List of top Questions asked in JEE Main

Let \( g(x) = 3f\left(\frac{x}{3}\right) + f(3 - x) \) and \( f''(x) >0 \) for all \( x \in (0, 3) \). If \( g \) is decreasing in \( (0, \alpha) \) and increasing in \( (\alpha, 3) \), then \( 8\alpha \) is:

Let \( R \) be the interior region between the lines \( 3x - y + 1 = 0 \) and \( x + 2y - 5 = 0 \) containing the origin. The set of all values of \( a \), for which the points \( (a^2, a + 1) \) lie in \( R \), is:

Considering only the principal values of inverse trigonometric functions, the number of positive real values of \( x \) satisfying \[ \tan^{-1}(x) + \tan^{-1}(2x) = \frac{\pi}{4} \] is:

Let \(\alpha, \beta, \gamma\) be the foot of perpendicular from the point \((1, 2, 3)\) on the line \(\frac{x + 3}{5} = \frac{y - 1}{2} = \frac{z + 4}{3}\). Then \(19(\alpha + \beta + \gamma)\) is equal to:

The compound formed by the reaction of ethanal with semicarbazide contains _____number of nitrogen atoms.

On a thin layer chromatographic plate, an organic compound moved by 3.5 cm, while the solvent moved by 5 cm. The retardation factor of the organic compound is \( \_\_\_\_ \times 10^{-1} \).

If IUPAC name of an element is “Unununnium” then the element belongs to nth group of periodic table. The value of n is______

The pH at which Mg(OH)\(_2\) \([K_{sp} = 1 \times 10^{-11}]\) begins to precipitate from a solution containing 0.10 M Mg\(^{2+}\) ions is \( \_\_\_\_ \).

Choose the correct statements from the following:
A Ethane-1,2-diamine is a chelating ligand.
B Metallic aluminium is produced by electrolysis of aluminium oxide in presence of cryolite.
C Cyanide ion is used as a ligand for leaching of silver.
D Phosphine acts as a ligand in Wilkinson catalyst.
E The stability constants of \( \text{Ca}^{2+} \) and \( \text{Mg}^{2+} \) are similar to EDTA complexes.

The Lassaigne’s extract is boiled with dil HNO\(_3\) before testing for halogens because

Following is a confirmatory test for aromatic primary amines. Identify reagent (A) and (B)

Match List-I with List-II
\[ \begin{array}{|c|c|} \hline \text{List-I (Species)} & \text{List-II (Electronic distribution)} \\ \hline \text{(A) Cr}^{+2} & \text{(I) } 3d^8 \\ \text{(B) Mn}^{+} & \text{(II) } 3d^3 4s^1 \\ \text{(C) Ni}^{+2} & \text{(III) } 3d^4 \\ \text{(D) V}^{+} & \text{(IV) } 3d^5 4s^1 \\ \hline \end{array} \]

What happens to freezing point of benzene when small quantity of napthalene is added to benzene?

In the given reactions identify the reagent A and reagent B

Structure of 4-Methylpent-2-enal is

Example of vinylic halide is

Given below are the two statements: one is labelled as Assertion (A) and the other is labeled as Reason (R).
Assertion (A): There is a considerable increase in covalent radius from N to P. However from As to Bi only a small increase in covalent radius is observed.
Reason (R): covalent and ionic radii in a particular oxidation state increases down the group.
In the light of the above statement, choose the most appropriate answer from the options given below:

Given below are two statements:
Statement-I: The gas liberated on warming a salt with dil H₂SO₄, turns a piece of paper dipped in lead acetate into black, it is a confirmatory test for sulphide ion.
Statement-II: In statement-I the colour of paper turns black because of formation of lead sulphite. In the light of the above statements, choose the most appropriate answer from the options given below:

In a closed organ pipe, the frequency of the fundamental note is 30 Hz. A certain amount of water is now poured in the organ pipe so that the fundamental frequency is increased to 110 Hz. If the organ pipe has a cross-sectional area of 2 cm\(^2\), the amount of water poured in the organ tube is \( \_\_\_\_\_\_ \) g. (Take speed of sound in air as 330 m/s)

A capacitor of capacitance \( C \) and potential \( V \) has energy \( E \). It is connected to another capacitor of capacitance \( 2C \) and potential \( 2V \). Then the loss of energy is \( \frac{x}{3} E \), where \( x \) is \( \_\_\_\_ \).

The displacement and the increase in the velocity of a moving particle in the time interval of \( t \) to \( (t + 1) \) s are 125 m and 50 m/s, respectively. The distance travelled by the particle in \( (t + 2)^{\text{th}} \) s is \( \_\_\_\_ \) m.

Each of three blocks \( P \), \( Q \), and \( R \) shown in the figure has a mass of 3 kg. Each of the wires \( A \) and \( B \) has a cross-sectional area of 0.005 cm\(^2\) and Young's modulus \( 2 \times 10^{11} \, \text{N} \, \text{m}^{-2} \). Neglecting friction, the longitudinal strain on wire \( B \) is \( \ldots \times 10^{-4} \). (Take \( g = 10 \, \text{m/s}^2 \))

An electron of a hydrogen atom in an excited state is having energy \( E_n = -0.85 \, \text{eV} \). The maximum number of allowed transitions to lower energy levels is \( \ldots \).

The horizontal component of earth’s magnetic field at a place is \( 3.5 \times 10^{-5} \, \text{T} \). A very long straight conductor carrying current of \( \sqrt{2} \, \text{A} \) in the direction from South East to North West is placed. The force per unit length experienced by the conductor is \( \ldots \times 10^{-6} \, \text{N/m} \).

A Zener diode of breakdown voltage 10V is used as a voltage regulator as shown in the figure. The current through the Zener diode is