List of top Questions asked in JEE Main

Low oxidation state of metals in their complexes are common when ligands :

Manganese (VI) has ability to disproportionate in acidic solution. The difference in oxidation states of two ions it forms in acidic solution is _____.

Oxidation of toluene to benzaldehyde can be easily carried out with which of the following reagents?

The correct order of nucleophilicity is

The set of values of \(k\), for which the circle \(C : 4x^2 + 4y^2 – 12x + 8y + k = 0\) lies inside the fourth quadrant and the point \(\bigg(1, -\frac{1}{3}\bigg)\) lies on or inside the circle \(C\), is

\(∫^5_0\,cos(π(x-[\frac{x}{2}]))dx \), where [t] denotes greatest integer less than or equal to t, is equal to

An element M crystallises in a body centred cubic unit cell with a cell edge of 300 pm. The density of the element is 6.0 g cm^–3. The number of atoms present in 180 g of the element is ______× 10²³. (Nearest integer)

Let \(x * y\) = \(x^2 + y^3\) and \((x * 1) * 1\) = \(x * (1 * 1)\). Then a value of \(2 sin^{-1}\bigg(\frac{x^4+x^2-2}{x^4+x^2+2}\bigg)\) is

In the wave equation $y=05 \sin \frac{2 \pi}{\lambda}(400 t-x) m$ the velocity of the wave will be :

Given below are two statements: 
Statement I: The average momentum of a molecule in a sample of an ideal gas depends on temperature. 
Statement II: The rms speed of oxygen molecules in a gas is $v$ If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become $2 v$ In the light of the above statements, choose the correct answer from the options given below:

If a point \(A(x, y)\) lies in the region bounded by the \(y\)-axis, straight lines  \(2y + x = 6\) and \(5x – 6y = 30\), then the probability that \(y < 1\) is

The probability that a relation R from {x, y} to {x, y} is both symmetric and transitive, is equal to

Let 

p : Ramesh listens to music. 

q : Ramesh is out of his village. 

r : It is Sunday. 

s : It is Saturday. 

Then the statement “Ramesh listens to music only if he is in his village and it is Sunday or Saturday” can be expressed as

If the minimum value of \(f(x)=\frac{5 x^2}{2}+\frac{\alpha}{x^5}, x>0\), is 14 , then the value of \(\alpha\) is equal to:

Let a, b and c be the length of sides of a triangle ABC such that:
\(\frac {a+b}{7}=\frac {b+c}{8}=\frac {c+a}{9}\)
If \(r\) and \(R\) are the radius of incircle and radius of circumcircle of the triangle ABC, respectively, then the value of \(\frac Rr\) is equal to :

Let \(ƒ : R→R\) be defined as \(ƒ(x) = x^3 + x – 5\) . If g(x) is a function such that \(ƒ(g(x)) = x\), ∀‘x‘∈R. Then \(g^′(63)\) is equal to_____.

Let \(Q\) be the mirror image of the point \(P(1, 0, 1)\) with respect to the plane \(S\): \(x + y + z = 5\). If a line L passing through \((1, –1, –1)\), parallel to the line \(PQ\) meets the plane \(S\) at \(R\), then \(QR_2\) is equal to :

In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of 0.5 s is measured from time of 100 oscillations with a watch of 1 s resolution. If measured value of length is 10 cm known to 1 mm accuracy, the accuracy in the determination of g is found to be x %. The value of x is _________ .

A tower $PQ$ stands on a horizontal ground with base $Q$ on the ground The point $R$ divides the tower in two parts such that $QR =15 \,m$ If from a point $A$ on the ground the angle of elevation of $R$ is $60^{\circ}$ and the part $PR$ of the tower subtends an angle of $15^{\circ}$ at $A$, then the height of the tower is :

The number of elements in the set \(S = \{ \theta \in [-4\pi, 4\pi] : 3 \cos^2(2\theta) + 6 \cos^2(\theta) - 10\cos(2\theta) + 5 = 0 \}\) is______.

\(cos^{-1}(\frac{2sin^{-1}(\frac{1}{4x^2-1})}{π})\) is:

The value of \( tan^{-1}(\frac{cos\frac{15}{4}-1}{sin(\frac{π}{4})} )\) is equal to:

If \(cos^{-1}(\frac{y}{2})=log_e(\frac{x}{5})^5, |y| < 2\) then:

The distance between the two points A and A′ which lie on y = 2 such that both the line segments AB and A′B (where B is the point (2, 3)) subtend angle π/4 at the origin, is equal to