in the expansion of (ax^2 + bx + c)(1 - 2x)^ 26 is -56 and the coefficients of x^2 and x^3 are both zero,...
- If x^2 + x + 1 = 0, then the value of (x + 1 x )^4 + (x^2 + 1 x^2 )^4 + (x^3 + 1 x^3 )^4 + + (x^ 25 + 1 x^ 25 )^4 is :
- The value of 10° - 3 10° is equal to:
- The sum of all the roots of the equation (x-1)^2 - 5|x-1| + 6 = 0, is:
- Let a_1 = 1 and for n 1, a_ n+1 = 1 2 a_n + n^2 - 2n - 1 n^2(n+1)^2 . Then | _ n=1 ^ (a_n - 2 n^2 ) | is equal to
- For some , R, let A = bmatrix & 2 1 & 2 bmatrix and B = bmatrix 1 & 1 1 & bmatrix be such that A^2 - 4A + 2I = B^2 - 3B + I = O....
- 6 _0^ |( 3x + 2x + x)| ,dx is equal to _____
- The positive integer n, for which the solutions of the equation x(x+2)+(x+2)(x+4)+....+(x+2n-2)(x+2n) = 8n 3 are two consecutive...
- Let f : R R be a twice differentiable function such that f''(x) > 0 for all x R and f'(a-1) = 0, where a is a real number. Let...
- Let f(x) = x^3 + x^2 f'(1) + 2xf''(2) + f'''(3), x R. Then the value of f'(5) is:
- If the line x + 4y = 7 , where R, touches the ellipse 3x^2 + 4y^2 = 1 at the point P in the first quadrant, then one of the focal...
- Let y^2 = 12x be the parabola with its vertex at O. Let P be a point on the parabola and A be a point on the x-axis such that OPA...
- Let one end of a focal chord of the parabola y^2 = 16x be (16, 16). If P( , ) divides this focal chord internally in the ratio...
- Let the line L pass through the point (-3, 5, 2) and make equal angles with the positive coordinate axes. If the distance of L...
- Let and be the roots of equation x^2 + 2ax + (3a + 10) = 0 such that < 1 < . Then the set of all possible values of a is: