JEE Main questions
34495 published questions with worked solutions.
- Let f(x) + 2f ( 1 x ) = x^2 + 5 and 2g(x) - 3g ( 1 x ) = x, x > 0. If = _1^2 f(x)dx, and = _1^2 g(x)dx, then the value of 9 + is :
- Let A = –3, –2, –1, 0, 1, 2, 3 and R be a relation on A defined by xRy if and only if 2x - y 0, 1 . Let l be the number of...
- The centre of a circle C is at the centre of the ellipse E : x^2 a^2 + y^2 b^2 = 1, a > b. Let C pass through the foci F_1 and...
- Let the values of p, for which the shortest distance between the lines x+1 3 = y 4 = z 5 and r = (p i + 2 j + k ) + (2 i + 3 j +...
- Let the mean and the standard deviation of the observation 2, 3, 3, 4, 5, 7, a, b be 4 and 2 respectively. Then the mean...
- The sum of the infinite series ^ -1 ( 7 4 ) + ^ -1 ( 19 4 ) + ^ -1 ( 39 4 ) + ^ -1 ( 67 4 ) + is :
- If is a root of the equation x^2 + x + 1 = 0 and _ k=1 ^ n ( ^k + 1 ^k )^2 = 20, then n is equal to _____.
- If ( 1+x^2 +x)^ 10 ( 1+x^2 -x)^9 dx = 1 m (( 1+x^2 +x)^n(n 1+x^2 -x) )+c where C is the constant of integration and m, n N , then...
- Let the three sides of a triangle ABC be given by the vectors 2 i - j + k , i - 3 j - 5 k and 3 i - 4 j - 4 k . Let G be the...
- Displacement of a wave is expressed as x(t) = 5 (628t + 2 ) m. The wavelength of the wave when its velocity is 300 m/s is : ( =...
- In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension...
- Consider a n-type semiconductor in which n_e and n_h are number of electrons and holes, respectively. (A) Holes are minority...Not in JEE Advanced syllabus
- For the determination of refractive index of glass slab, a travelling microscope is used whose main scale contains 300 equal...
- An object is kept at rest at a distance of 3R above the earth's surface where R is earth's radius. The minimum speed with which...
- A wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim is 8 m/s. The speed of the...
- Two polarisers P_1 and P_2 are placed in such a way that the intensity of the transmitted light will be zero. A third polariser...
- Consider a rectangular sheet of solid material of length = 9 cm and width d = 4 cm. The coefficient of linear expansion is = 3.1...
- There are n number of identical electric bulbs, each is designed to draw a power p independently from the mains supply. They are...
- A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of 10^5 N at the top....
- A block of mass 25 kg is pulled along a horizontal surface by a force at an angle 45° with the horizontal. The friction...