JEE Main questions
34495 published questions with worked solutions.
- If for x (0, 1 4 ), the derivative of ^ -1 ( 6x x 1 - 9x^3 ) is x g(x), then g(x) equals :
- The normal to the curve y(x – 2)(x – 3) = x + 6 at the point where the curve intersects the y-axis passes through the point :
- Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq....
- Let I_n = ^nx ,dx, (n > 1). If I_4 + I_6 = a ^5x + bx^5 + C, where C is a constant of integration, then the ordered pair (a, b)...
- The integral _ 4 ^ 3 4 dx 1 + x is equal to :
- The area (in sq. units) of the region (x, y) : x ≥ 0, x + y ≤ 3, x^2 4y and y 1 + x is :
- If (2 + x) dy dx + (y + 1) x = 0 and y(0) = 1, then y ( 2 ) is equal to :
- Let k be an integer such that the triangle with vertices (k, –3k), (5, k) and (–k, 2) has area 28 sq. units. Then the orthocentre...
- The radius of a circle, having minimum area, which touches the curve y = 4 - x^2 and the lines, y = |x| is :
- The eccentricity of an ellipse whose centre is at the origin is 1 2 . If one of its directrices is x = – 4, then the equation of...
- A hyperbola passes through the point P( 2 , 3 ) and has foci at (±2, 0). Then the tangent to this hyperbola at P also passes...
- The distance of the point (1, 3, –7) from the plane passing through the point (1, –1, –1), having normal perpendicular to both...
- Let a = 2 i + j - 2 k and b = i + j . Let c be a vector such that | c - a | = 3, |( a b ) c | = 3 and the angle between c and a b...
- A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of...
- For three events A, B and C, P (Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P(Exactly one of C or A occurs)...
- If two different numbers are taken from the set 0, 1, 2, 3, ……, 10 , then the probability that their sum as well as absolute...
- If 5( ^2x - ^2x) = 2 2x + 9, then the value of cos4x is :
- Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that...
- The following statement (p q) [( p q) q] is :Not in JEE syllabus
- The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative...