List of top Questions asked in JEE Main, VITEEE

A molecule \( (X) \) with the following structure under mild acidic conditions is hydrolyzed to produce \( (Y) \) and \( (Z) \). Identify the correct statements about \( (Y) \) and \( (Z) \).}

If the sum of the first four terms of an A.P. is \(6\) and the sum of its first six terms is \(4\), then the sum of its first twelve terms is

The coefficient of \(x^{48}\) in \[ (1+x) + 2(1+x)^2 + 3(1+x)^3 + \cdots + 100(1+x)^{100} \] is equal to

One side of an equilateral prism is painted by a transparent material of refractive index \( n_2 \). The refractive index of prism is 1.6. The minimum value of \( n_2 \) required for total internal reflection from the painted face is _______.

Two wires \(A\) and \(B\) made of different materials have lengths \(6.0\) cm and \(5.4\) cm, and areas of cross-sections \(3.0\times10^{-5}\,\text{m}^2\) and \(4.5\times10^{-5}\,\text{m}^2\), respectively. They are stretched by the same magnitude under the same load. If the ratio of Young’s modulus of \(A\) to that of \(B\) is \(x:3\), find the value of \(x\).

Find \(x\): \(2x + 3 = 7x - 8\).

Choose the correct preposition: "The property was divided ___ the four brothers."

What is the mole fraction of water in \(10%\) by weight (w/w) of aqueous urea solution? [Given: Molar mass of H, O, C and N are 1, 16, 12 and \(14 \text{ g mol}^{-1}\) respectively.]

$2.8 \times 10^{-3}$ mol of CO$_2$ is left after removing $10^{21}$ molecules from its $x$ mg sample. The mass of CO$_2$ taken initially is: Given: $N_A = 6.02 \times 10^{23}\,\text{mol}^{-1}$

The mass of iron converted into \(Fe_3O_4\) by the action of \(18\) g of steam is: (Given: Molar mass of H, O and Fe are \(1, 16\) and \(56\) g mol\(^{-1}\) respectively). Assume iron is present in excess.

If \(a_1 = 1\) and for all \(n \ge 1\), \[ a_{n+1} = \frac{1}{2}a_n + \frac{n^2 - 2n - 1}{n^2 (n+1)^2}, \] then the value of \[ \sum_{n=1}^{\infty} \left( a_n - \frac{2}{n^2} \right) \] is equal to:

In a microscope of tube length $10\,\text{cm}$ two convex lenses are arranged with focal lengths $2\,\text{cm}$ and $5\,\text{cm}$. Total magnification obtained with this system for normal adjustment is $(5)^k$. The value of $k$ is ___.

Consider the isomers of hydrocarbon with molecular formula \(C_5H_{10}\). These isomers do not decolourise \(KMnO_4\) solution. These isomers are subjected to chlorination with chlorine in presence of light to give monochloro compounds. The total number of monochloro compounds (structural isomers only) formed is ______.}

Let $a_1,a_2,a_3,a_4$ be an A.P. of four terms such that each term of the A.P. and its common difference are integers. If $a_1+a_2+a_3+a_4=48$ and $a_1^2a_2a_3a_4+1^4=361$, then the largest term of the A.P. is equal to

Let the sum of the first n terms of an A.P. be $3n^2 + 5n$. Then the sum of squares of the first 10 terms of the A.P. is:

Let \( \alpha \) and \( \beta \) respectively be the maximum and the minimum values of the function \( f(\theta) = 4\left(\sin^4\left(\frac{7\pi}{2} - \theta\right) + \sin^4(11\pi + \theta)\right) - 2\left(\sin^6\left(\frac{3\pi}{2} - \theta\right) + \sin^6(9\pi - \theta)\right) \). Then \( \alpha + 2\beta \) is equal to :

A solid sphere of mass $5$ kg and radius $10$ cm is kept in contact with another solid sphere of mass $10$ kg and radius $20$ cm. The moment of inertia of this pair of spheres about the tangent passing through the point of contact is ___________ kg$\cdot$m$^2$.

If the frequency of incident light is doubled, what happens to the stopping potential? ____.

From the following, the least stable structure is:
(Assume standard resonance structures)

Number of moles and number of molecules in 1.4187 L of SO₂ at STP respectively are

The value of the integral $\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{32 \cos^4 x}{1 + e^{\sin x}} dx$ is:

In a common emitter transistor, \( \beta = 100 \), \( R_c = 2\,\text{k}\Omega \), and the output voltage is \(2\,\text{V}\). If \( R_b = 1\,\text{k}\Omega \), find the input voltage.

A thin convex lens of focal length \( 5 \) cm and a thin concave lens of focal length \( 4 \) cm are combined together (without any gap), and this combination has magnification \( m_1 \) when an object is placed \( 10 \) cm before the convex lens.

Keeping the positions of the convex lens and the object undisturbed, a gap of \( 1 \) cm is introduced between the lenses by moving the concave lens away. This leads to a change in magnification of the total lens system to \( m_2 \).

The value of \( \dfrac{m_1}{m_2} \) is

What happens to the magnetic field at the center of a circular coil if the number of turns is doubled while current remains constant?