Practice questions
88551 published questions with worked solutions.
- Suppose that the number of terms in an A.P is 2k, k N. If the sum of all odd terms of the A.P. is 40, the sum of all even terms...
- If _ x ( ( e 1-e ) ( 1 e - x 1+x ) )^x = , then the value of _e 1+ _e equals :
- Let f(x) = _0^ x^2 t^2-8t+15 e^t ,dt, x R . Then the number of local maximum and local minimum points of f, respectively, are :
- If x = f(y) is the solution of the differential equation (1+y^2) + (x - 2e^ ^ -1 y ) dy dx = 0, y (- 2 , 2 ) With f(0) = 1, then...
- If e^x ( x ^ -1 x 1-x^2 + ^ -1 x (1-x^2)^ 3/2 + x 1-x^2 )dx = g(x)+C, Where C is the constant of integration, then g ( 1 2 )...
- Let _ and _ be the distinct roots of 2x^2 + ( )x - 1 = 0, (0, 2 ). If m and M are the minimum and the maximum values of _ ^4+ _...
- If the system of linear equations : x + y + 2z = 6, 2x + 3y + az = a + 1, –x – 3y + bz = 2b, Where a, b R has infinitely many...
- Let a and b be two unit vectors such that the angle between them is 3 . If a +2 b and 3 a - b are perpendicular to each other,...
- Let E: x^2 a^2 + y^2 b^2 =1, a > b and H: x^2 A^2 - y^2 B^2 =1. Let the distance between the foci of E and the foci of H be 2 3....
- If A and B are two events such that P(A B) = 0.1, and P(A|B) and P(B|A) are the roots of the equation 12x^2-7x+1=0, then the...
- The sum of all values of [0, 2 ] satisfying 2 ^2 = 2 and 2 ^2 = 3 isNot in JEE Main syllabus
- Let y = f(x) be the solution of the differential equation dy dx + xy x^2-1 = x^6+4x 1-x^2 , -1 < x < 1 such that f(0) = 0. If 6 _...
- Let A(6, 8), B(10 , -10 ) and C(-10 , 10 ), be the vertices of a triangle. If L(a, 9) and G(h, k) be its orthocenter and centroid...
- If _ r=1 ^ 30 r^2 ( ^ 30 C_r )^2 ^ 30 C_ r-1 = 2^ 29 , then is equal to _______.
- Let A = 1, 2, 3 . The number of relations on A, containing (1, 2) and (2, 3), which are reflexive and transitive but not...
- The maximum percentage error in the measurement of density of a wire is [Given, mass of wire = (0.60 ± 0.003)g radius of wire =...
- Which one of the following is the correct dimensional formula for the capacitance in F ? M, L, T and C stand for unit of mass,...
- An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr's quantization is applicable, then...
- For a diatomic gas, if _1 = ( C_p C_v ) for rigid molecules and _2 = ( C_p C_v ) for another diatomic molecules, but also having...
- A light source of wavelength illuminates a metal surface and electrons are ejected with maximum kinetic energy of 2 eV. If the...