JEE Advanced questions
1003 published questions with worked solutions.
- An aqueous solution of hydrazine ( N _2 H _4) is electrochemically oxidized by O _2, thereby releasing chemical energy in the...
- To form a complete monolayer of acetic acid on 1g of charcoal, 100 mL of 0.5 M acetic acid was used. Some of the acetic acid...
- Vessel-1 contains w _2 g of a non-volatile solute **X** dissolved in w _1 g of water. Vessel-2 contains w _2 g of another...
- Among [ Co(CN) _4]^ 4- , [ Co(CO) _3( NO )], XeF _4, [ PCl _4]^+, [ PdCl _4]^ 2- , [ ICl _4]^-, [ Cu(CN) _4]^ 3- and P _4 the...
- An organic compound P having molecular formula C _6 H _6 O _3 gives ferric chloride test and does not have intramolecular...
- Let ℝ denote the set of all real numbers. Then the area of the region (x, y) R R : x > 0, y > 1 x , 5x - 4y - 1 > 0, 4x + 4y - 17...
- The total number of real solutions of the equation = ^ -1 (2 ) - 1 2 ^ -1 ( 6 9 + ^2 ) is (Here, the inverse trigonometric...
- Let S denote the locus of the point of intersection of the pair of lines 4x - 3y = 12 , 4 x + 3 y = 12, where α varies over the...
- Let S denote the locus of the mid-points of those chords of the parabola y^2 = x, such that the area of the region enclosed...
- Let P(x_1, y_1) and Q(x_2, y_2) be two distinct points on the ellipse x^2 9 + y^2 4 = 1 such that y_1 > 0, and y_2 > 0. Let C...
- Let ℝ denote the set of all real numbers. Let f : ℝ → ℝ be defined by f(x) = cases 6x + x 2x + x & if x 0, 7 3 & if x = 0. cases...
- Let y(x) be the solution of the differential equation x^2 dy dx + xy = x^2 + y^2, x > 1 e , satisfying y(1) = 0. Then the value...
- Let a_0, a_1, , a_ 23 be real numbers such that (1 + 2 5 x )^ 23 = _ i=0 ^ 23 a_ix^i for every real number x. Let a_r be the...
- A factory has a total of three manufacturing units, M_1, M_2, and M_3, which produce bulbs independent of each other. The units...
- Consider the vectors x = i + 2 j + 3 k, y = 2 i + 3 j + k, and z = 3 i + j + 2 k. For two distinct positive real numbers α and β,...
- For a non-zero complex number z, let arg(z) denote the principal argument of z, with −π < arg(z) ≤ π. Let ω be the cube root of...
- Let ℝ denote the set of all real numbers. Let f : ℝ → ℝ and g : ℝ → (0, 4) be functions defined by f(x) = _e(x^2 + 2x + 4), and...
- Let = 1 60^ 61^ + 1 62^ 63^ + + 1 118^ 119^ . Then the value of ( cosec ,1^ )^2 is _____.
- If = _ 1 2 ^ 2 ^ -1 x 2x^2 - 3x + 2 ,dx, then the value of 7 ( 2 7 ) is _____. (Here, the inverse trigonometric function ^ -1 x...
- Consider a star of mass m_2 kg revolving in a circular orbit around another star of mass m_1 kg with m_1 m_2. The heavier star...