JEE Advanced questions
3844 published questions with worked solutions.
- Let df(x) dx = e^ x x , x>0. If _1^4 3e^ x^3 x ,dx=f(k)-f(1) then one of the possible values of k is
- The differential equation (x) ,dy=y '(x)-y ,dx is changed in the form df(x,y)=0. Then f(x,y) is
- The solution of primitive integral equation (x^2+y^2) ,dy=xy dx is y=y(x). If y(1)=1 and y(x_0)=e then x_0 is
- ABCDEF is a regular hexagon where centre O is the origin. If the position vectors of A and B are i - j + 2 k and 2 i + j + k...
- The position vectors of two vertices and the centroid of a triangle are i + j, 2 i - j + k and k respectively. The position...
- Let the position vectors of the points A, B, C be i + 2 j + 3 k, - i - j + 8 k and -4 i + 4 j + 6 k respectively. Then the ABC is
- a, b, c are three vectors of which every pair is noncollinear. If the vectors a + b and b + c are collinear with c and a...
- If r = 3 i + 2 j - 5 k, a = 2 i - j + k, b = i + 3 j - 2 k and c = -2 i + j - 3 k such that r = a + b + c then
- The position vectors of three points are 2 a - b + 3 c, a - 2 b + c and a - 5 b where a, b, c are noncoplanar vectors. The points...
- If a = i + j + k, b = 4 i + 3 j + 4 k and c = i + j + k are linearly dependent vectors and | c| = 3 then
- Let OA = a and OB = b. A vector along one of the bisectors of the angle AOB is
- A vector has components 2p and 1 with respect to a rectangular cartesian system. The axes are rotated through an angle about the...
- Let | a| = | b| = | a - b| = 1. Then the angle between a and b is
- If a + b = 2 i and 2 a - b = i - j then the angle between a and b is
- Let | a| = 1, | b| = 2, | c| = 3, and a ( b + c), b ( c + a) and c ( a + b). Then | a + b + c| is
- ( a i) i + ( a j) j + ( a k) k is equal to
- If a, b are unit vectors such that a + b is also a unit vector then the angle between the vectors a and b is
- If a i = a ( i + j) = a ( i + j + k) = 1 then a is
- ( a i)^2 + ( a j)^2 + ( a k)^2 is equal to
- | a + b|^2 - | a - b|^2 is equal to