JEE Advanced questions
3844 published questions with worked solutions.
- Let f: R R be a function defined by f(x)= cases [x], & x 2 0, & x>2 cases , where [x] is the greatest integer less than or equal...
- A cylindrical container is to be made from certain solid material with the following constraints: It has a fixed inner volume of...
- Let X and Y be two arbitrary, 3 3, non-zero, skew-symmetric matrices and Z be an arbitrary 3 3, non-zero, symmetric matrix. Then...
- Which of the following values of satisfy the equation vmatrix (1+ )^2 & (1+2 )^2 & (1+3 )^2 (2+ )^2 & (2+2 )^2 & (2+3 )^2 (3+ )^2...
- In R ^3, consider the planes P_1:y=0 and P_2:x+z=1. Let P_3 be a plane, different from P_1 and P_2, which passes through the...
- In R ^3, let L be a straight line passing through the origin. Suppose that all the points on L are at a constant distance from...
- Let P and Q be distinct points on the parabola y^2=2x such that a circle with PQ as diameter passes through the vertex O of the...
- Let y(x) be a solution of the differential equation (1+e^x)y'+ye^x=1. If y(0)=2, then which of the following statements is (are)...
- Consider the family of all circles whose centers lie on the straight line y=x. If this family of circles is represented by the...
- Let g: R R be a differentiable function with g(0)=0, g'(0)=0 and g'(1) 0. Let f(x)= cases x |x| g(x), & x 0 0, & x=0 cases and...
- Let f(x)= ( 6 ( 2 x ) ) for all x R and g(x)= 2 x for all x R . Let (f g)(x) denote f(g(x)) and (g f)(x) denote g(f(x)). Then...
- Let PQR be a triangle. Let a = QR , b = RP and c = PQ . If | a |=12, | b |=4 3 and b c =24, then which of the following is (are)...
- The energy of a system as a function of time t is given as E(t)=A^2 (- t), where =0.2 s ^ -1 . The measurement of A has an error...
- The densities of two solid spheres A and B of the same radii R vary with radial distance r as _A(r)=k ( r R ) and _B(r)=k ( r R...
- Four harmonic waves of equal frequencies and equal intensities I_0 have phase angles 0, /3, 2 /3 and . When they are superposed,...
- For a radioactive material, its activity A and rate of change of its activity R are defined as A=- dN dt and R=- dA dt , where...
- In terms of potential difference V, electric current I, permittivity _0, permeability _0 and speed of light c, the dimensionally...
- A spherical body of radius R consists of a fluid of constant density and is in equilibrium under its own gravity. If P(r) is the...
- A fission reaction is given by ^ 236 _ 92 U ^ 140 _ 54 Xe + ^ 94 _ 38 Sr +x+y, where x and y are two particles. Considering ^ 236...
- Among the complex ions, [Co(NH_2 - CH_2 - CH_2 - NH_2)_2Cl_2]^+ , [CrCl_2(C_2O_4)_2]^ 3- , [Fe(H_2O)_4(OH)_2]^+ ,...