JEE Main questions
34495 published questions with worked solutions.
- Let y^2 = 12x be the parabola with its vertex at O. Let P be a point on the parabola and A be a point on the x-axis such that OPA...
- Let one end of a focal chord of the parabola y^2 = 16x be (16, 16). If P( , ) divides this focal chord internally in the ratio...
- Let the line L pass through the point (-3, 5, 2) and make equal angles with the positive coordinate axes. If the distance of L...
- Let and be the roots of equation x^2 + 2ax + (3a + 10) = 0 such that < 1 < . Then the set of all possible values of a is:
- Let a_1, a_2 2 , a_3 2^2 , , a_ 10 2^9 be a G.P. of common ratio 1 2 . If a_1 + a_2 + + a_ 10 = 62, then a_1 is equal to:
- Let A = x : |x^2 - 10| 6 and B = x : |x - 2| > 1 . Then
- For a triangle ABC, let p = BC , q = CA and r = BA . If | p | = 2 3 , | q | = 2 and = 1 3 , where is the angle between p and q ,...
- Let y = y(x) be the solution of the differential equation x dy dx - 2y = 2 + 3 x, x (- 2 , 2 ), y(0) = - 7 4 . Then y ( 6 ) is...
- Let A = 2, 3, 5, 7, 9 . Let R be the relation on A defined by x R y if and only if 2x 3y. Let be the number of elements in R, and...
- If the system of equations 3x + y + 4z = 3 2x + y - z = -3 x + 2y + z = 4 has no solution, then the value of is equal to:
- The largest n N, for which 7^n divides 101!, is:
- Let [.] denote the greatest integer function and f(x) = _ n 1 n^3 _ k=1 ^ n [ k^2 3^x ]. Then 12 _ j=1 ^ f(j) is equal to _____.
- If _0^1 4 ^ -1 (1 - 2x + 4x^2) , dx = a ^ -1 (2) - b _e(5), where a, b N, then (2a + b) is equal to _____.
- Let the maximum value of ( ^ -1 x)^2 + ( ^ -1 x)^2 for x [- 3 2 , 1 2 ] be m n ^2, where (m, n) = 1. Then m + n is equal to _____.
- If ( 1 ^ 15 C_0 + 1 ^ 15 C_1 ) ( 1 ^ 15 C_1 + 1 ^ 15 C_2 ) ( 1 ^ 15 C_ 12 + 1 ^ 15 C_ 13 ) = ^ 13 ^ 14 C_0 ,^ 14 C_1 , ^ 14 C_ 12...
- If P is a point on the circle x^2 + y^2 = 4, Q is a point on the straight line 5x + y + 2 = 0 and x - y + 1 = 0 is the...
- Consider two identical metallic spheres of radius R each having charge Q and mass m. Their centers have an initial separation of...
- A capacitor C is first charged fully with potential difference of V_0 and disconnected from the battery. The charged capacitor is...
- The r.m.s speed of oxygen molecules at 47°C is equal to that of the hydrogen molecules kept at _____ °C. (Mass of oxygen...
- The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of 176 rad/s. The frequency of this...