JEE Main questions
34568 published questions with worked solutions.
- Let = (4!)! (4!)^ 3! and = (5!)! (5!)^ 4! . Then:
- An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability, that...
- If the area of the region (x, y) : 0 ≤ y ≤ min 2x, 6x – x² is A, then 12 A is equal to ____
- Let f(x) = _0^xg(t) _e ( 1-t 1+t )dt, where g is a continuous odd function. If _ - /2 ^ /2 (f(x) + x^2 x 1 + e^x )dx = ( )^2 - ,...
- Let the complex number α and 1 lie on the circles |z – z₀|² = 4 and |z – z₀|² = 16 respectively, where z₀ = 1 + i. Then, the...
- If the sum of squares of all real values of α, for which the lines 2x – y + 3 = 0, 6x + 3y + 1 = 0 and αx + 2y – 2 = 0 do not...
- The coefficient of x²⁰¹² in the expansion of (1 – x)²⁰⁰⁸(1 + x + x²)²⁰⁰⁷ is equal to ____.
- The lines x-2 2 = y -2 = z-7 16 and x+3 4 = y+2 3 = z+2 1 intersect at the point P. If the distance of P from the line x+1 2 =...
- The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was found that an...
- Let A be a 2 × 2 real matrix and I be the identity matrix of order 2. If the roots of the equation |A – xI| = 0 be –1 and 3, then...
- Consider a circle (x – α)² + (y – β)² = 50, where α, β > 0. If the circle touches the line y + x = 0 at the point P, whose...
- If the solution curve, of the differential equation dy dx = x + y - 2 x - y passing through the point (2, 1) is ^ -1 ( y-1 x-1 )...
- Given below are two statements: Statement-I: Viscosity of gases is greater than that of liquids. Statement-II: Surface tension of...
- 0.08 kg air is heated at constant volume through 5°C. The specific heat of air at constant volume is 0.17 kcal/kg°C and J = 4.18...
- Identify the physical quantity that cannot be measured using spherometer :
- Position of an ant (S in metres) moving in Y-Z plane is given by S = 2t^2 j + 5 k (where t is in second). The magnitude and...
- An electric charge 10^ -6 C is placed at origin (0, 0) m of X – Y co-ordinate system. Two points P and Q are situated at ( 3, 3)...
- A proton moving with a constant velocity passes through a region of space without any change in its velocity. If E and B...
- The average kinetic energy of a monoatomic molecule is 0.414 eV at temperature : (Use K_B = 1.38 10^ -23 J/mol-K)
- A rectangular loop of length 2.5 m and width 2 m is placed at 60° to a magnetic field of 4T. The loop is removed from the field...