JEE Advanced questions
3844 published questions with worked solutions.
- Let a, b, c be the lengths of sides of a scalene triangle. If the roots of the equation x^2 + 2(a+b+c)x + 3 (ab + bc + ca) = 0 (...
- If A = bmatrix 1 & 0 & 0 0 & 1 & 1 0 & -2 & 4 bmatrix and A^ -1 = 16(A^2 + cA + dI), where I is the identity matrix, then the...
- Let A be a vector parallel to the line of intersection of the planes P_1 and P_2 through the origin. The plane P_1 is parallel to...
- The equations of common tangents to the parabolas y = x^2 and y = -(x-2)^2 are
- Let f(x) = cases e^x & for 0 x 1 2 - e^ x-1 & for 1 < x 2 x - e & for 2 < x 3 cases and g(x) = _0^x f(t) ,dt, 1 x 3. Then g(x) has
- Normals are drawn at points P, Q and R lying on the parabola y^2 = 4x and they intersect at (3, 0). Then Column I: (i) Area of...
- The value of 5050 _0^1(1 - x^ 50 )^ 100 ,dx _0^1(1 - x^ 50 )^ 101 ,dx is
- Let = - 12 + i 3 2 . Then the value of the determinant vmatrix 1 & 1 & 1 1 & -1- ^2 & ^2 1 & ^2 & ^4 vmatrix is
- For all complex numbers z_1, z_2 satisfying |z_1| = 12 and |z_2 - 3 - 4i| = 5, the minimum value of |z_1 - z_2| is
- The number of values of k for which the system of equations cases (k+1)x + 8y = 4k, k x + (k+3)y = 3k - 1 cases has infinitely...
- The length of the longest interval in which the function 3 x - 4 ^3 x is increasing is
- Let 0 < < 2 be a fixed angle. If P = ( , ) and Q = ( ( - ), ( - ) ) then Q is obtained from P by
- If the tangent at the point P on the circle x^2 + y^2 + 6x + 6y = 2 meets the straight line 5x - 2y + 6 = 0 at a point Q on the...
- The locus of the midpoint of the line segment joining the focus to a moving point on the parabola y^2 = 4ax is another parabola...
- The area bounded by the curves y = |x| - 1 and y = -|x| + 1 is
- Suppose f(x) = (x+1)^2 for x -1. If g(x) is the function whose graph is the reflection of the graph of f(x) with respect to the...
- The domain of the derivative of the function f(x) = cases ^ -1 x & for |x| 1 [2pt] 12(|x| - 1) & for |x| > 1 cases is
- The integer n for which _ x 0 ( x - 1)( x - e^x) x^n is a finite nonzero number is
- Let f: R R be such that f(1) = 3 and f'(1) = 6. Then _ x 0 f(1+x) f(1) ^ 1/x equals
- The point(s) on the curve y^3 + 3x^2 = 12y, where the tangent is vertical (i.e., parallel to the y-axis), is/are