List of top Questions asked in JEE Main

Let s₁, s₂, s₃,…..,s₁₀ respectively be the sum to 12 terms of 10 A.P.s whose first terms are 1,2,3, …. ,10 and the common differences are 1, 3, 5, …. , 19 respectively. Then  \(10∑^{10}_{i=1} s_i\) is

Match List-I with List-II :

	List-I		List-II
A	Saccharin	I	High potency sweetener
B	Aspartame	II	First artificial sweetening agent
C	Alitame	III	Stable at cooking temperature
D	Sucralose	IV	Unstable at cooking temperature

Choose the correct answer from the options given below :

Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth It is found that when a particle is released in this tunnel, it executes a simple harmonic motion The mass of the particle is $100 \,g$ The time period of the motion of the particle will be (approximately)(Take $g=10 \, m s ^{-2}$, radius of earth $=6400 \,km$ )

$T$ is the time period of simple pendulum on the earth's surface Its time period becomes $x T$ when taken to a height $R$ (equal to earth's radius) above the earth's surface Then, the value of $x$ will be:

A Carnot engine with efficiency $50 \%$ takes heat from a source at $600 \,K$ In order to increase the efficiency to $70 \%$, keeping the temperature of sink same, the new temperature of the source will be :

For the system of linear equations  
2x+4y+2az=b
x+2y+3z=4 
2x-5y+2z=8 
which of the following is NOT correct ?  

An object of mass $8 kg$ is hanging from one end of a uniform rod CD of mass $2 kg$ and length $1 m$ pivoted at its end $C$ on a vertical wall as shown in figure It is supported by a cable $AB$ such that the system is in equilibrium The tension in the cable is : (Take $g =10 m / s ^2$ )

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.  
Assertion A: Butan -1- ol has higher boiling point than ethoxyethane.  
Reason R: Extensive hydrogen bonding leads to stronger association of molecules.  
In the light of the above statements, choose the correct answer from the options given below: 

The major product formed in the following reaction is

20 mL of calcium hydroxide was consumed when it was reacted with 10 mL of unknown solution of H₂SO4. Also 20 mL standard solution of 0.5 M HCI containing 2 drops of phenolphthalein was titrated with calcium hydroxide the mixture showed pink colour when burette displayed the value of 35.5 mL whereas the burette showed 25.5 mL initially. The concentration of H₂SO₄ is_____M (Nearest integer)

Choose the halogen which is most reactive towards SN1 reaction in the given compounds (A, B, C & D)

The correct order of spin only magnetic moments for the following complex ions is

An organic compound on combustion gives 0.22 g of CO₂ and 0.126 g of H₂O. If the percentage of C in given organic compound is 40%, the percentage of H will be?

Let \(α=8−14𝑖\), \(𝐴=\{z∈C:\frac {αz−\bar α\bar z}{z^2−(\bar z)^2−112i }=1\}\) and \(𝐵={𝑧∈C:|𝑧+3𝑖|=4}\). Then \(∑_{𝑧∈𝐴∩𝐵 }(\text {𝑅𝑒}\ ⁡𝑧−\text {𝐼𝑚⁡}\ 𝑧)\) is equal to _____ .

Let \(𝑋={11,12,13,…,40,41}\) and \(𝑌={61,62,63,…,90,91}\) be the two sets of observations. If \(\bar 𝑥\) and \(\bar 𝑦\) are their respective means and \(σ^2\) is the variance of all the observations in \(𝑋∪𝑌\), then \(|\bar 𝑥+\bar 𝑦−σ^2|\) is equal to ____ .

Let \({a_k}\) and \({b_k}\), \(𝑘∈N\), be two G.P.s with common ratios \(r_1\) and \(r_2\) respectively such that \(a_1= b_1=4\) and \(r_1<r_2\). Let \(c_k=a_k+b_k\), \(k∈N\). If \(c_2=5\) and \(c_3=\frac {13}{4}\), then \( \displaystyle\sum_{k=1}^{∞ }c_k−(12a_6+8b_4)\) is equal to _____ .

Bob P is released from the position of rest at the moment shown. If it collides elastically with an identical bob Q hanging freely then velocity of Q, just after collision is (g = 10 m/s²).

In Young's double slit experiment, two slits $S_1$ and $S_2$ are ' $d$ ' distance apart and the separation from slits to screen is $D$ (as shown in figure) Now if two transparent slabs of equal thickness $0.1 \,mm$ but refractive index $1.51$ and $1.55$ are introduced in the path of beam $(\lambda=4000 \mathring {A})$ from $S_1$ and $S_2$ respectively, The central bright fringe spot will shift by ______ number of fringes

A metal surface of 100 cm2 area has to be coated with nickel layer of thickness 0.001mm. A current of 2A was passed through a solution of Ni (NO₃)₂ for 'x' seconds to coat the desired layer. The value of x is_____ (Nearest integer)
 (P_Ni (density of Nickel) is 10 gmL^-1, Molar mass of Nickel is 60 gmol^-1 F = 96500 C mol^-1)

A thin uniform rod of length $2 m$, cross sectional area ' $A$ ' and density ' $d$ ' is rotated about an axis passing through the centre and perpendicular to its length with angular velocity $\omega$ If value of $\omega$ in terms of its rotational kinetic energy $E$ is $\sqrt{\frac{\alpha Ad }{ Ad }}$ then value of $\alpha$ is _____ .

Let \(A\) be a symmetric matrix such that \(|A|=2\) and \(\begin{bmatrix} 2 & 1 \\[0.3em] 3 & \frac 32 \\[0.3em] \end{bmatrix}𝐴−\begin{bmatrix} 1 & 2 \\[0.3em] α & β \\[0.3em] \end{bmatrix}\). If the sum of the diagonal elements of \(A\) is \(s\), then \(\frac {βs}{α^2}\) is equal to ____ .

In an experiment for estimating the value of focal length of converging mirror, image of an object placed at $40\, cm$ from the pole of the mirror is formed at distance $120 \,cm$ from the pole of the mirror These distances are measured with a modified scale in which there are $20$ small divisions in $1 \,cm$ The value of error in measurement of focal length of the mirror is $\frac{1}{ K } cm$ The value of $K$ is _____

A point source of light is placed at the centre of curvature of a hemispherical surface The source emits a power of $24\, W$ The radius of curvature of hemisphere is $10\, cm$ and the inner surface is completely reflecting The force on the hemisphere due to the light falling on it is ______ $\times 10^{-8} N$

25.0 mL of 0.050 M Ba(NO₃)₂ is mixed with 25.0 mL of 0.020 M NaF. K_sp of BaF₂ is 0.5 x 10^-6 at 298 K. The ratio of [Ba2+] [F^-]² and K_sp is__ (Nearest integer)