List of top Questions asked in JEE Main

Let
\(S = \left\{z∈C : z^2+\overline{z} = 0 \right\}\). Then \(∑_{z∈S}(Re(z)+Im(z))\)
is equal to____.

A car is moving with speed of 150 km/h and after applying the break it will move 27 m before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling ___ m distance.
Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Phenolphthalein is a pH dependent indicator, remains colourless in acidic solution and gives pink colour in basic medium.
Reason R: Phenolphthalein is a weak acid. It doesn’t dissociate in basic medium.
In the light of the above statements, choose the most appropriate answer from the options given below.
Which of the following methods are not used to refine any metal?
  1. Liquation
  2. Calcination
  3. Electrolysis
  4. Leaching
  5. Distillation
Choose the correct answer from the options given below :
Which of the following reactions will yield benzaldehyde as a product?
reactions will yield benzaldehyde as a product
Transition metal complex with highest value of crystal field splitting \((Δ_0)\) will be
Let α→ = \(2\^{i}-\^{j}+5\^{k} and b→= α\^{i}+β\^{j}+2\^{k}. If ((α→×b→)×\^{i}).\^{k} \)=\(\frac{ 23}{2}\),then \(|b→×2\^{j}\| \)is equal to

Let ℝ → ℝ be function defined as
f(x) = αsin(\((\frac{π[x]}{2})\)+[2-x],α∈R
where [t] is the greatest integer less than or equal to t.
If lim x→1 f(x) exists, then the value of\(∫_0^4\) f(x)dx
is equal to

The moles of methane required to produce 81 g of water after complete combustion is _____ × 10–2 mol. [nearest integer]

A system to 10 balls each of mass 2 kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the 7th and 8th ball is ______ N when 6th ball just leaves the table.
 

Fig. Tension on String

If the coefficients of x and x2 in the expansion of (1 + x)p (1 – x)q, p, q≤15, are – 3 and – 5 respectively, then coefficient of x3 is equal to ______.

A batsman hits back a ball of mass 0.4 kg straight in the direction of the bowler without changing its initial speed of 15 ms–1. The impulse imparted to the ball is _________ Ns.

Then the number of elements in the set {(n, m) : n, m ∈ { 1, 2….., 10} and nAn + mBm = I} is _______.

\(\begin{array}{l}(p \land r )\Leftrightarrow ( p \land (\sim q))\end{array}\)is equivalent to (~ p) when r is

If the sum of all the roots of the equation \(e^{2x} - 11e^x - 45e^{-x} + \frac{81}{2} = 0\)
 is logeP, then p is equal to _____.

At 345 K, the half life for the decomposition of a sample of a gaseous compound initially at 55.5 kPa was 340 s. When the pressure was 27.8 kPa, the half life was found to be 170 s. The order of the reaction is ________. [integer answer]
The electronic configuration of Pt(atomic number 78) is:
\(N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)\)
Consider the above reaction, the limiting reagent of the reaction and number of moles of NH3 formed, respectively are :
2.2 g of nitrous oxide (N2O) gas is cooled at a constant pressure of 1 atm from 310 K to 270 K causing the compression of the gas from 217.1 mL to 167.75 mL. The change in internal energy of the process, ΔU is ‘–x’ J. The value of ‘x’ is ____. [nearest integer]
(Given : atomic mass of N = 14 g mol–1 and of O = 16 g mol–1
Molar heat capacity of N2O is 100 J K–1 mol–1)
Let A = {1, 2, 3, 4, 5, 6, 7} and B = {3, 6, 7, 9}. Then the number of elements in the set {C ⊆ A :Cߏ∩B ≠ φ} is _____________.
A body is projected from the ground at an angle of 45° with the horizontal. Its velocity after \(2\) \(s\) is \(20\) \(ms^{–1}\). The maximum height reached by the body during its motion is ________ m. (use \(g\) = \(10\) \(ms^{–2}\))
Let the matrix \(A=\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{bmatrix}\) and the matrix \(B_0=A^{49}+2 A^{98}\) If \(B_n=\text{Adj}\left(B_{n-1}\right)\) for all \(n \geq 1\), then \(\text{det}\left( B _4\right)\) is equal to :

Consider the above reactions, the product A and product B, respectively are

Consider the species
\(CH_4,NH_{4}^+ and BH_{4}^−.\)
Choose the correct option with respect to these species.

The solubility of AgCl will be maximum in which of the following?