JEE Main questions
34495 published questions with worked solutions.
- The smallest natural number n, such that the coefficient of x in the expansion of (x^2 + 1 x^3 )^n is ^nC_ 23 , is:
- The sum of the real roots of the equation vmatrix x & -6 & -1 2 & -3x & x-3 -3 & 2x & x+2 vmatrix = 0, is equal to:
- If 5x + 9 = 0 is the directrix of the hyperbola 16x^2 - 9y^2 = 144, then its corresponding focus is:
- The area (in sq. units) of the region bounded by the curves y = 2^x and y = |x + 1|, in the first quadrant is:
- If the line ax + y = c, touches both the curves x^2 + y^2 = 1 and y^2 = 4 2 ,x, then |c| is equal to:
- The integral _ /6 ^ /3 ^ 2/3 x , cosec ^ 4/3 x ,dx is equal to:
- Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar...
- If x^5e^ -x^2 dx = g(x)e^ -x^2 + c, where c is a constant of integration, then g(−1) is equal to:
- Let y = y(x) be the solution of the differential equation, dy dx + y x = 2x + x^2 x, x (- 2 , 2 ), such that y(0) = 1. Then:
- The tangent and normal to the ellipse 3x^2 + 5y^2 = 32 at the point P(2, 2) meet the x-axis at Q and R, respectively. Then the...
- If the tangent to the curve y = x x^2-3 , x R , (x 3), at a point (α, β) ≠ (0, 0) on it is parallel to the line 2x + 6y - 11 = 0,...
- Lines are drawn parallel to the line 4x - 3y + 2 = 0, at a distance 3 5 from the origin. Then which one of the following points...
- The negation of the Boolean expression s ( r s) is equivalent to:Not in JEE syllabus
- If both the mean and the standard deviation of 50 observations x_1, x_2, , x_ 50 are equal to 16, then the mean of (x_1 - 4)^2,...
- Let a_1, a_2, a_3, be an A.P. with a_6 = 2. Then the common difference of this A.P., which maximises the product a_1a_4a_5, is:
- If ^ -1 x - ^ -1 y 2 = , where -1 x 1, -2 y 2, x y 2 , then for all x, y, 4x^2 - 4xy + y^2 is equal to:
- A perpendicular is drawn from a point on the line x-1 2 = y+1 -1 = z 1 to the plane x + y + z = 3 such that the foot of the...
- The relative error in the determination of the surface area of a sphere is . Then the relative error in the determination of its...
- An ideal capacitor of capacitance 0.2 µF is charged to a potential difference of 10V. The charging battery is then disconnected....
- Two electrons are moving with non-relativistic speeds perpendicular to each other. If corresponding de Broglie wavelengths are _1...