List of top Questions asked in JEE Main

The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observation was recorded as 50 instead of 40. Then the correct variance is:

The heat passing through the cross-section of a conductor, varies with time ‘t’ as \(Q(t) = αt – βt^2 + γt^3\). (\(α, β\) and \(γ\) are positive constants.) The minimum heat current through the conductor is
Match List l with List ll.
List I Coordination Complex List II Number of unpaired electrons
(I) [Cr(CN)6]3- (a) 0
(II) [Fe(H2O)6]2+ (b) 3
(III) [Co(NH3)6]3+ (c) 2
(IV) [Ni(NH3)6]2+ (d) 4
Choose the correct answer from the options given below:
Which of the following statements is correct about freons?

Separation between earth and sun is given by 1.5 × 106 km. Time period of another planet is 2.83 year. Find distance of another planet from sun?

Match List I with List II 

List IList II
AIFittig reaction
BIIWurtz Fittig reaction
CIIIFinkelstein reaction
D\(C_{2}H_{5}CI + NaI \rightarrow C_{2}H_{5}I + NaCl\)IVSandmeyer reaction

 Choose the correct answer from the options given below:

If $\int \limits_0^\pi \frac{5^{\cos x}\left(1+\cos x \cos 3 x+\cos ^2 x+\cos ^3 x \cos 3 x\right) d x}{1+5^{\cos x}}=\frac{ k \pi}{16}$, then $k$ is equal to
The resistance of a wire is $5 \Omega$. It's new resistance in ohm if stretched to 5 times of it's original length will be:

How many moles of Ba3(PO4)2 will be formed by the reaction of 5 moles of BaCl2 and 3 moles of Na3(PO4).

Which of the following compounds is an example of Freon?
Let C be the circle in the complex plane with centre z0 = \(\frac{1}{2}\) (1+3i) and radius r = 1. Let z1 = 1+ i and the complex number z2 be outside the circle C such that |z1 – z0| |z2 – z0| = 1. If z0, z1 and z2 are collinear, then the smaller value of |z2|2 is equal to

For which of the following aqueous ion, spin only magnetic moment is 3.87 BM?

During the qualitative analysis of $SO _3^2$ using dilute $H _2 SO _4, SO _2$ gas is evolved which turns $K _2 Cr _2 O _7$ solution (acidified with dilute $H _2 SO _4$ ) :
The minimum number of elements that must be added to the relation $R=\{(a, b),(b, c),(b, d)\}$ on the set $\{a, b, c, d\}$ so that it is an equivalence relation, is _______
The dissociation constant of acetic acid is $x \times 10^{-5}$ When $25 \,mL$ of $0.2 \,M \,CH _3 COONa$ solution is mixed with $25 \,mL$ of $0.02\, M \,CH _3 COOH$ solution, the $pH$ of the resultant solution is found to be equal to 5. The value of $x$ is ___
If \(a_1,a_2,.......a_n\) are in arithmetic progression with common difference \(d>n\), then find limit \(\lim_{n \to \infty}\sqrt{\frac{d}{n}}(\frac{1}{\sqrt{a_1}+\sqrt{a_2}})+\frac{1}{\sqrt{a_2}+\sqrt{a_3}}+.......+\frac{1}{\sqrt{a_n}+\sqrt{a_{n-1}}})\) is____.
Element not present in Nessler’s reagent is
The solubility product of BaSO₄ is \(1 \times 10^{-10}\) at 298 K. The solubility of BaSO₄ in 0.1 M K₂SO₄(aq) is \(x \times 10^{-9}\) g L⁻¹. Calculate the value of \(x\).

A radioactive element \({}^{242}_{92}X\) emits two \(\alpha\)-particles, one electron, and two positrons. The product nucleus is represented by \({}^{234}_{P}Y.\) The value of \(P\) is _______.

Let \(A = \{x \in \mathbb{R}: |x+3| + |x+4| \le 3\}\),} \[ B = \left\{ x \in \mathbb{R} : 3 \cdot \sum_{r=1}^{\infty} \frac{3^{x-3}}{10^r} < 3^{-3x} \right\}, \] where \([x]\) denotes the greatest integer function. Then,
A person has been using spectacles of power $-1.0$ dioptre for distant vision and a separate reading glass of power $2.0$ dioptres What is the least distance of distinct vision for this person :
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 $g =10 m / s ^2$ )
An object of mass 8 kg is hanging from one end of a uniform rod CD of mass 2 kg and length
The frequency (\( \nu \)) of an oscillating liquid drop may depend upon the radius (\( r \)) of the drop, density (\( \rho \)) of the liquid, and the surface tension (\( s \)) of the liquid as: \[ \nu = k r^a \rho^b s^c \]
The values of \( a \), \( b \), and \( c \) respectively are:

Let \(\alpha x+\beta y+y z=1\) be the equation of a plane passing through the point\((3,-2,5)\)and perpendicular to the line joining the points \((1,2,3)\) and \((-2,3,5)\) Then the value of \(\alpha \beta y\)is equal to ____

The density of a monobasic strong acid (Molar mass $242 \,g$ mol) is $121 \,kg \,L$ The volume of its solution required for the complete neutralization of $25 \,mL$ of $024\, M\, NaOH$ is ___$\times 10^{-2} mL$ (Nearest integer)