Mathematics questions
18011 published questions with worked solutions.
- Let S be the set of all real roots of the equation, 3^x(3^x-1)+2=|3^x-1|+|3^x-2|. Then S :
- The differential equation of the family of curves, x^2=4b(y+b), b R, is :
- If a line, y = mx + c is a tangent to the circle, (x-3)^2+y^2=1 and it is perpendicular to a line L_1, where L_1 is the tangent...
- The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation...
- Let a line y = mx (m > 0) intersect the parabola, y^2=x at a point P, other than the origin. Let the tangent to it at P meet the...
- The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word 'EXAMINATION' is...
- The sum, _ n=1 ^ 7 n(n+1)(2n+1) 4 is equal to ______.
- If 2 1+ 2 = 1 7 and 1- 2 2 = 1 10 , , (0, 2 ), then ( +2 ) is equal to _______.
- Let f(x) be a polynomial of degree 3 such that f(– 1) = 10, f(1) = – 6, f(x) has a critical point at x = – 1 and f '(x) has a...
- The area (in sq. units) of an equilateral triangle inscribed in the parabola y^2=8x, with one of its vertices on the vertex of...
- Let n > 2 be an integer. Suppose that there are n Metro stations in a city located along a circular path. Each pair of stations...
- If the equation ^4 + ^4 + =0 has real solutions for , then lies in the interval :Not in JEE Main syllabus
- Let f(x) be a quadratic polynomial such that f(–1) + f(2) = 0. If one of the roots of f(x) = 0 is 3, then its other root lies in :
- Let a, b, c R be all non-zero and satisfy a^3+b^3+c^3=2. If the matrix A= pmatrix a&b&c &c&a &a&b pmatrix satisfies A^TA=I, then...
- Let f : (–1, ∞) → R be defined by f(0) = 1 and f(x)= 1 x _e(1+x), x 0. Then the function f :
- If the sum of first 11 terms of an A.P., a_1, a_2, a_3, ........ is 0 (a_1 0), then the sum of the A.P., a_1, a_3, a_5, ..., a_...
- The imaginary part of (3+2 -54 )^ 1/2 - (3-2 -54 )^ 1/2 can be :
- _ x 0 ( ( 4 +x ) )^ 1/x is equal to :
- The equation of the normal to the curve y=(1+x)^ 2y + ^2( ^ -1 x) at x = 0 is :
- For some (0, 2 ), if the eccentricity of the hyperbola, x^2-y^2 ^2 =10 is 5 times the eccentricity of the ellipse, x^2 ^2 +y^2=5,...