JEE Advanced questions
3844 published questions with worked solutions.
- The area of the region between the curves y = x + x and y = x - x bounded by the lines x = 0 and x = 4 is
- Consider a branch of the hyperbola x^2 - 2y^2 - 2 2 x - 4 2 y - 6 = 0 with vertex at the point A. Let B be one end of its latus...
- The edges of a parallelopiped are of unit length and are parallel to noncoplanar unit vectors a, b, c such that a b = b c = c a =...
- If 0 < x < 1, then 1 + x^2 [ x ( ^ -1 x) + ( ^ -1 x) ^2 - 1 ]^ 1/2 =
- Let two non-collinear unit vectors a and b form an acute angle. A point P moves so that at any time t the position vector OP...
- A particle P starts from the point z_0 = 1 + 2i, where i = -1 . It moves first horizontally away from origin by 5 units and then...
- Let a, b be non-zero real numbers. The equation (ax^2 + by^2 + c)(x^2 - 5xy + 6y^2) = 0 represents
- Let f(x) be a non-constant twice differentiable function defined on (- , ) such that f(x) = f(1 - x) and f' ( 14 ) = 0. Then,
- Let P(x_1, y_1) and Q(x_2, y_2); where y_1 < 0, y < 0 be the end points of the latus rectum of the ellipse x^2 + 4y^2 = 4. The...
- Suppose four distinct positive numbers a_1, a_2, a_3, a_4 are in GP. Let b_1 = a_1, b_2 = b_1 + a_2, b_3 = b_2 + a_3 and b_4 =...
- Consider the system of equations cases x - 2y + 3z = -1 -x + y - 2z = k x - 3y + 4z = 1 cases STATEMENT-1: The system of...
- Consider the system of equations ax + by = 0, cx + dy = 0; where a, b, c, d 0, 1 . STATEMENT-1: The probability that the system...
- Let f and g be real-valued functions defined on interval (-1, 1) such that g''(x) is continuous, g(0) 0, g'(0) = 0, g''(0) 0 and...
- Consider L_1 : 2x + 3y + p - 3 = 0, L_2 : 2x + 3y + p + 3 = 0, where p is a real number and C : x^2 + y^2 + 6x - 10y + 30 = 0....
- Let a, b, c, p, q be real numbers. Suppose , are the roots of the equation x^2 + 2px + q = 0 and , 1 are the roots of the...
- Let a solution y = y(x) of the differential equation x x^2 - 1 ,dy - y y^2 - 1 ,dx = 0 satisfy y(2) = 2 3 . STATEMENT-1: y(x) = (...
- Consider the lines given by L_1 : x + 3y - 5 = 0, L_2 : 3x - ky - 1 = 0, L_3 : 5x + 2y - 12 = 0 Column I: (A) L_1, L_2, L_3 are...
- Consider all possible permutations of letters of the word ENDEANOEL. Column I: (A) The number of permutations containing the word...
- Tangents drawn from the point P(1, 8) to the circle x^2 + y^2 - 6x - 4y - 11 = 0 touch the circle at the points A and B. The...
- The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse x^2 + 9y^2 = 9 meets...