JEE Advanced questions
579 published questions with worked solutions.
- Let complex numbers α and 1 lie on circles (x - x_0)^2 + (y - y_0)^2 = r^2 and (x - x_0)^2 + (y - y_0)^2 = 4r^2, respectively. If...
- Four persons independently solve a certain problem correctly with probabilities 1 2 , 3 4 , 1 4 , 1 8 . Then the probability that...
- The number of points in (−∞, ∞), for which x^2 - x x - x = 0, is
- The area enclosed by the curves y = x + x and y = | x - x| over the interval [0, 2 ] is
- A curve passes through the point (1, 6 ). Let the slope of the curve at each point (x, y) be y x + ( y x ), x > 0. Then the...
- The value of ( _ n=1 ^ 23 ^ -1 (1 + _ k=1 ^ n 2k ) ) is
- Perpendiculars are drawn from points on the line x + 2 2 = y + 1 -1 = z 3 to the plane x + y + z = 3. The feet of perpendiculars...
- Let PR = 3 i + j - 2 k and SQ = i - 3 j - 4 k determine diagonals of a parallelogram PQRS and PT = i + 2 j + 3 k be another...
- Let S_n = _ k=1 ^ 4n (-1)^ k(k+1) 2 k^2. Then S_n can take value(s)
- For 3 × 3 matrices M and N, which of the following statement(s) is (are) **NOT** correct ?
- Let f(x) = x x, x > 0. Then for all natural numbers n, f'(x) vanishes at
- A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8 : 15 is converted into an open rectangular...
- A line l passing through the origin is perpendicular to the lines l_1 : (3 + t) i + (-1 + 2t) j + (4 + 2t) k, - < t < l_2 : (3 +...
- A vertical line passing through the point (h, 0) intersects the ellipse x^2 4 + y^2 3 = 1 at the points P and Q. Let the tangents...
- Consider the set of eight vectors V = a i + b j + c k : a, b, c -1, 1 . Three non-coplanar vectors can be chosen from V in 2^p...
- Using the expression 2d sin θ = λ, one calculates the values of d by measuring the corresponding angles θ in the range 0 to 90°....
- Two bodies, each of mass M, are kept fixed with a separation 2L. A particle of mass m is projected from the midpoint of the line...
- A particle of mass m is attached to one end of a mass-less spring of force constant k, lying on a frictionless horizontal plane....
- A steady current I flows along an infinitely long hollow cylindrical conductor of radius R. This cylinder is placed coaxially...
- Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other. Wind blows along the...