Mathematics questions
18011 published questions with worked solutions.
- Let f : R R be defined as f(x) = e^ -x x. If F : [0, 1] R is a differentiable function such that F(x) = _0^xf(t)dt, then the...
- If the integral _0^ 10 [ 2 x] e^ x-[x] dx= e^ -1 + e^ - 1 2 + (given), where , , are integers and [x] denotes the greatest...
- Let y = y(x) be the solution of the differential equation x(3 x+ x+3)dy=(1+y x(3 x+ x+3))dx, 0 x 2 , y(0) = 0. Then y ( 3 ) is...
- The value of _ r=0 ^6( ^6C_r. ^6C_ 6-r ) is equal to :
- The value of _ n [r]+[2r]+ +[nr] n^2 , where r is non-zero real number and [r] denotes the greatest integer less than or equal to...
- The number of solutions of the equation ^ -1 [x^2+ 1 3 ]+ ^ -1 [x^2- 2 3 ]=x^2, for x [–1, 1], and [x] denotes the greatest...Not in JEE Main syllabus
- Let k be an integer such that the triangle with vertices (k, –3k), (5, k) and (–k, 2) has area 28 sq. units. Then the orthocentre...
- Let (4x^2)+4-4(4^x)-32=0 have the solution x = 2. Then evaluating the determinant vmatrix 3&1&4 1&0&2 2&1&0 vmatrix gives :
- For |z-1| 2, z lies on and inside the circle of radius 2 units and centre (1, 0). Let S_1, S_2, S_3 be sets defined using this...
- If the curve y = y(x) is the solution of the differential equation 2(x^2+x^ 5/4 )dy-y(x+x^ 1/4 )dx=2x^ 9/4 dx, x > 0, which...
- If x, y, z are in arithmetic progression with common difference d, x 3d, and the determinant of the matrix vmatrix 3&4 2&x 4&5...
- Let O be the origin. Let OP =x i +y j - k and OQ =- i +2 j +3x k , x, y R, x > 0, be such that | PQ |= 20 and the vector OP is...
- Consider the function f : R R defined by f(x)= (2- ( 1 x ) )|x|, x 0; 0, x=0 . Then f is :
- Let L be a tangent line to the parabola y^2=4x-20 at (6, 2). If L is also a tangent to the ellipse x^2 2 + y^2 b =1, then the...
- The value of the limit _ 0 ( ^2 ) (2 ^2 ) is equal to :
- Let the tangent to the circle x^2+y^2=25 at the point R(3, 4) meet x-axis and y-axis at point P and Q, respectively. If r is the...
- If the Boolean expression (p q) (p q) is a tautology, then and are respectively given byNot in JEE syllabus
- If the equation of plane passing through the mirror image of a point (2, 3, 1) with respect to line x+1 2 = y-3 1 = z+2 -1 and...
- If 1, _ 10 (4^x-2) and _ 10 (4^x+ 18 5 ) are in arithmetic progression for a real number x, then the value of the determinant...
- Let f : [–1, 1] R be defined as f(x) = ax^2+bx+c for all x [–1, 1], where a, b, c R such that f(–1) = 2, f'(–1) = 1 and for x...