JEE Main questions
34495 published questions with worked solutions.
- Let A = (x, y) R × R : |x + y| 3 and B = (x, y) R × R : |x| + |y| 3 . If C = (x, y) A B : x = 0 or y = 0 , then _ (x,y) C |x+y| is
- The system of equations x + y + z = 6, x + 2y + 5z = 9, x + 5y + = , has no solution if
- Let x^3 x ,dx = g(x) + C, where C is the constant of integration. If 8 (g ( 2 ) + g' ( 2 ) ) = ^3 + ^2 + , , , Z. Then + - equals...
- A rod of length eight units moves such that its ends A and B always lie on the lines x – y + 2 = 0 and y + 2 = 0, respectively....
- The distance of the line x-2 2 = y-6 3 = z-3 4 from the point (1, 4, 0) along the line x 1 = y-2 2 = z+3 3 is :
- Let the point A divide the line segment joining the points P(–1, –1, 2) and Q(5, 5,10) internally in the ratio r : 1 (r > 0). If...
- If the area of the region (x, y) : –1 x 1, 0 y a + e^ |x| –e^ –x , a > 0 is e^2 + 8e + 1 e , then the value of a is :
- Let x = x(y) be the solution of the differential equation y = (x - y dx dy ) ( x y ), y > 0 and x(1) = 2 . Then (x(2)) is equal...
- Let the range of the function f(x) = 6 + 16 x ( 3 -x ) ( 3 +x ) 3x 6x, x R be [ , ]. Then the distance of the point ( , ) from...
- Let the shortest distance from (a, 0), a > 0, to the parabola y^2 = 4x be 4. Then the equation of the circle passing through the...
- Let X = R × R. Define a relation R on X as: (a_1, b_1) R (a_2, b_2) b_1 = b_2. Statement-I: R is an equivalence relation....
- The length of the chord of the ellipse x^2 4 + y^2 2 = 1, whose mid-point is (1, 1 2 ), is :
- Let A = [a_ ij ] be a 3 × 3 matrix such that A bmatrix 0 1 0 bmatrix = bmatrix 0 0 1 bmatrix , A bmatrix 4 1 3 bmatrix = bmatrix...
- The number of complex numbers z, satisfying |z| = 1 and | z z + z z | = 1, is
- If the square of the shortest distance between the lines x-2 1 = y-1 2 = z+3 -3 and x+1 2 = y+3 4 = z+5 -5 is m n , where m, n...
- If I = _0^ /2 ^ 3/2 x ^ 3/2 x + ^ 3/2 x dx, then _0^ 2I x x x ^4 x + ^4 x dx, equals :
- _ x (2x^2 - 3x + 5)(3x-1)^ x/2 (3x^2+5x+4) (3x+2)^x is equal to:
- The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together, is...
- The variance of the numbers 8, 21, 34, 47, …, 320, is _____.
- The roots of the quadratic equation 3x^2 – px + q = 0 are 10th and 11th terms of an arithmetic progression with common difference...