JEE Main 2027: Sample Paper

A block of mass \(m\) is attached to a spring of spring constant \(k\) and suspended vertically. If the mass is released from rest when the spring is in its natural length, the maximum extension produced in the spring is:

A disk of mass \(M\) and radius \(R\) rolls without slipping down an inclined plane of angle \(\theta\). The acceleration of the center of mass of the disk is:

Two charges \(+q\) and \(-q\) are placed at a distance \(2a\) apart. The electric potential at a point on the equatorial axis at a distance \(r\) (\(r \gg a\)) from the center of the dipole is:

A Carnot engine operating between temperatures \(T_1 = 500\text{ K}\) and \(T_2 = 300\text{ K}\) absorbs \(600\text{ J}\) of heat per cycle. The work done per cycle is:

A wire of length \(L\) carries a current \(I\) along the positive x-axis in a magnetic field \(\vec{B} = B_0(\hat{i} + 2\hat{j} – \hat{k})\). The magnitude of force on the wire is:

In Young’s double slit experiment, if the distance between slits is halved and distance to screen is doubled, the fringe width becomes:

The de Broglie wavelength of an electron accelerated through a potential difference of \(V\) volts is approximately:

A nucleus \(X\) decays as: \(X \xrightarrow{\alpha} X_1 \xrightarrow{\beta^-} X_2 \xrightarrow{\alpha} X_3\). If \(X\) has atomic number 92 and mass number 238, those of \(X_3\) are:

A uniform rod of length \(1\text{ m}\) and mass \(2\text{ kg}\) is pivoted at one end. A force of \(6\text{ N}\) is applied perpendicular to the rod at its free end. The angular acceleration produced is ________ \(\text{rad/s}^2\).

In a series LCR circuit with \(R = 10\ \Omega\), \(L = 0.1\text{ H}\), and \(C = 10\ \mu\text{F}\), the resonant angular frequency \(\omega_0\) is ________ \(\text{rad/s}\).

Which of the following molecules has a square planar shape?

The set of quantum numbers not allowed for an electron in an atom is:

An aqueous solution of which salt will have \(\text{pH} > 7\) at \(25^\circ\text{C}\)?

When ethyl bromide reacts with alcoholic \(\text{KOH}\), the primary organic product obtained is:

The major product formed when phenol reacts with concentrated \(\text{HNO}_3\) in the presence of concentrated \(\text{H}_2\text{SO}_4\) is:

Which of the following transition metal ions is diamagnetic?

In a zero-order reaction \(A \rightarrow B\), the half-life (\(t_{1/2}\)) is directly proportional to:

The IUPAC name of \(\text{CH}_3-\text{CH(OH)}-\text{CH}_2-\text{CHO}\) is:

The molarity of a solution prepared by dissolving \(4\text{ g}\) of \(\text{NaOH}\) in enough water to form \(250\text{ mL}\) of solution is ________ \(\text{M}\).

The standard potential \(E^\circ\) for \(\text{Zn}^{2+}/\text{Zn}\) is \(-0.76\text{ V}\) and for \(\text{Cu}^{2+}/\text{Cu}\) is \(+0.34\text{ V}\). The standard EMF of the cell \(\text{Zn}|\text{Zn}^{2+} || \text{Cu}^{2+}|\text{Cu}\) is ________ \(\text{V}\).

The maximum value of the function \(f(x) = 3\sin x + 4\cos x\) is:

If \(\lim_{x \to 0} \frac{\sin(ax)}{bx} = 2\), where \(a, b \neq 0\), then the value of \(\frac{a}{b}\) is:

The derivative of \(\tan^{-1} x\) with respect to \(\cot^{-1} x\) is:

The value of the determinant \(\begin{vmatrix} 1 & a & b+c \\ 1 & b & c+a \\ 1 & c & a+b \end{vmatrix}\) is:

The area bounded by the curve \(y = x^2\) and the line \(y = 4\) is:

If two dice are thrown simultaneously, the probability of getting a sum of 8 is:

The general solution of the differential equation \(\frac{dy}{dx} = e^{x-y}\) is:

The vector equation of a line passing through \((1, 2, 3)\) and parallel to \(3\hat{i} + 2\hat{j} – 2\hat{k}\) is:

The sum of the roots of the quadratic equation \(2x^2 – 8x + 5 = 0\) is ________.

Evaluate the definite integral \(\int_{0}^{2} (3x^2 + 2x + 1) \, dx\). The numerical answer is ________.