List of top Questions asked in JEE Main

Let \( f: \mathbb{R} \to \mathbb{R} \) and \( g: \mathbb{R} \to \mathbb{R} \) be defined as: \(f(x) = \begin{cases} \log_e x, & \text{if } x > 0, \\ e^{-x}, & \text{if } x \leq 0, \end{cases}\) and
\(g(x) = \begin{cases} x, & \text{if } x \geq 0, \\ e^x, & \text{if } x < 0. \end{cases}\) Then \( g \circ f: \mathbb{R} \to \mathbb{R} \) is:

The half-life of radio isotopic bromine - 82 is 36 hours. The fraction which remains after one day is ___________ ×10^–2.
(Given antilog 0.2006 = 1.587)

The total number of ‘Sigma’ and Pi bonds in 2 formylhex-4-enoic acid is ____.

A solution is prepared by adding 1 mole ethyl alcohol in 9 mole water. The mass percent of solute in the solution is ___________ (Integer Answer)
(Given : Molar mass in g mol$^{-1}$ Ethyl alcohol : 46, water : 18)

Total number of unpaired electrons in the complex ion [Co(NH$_3$)$_6$]$^{3+}$ and [NiCl$_4$]$^{2-}$ is

Total number of aromatic compounds among the following compounds is _______.

Molality of an aqueous solution of urea is 4.44 m. Mole fraction of urea in solution is x × 10^–3. Value of x is _______. (integer answer)

Two moles of benzaldehyde and one mole of acetone under alkaline conditions using aqueous NaOH after heating gives $x$ as the major product. The number of $\pi$ bonds in the product $x$ is ................

The total number of carbon atoms present in tyrosine, an amino acid, is _______.

Total number of optically active compounds from the following is _______.

The area enclosed by the curves xy + 4y = 16 and x + y = 6 is equal to :

\(\text{Let } S = \{x \in \mathbb{R} : (\sqrt{3} + \sqrt{2})^x + (\sqrt{3} - \sqrt{2})^x = 10\}\).Then the number of elements in \( S \) is:

Let the median and the mean deviation about the median of 7 observation 170, 125, 230, 190, 210, a, b be 170 and \(\frac{205}{7}\)respectively. Then the mean deviation about the mean of these 7 observations is :

Let \(\vec{a} = -5\hat{i} + \hat{j} - 3\hat{k}, \quad \vec{b} = \hat{i} + 2\hat{j} - 4\hat{k},\) and  \(\vec{c} = \left( \left( \left( \vec{a} \times \vec{b} \right) \times \hat{i} \right) \times \hat{i} \right) \times \hat{i}.\) Then  \(\vec{c} \cdot (-\hat{i} + \hat{j} + \hat{k})\) is equal to:  

If \(\tan A = \frac{1}{\sqrt{x(x^2 + x + 1)}}, \quad \tan B = \frac{\sqrt{x}}{\sqrt{x^2 + x + 1}}\) and \(\tan C = \left(x^3 + x^2 + x^{-1}\right)^{\frac{1}{2}}, \quad 0 < A, B, C < \frac{\pi}{2}\),then \( A + B \) is equal to:

If n is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then n is equal to:

Number of molecules having bond order 2 from the following molecule is ...................
$C_2, O_2, Be_2, Li_2, Ne_2, N_2, He_2$

The value of the integral \(\int_0^{\frac{\pi}{4}} \frac{x \, dx}{\sin^4(2x) + \cos^4(2x)}\)

$\Delta_{vap}H^\circ$ for water is $+40.49 \, \text{kJ mol}^{-1}$ at 1 bar and $100^\circ\text{C}$. Change in internal energy for this vaporisation under same condition is .............. kJ mol$^{-1}$. (Integer answer)
(Given R = 8.3 J K$^{-1}$ mol$^{-1}$)

Match List-I with List-II.

List-I (Complex ion)	List-II (Spin only magnetic moment in B.M.)
(A) [Cr(NH$_3$)$_6$]$^{3+}$	(I) 4.90
(B) [NiCl$_4$]$^{2-}$	(II) 3.87
(C) [CoF$_6$]$^{3-}$	(III) 0.0
(D) [Ni(CN)$_4$]$^{2-}$	(IV) 2.83

Choose the correct answer from the options given below:

If \( A = \begin{bmatrix} \sqrt{2} & 1 \\ -1 & \sqrt{2} \end{bmatrix} \), \( B = \begin{bmatrix} 1 & 0 \\ 1 & 1 \end{bmatrix} \), \( C = ABA^\top \) and \( X = A^\top C^2 A \), then \( \det (X) \) is equal to:

Given below are two statements:
Statement (I) : Fusion of MnO$_2$ with KOH and an oxidising agent gives dark green K$_2$MnO$_4$.
Statement (II) : Manganate ion on electrolytic oxidation in alkaline medium gives permanganate ion.
In the light of the above statements, choose the correct answer from the options given below.

The reaction;$\frac{1}{2}H_{2(g)} + AgCl_{(s)} \rightarrow H^+_{(aq)} + Cl^-_{(aq)} + Ag_{(s)}$ occurs in which of the following galvanic cell:

Given below are two statements :
Statement (I) : Kjeldahl method is applicable to estimate nitrogen in pyridine.
Statement (II) : The nitrogen present in pyridine can easily be converted into ammonium sulphate in Kjeldahl method.
In the light of the above statements, choose the correct answer from the options given below.

Identify the correct statements about p-block elements and their compounds.
(A) Non metals have higher electronegativity than metals.
(B) Non metals have lower ionisation enthalpy than metals.
(C) Compounds formed between highly reactive nonmetals and highly reactive metals are generally ionic.
(D) The non-metal oxides are generally basic in nature.
(E) The metal oxides are generally acidic or neutral in nature.