JEE Main 2023-24: Class XI Full Test 1

A sinusoidal traveling wave in a string has a propagation velocity of 300 m/s, and the time period of oscillations of the particles of the string is 0.04 s. What is the wavelength of the wave?

Two identical particles execute Simple Harmonic Motion (SHM). What conditions must be met for their motions to be considered identical?

Consider a wave propagating through a medium. If the frequency of the wave is doubled while the tension in the medium remains constant, how does the velocity of the wave change?

Two waves with slightly different frequencies interfere to produce beats. If the frequencies of the two waves are 440 Hz and 444 Hz, what is the beat frequency?

Which of the following oxides is the most acidic?

A mass is attached to a spring and undergoes SHM. If the mass is doubled while keeping the spring constant the same, how does the period of oscillation change?

Consider the following statements: (i) The ratio of the radii of the first three Bohr orbits of the hydrogen atom is 1 : 8 : 27. (ii) The ratio of the magnitude of Total Energy : Kinetic Energy : Potential Energy for any orbit is 1 : 1 : 2 (iii) The frequency of a green light is $6 \times 10^{14}$ Hz, (iv) The ratio of de-Broglie wavelength of a 'H' atom, 'He' atom and $CH_4$ molecule moving with equal kinetic energy is 4 : 2 : 1. which of the following options is correct?

A sound wave travels from air into water. How does the wavelength of the sound wave change as it enters the water, given that the speed of sound is greater in water than in air?

What is the correct order of bond angles in the following species: $ClO_2^+$, $ClO_2$, $ClO_2^−$ ?

Two identical sound sources emit waves in phase. At a certain point, the path difference between the waves is half a wavelength ($\lambda/2$). What is the nature of the interference at this point?

A closed organ pipe has a length $L$. What is the wavelength of the fundamental mode (first harmonic) of vibration?

In a collection of 'H' atoms, all electrons jump from n = 5 to finally the ground level (directly or indirectly). If during these transitions, no lines are emitted in the Paschen series, what is the number of possible different radiations?

Consider the molecule $CH_3-CH_2-CH_2-CH(CH_2COOH)-COOH$. What is the number of carbons in the selected principal carbon chain for IUPAC nomenclature of this molecule?

Which of the given options is correct?

Which combination of a diene and dienophile would you use to prepare the following compound? [Image of a Diels-Alder product]

Consider the equilibrium: $CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)$. If the equilibrium constant is 1, what can be inferred about the reaction?

Which halogen, when in its reference state, exhibits the greatest absolute entropy per mole?

Identify the least stable among the provided structures, considering factors like charge distribution and resonance.

Which alcohol, upon heating with $H_2SO_4$, will undergo dehydration at the fastest rate?

For the reversible reaction $I_2(g) + Br_2(g) \rightleftharpoons 2IBr(g)$, given $log K_P° = (\frac{170.2}{T} + 0.1)$, determine the absolute value of the standard Gibbs free energy change ($|\Delta_rG°|$) in kJ/mol.

Calculate the volume of 0.02 M $Ba(OH)_2$ needed to be mixed with 40 ml of 0.02 M $NaOH$ and 20 ml of 0.01 M $HNO_3$ to obtain a solution with pH = 12.3. (Use log 2 = 0.3)

How many different alkenes, upon catalytic hydrogenation, will yield iso-pentane as the sole product?

A 50 ml solution of 0.2 M $H_2A$ is mixed with 10 ml of 0.5 M $NaOH$ at 25°C. Given $K_{a1} = 10^{-6}$ and $K_{a2} = 10^{-12}$ for $H_2A$, what is the approximate pH of the resulting solution?

Which of the following silicon compounds, when hydrolyzed, would produce cyclic silicones?

In the redox reaction $HCl + KMnO_4 \rightarrow MnCl_2 + H_2O + Cl_2 + KCl$, what is the equivalent mass of $HCl$ in terms of its molecular mass 'M'?

Which of the following statements concerning periodic trends is incorrect?

If the reaction quotient (Q) for a reversible reaction is less than 1 (Q < 1), which statement about the change in Gibbs free energy is correct?

Consider the decomposition of $CaCO_3(s)$ into $CaO(s)$ and $CO_2(g)$. Given that $\Delta G^\degree = -57.575$ kJ/mol at 2727°C, what is the pressure of $CO_2(g)$ in bar? (R = 25/3 J/mol-K)

What is the approximate molarity of $H^+$ ions in a solution prepared by mixing 200 ml of 0.5 M $H_2SO_4$, 100 ml of 0.7 M $HNO_3$, and 100 ml of 0.3 M $HCl$? Assume the volumes are additive.

A solution contains two monoprotic acids, HA and HB. The ionization constant of HA is $1 \times 10^{-4}$ and that of HB is $1 \times 10^{-6}$. What does this indicate about their relative acid strengths at the same concentration?

Which of the following options accurately describes the impact of increased temperature on an endothermic reaction at equilibrium?

What is the radius of the circle defined by $Re(\frac{z}{iz - 1}) = 2$?

If $x$ and $y$ represent the number of sexagesimal and centesimal seconds in an angle respectively, what is the value of $\frac{x}{y}$?

Given that the derivative of $f(x)$ with respect to $x$ is $\frac{1}{2}sin^2(x)$, what is the period of $f(x)$?

What is the value of $\frac{cos^2(33^{\circ}) - cos^2(57^{\circ})}{sin(3^{\circ}) - sin(87^{\circ})}$?

A guard of 12 men is formed from a group of $n$ soldiers in all possible ways. If the number of times two particular soldiers A and B are together on guard is thrice the number of times three particular soldiers C, D, E are together on guard, then what is the value of $n$?

How many positive integer solutions $(x, y, z)$ exist for the equation $xyz = 24$?

What is the distance of the point $(-1, -5, -10)$ from the point of intersection of the line $\frac{x-2}{3} = \frac{y+1}{4} = \frac{z-2}{12}$ and the plane $x - y + z = 5$?

What is the value of $lim_{x \to 0} \frac{tan(e^2x) - tan(-e^2x)}{G.I.F. [\pi + x^2]}$, where G.I.F. represents the Greatest Integer Function?

A wave propagates from a source. What is the phase difference between the oscillations of particles located 10 m and 16 m away from the source, respectively, given that the wavelength of the wave is 12 m?

A uniform rod of mass m and length $\lambda$ is in equilibrium between two smooth vertical walls, as shown. The distance between the walls is d. Determine cos$\theta$ in terms of d and $\lambda$.

A cubical block of wood weighs 13 kg and has a relative density of 0.6. How much additional weight must be placed on the block for it to be 90% immersed in water?

Given two particles oscillating according to the equations $x_1 = 4 \sin(10t + \frac{\pi}{6})$ and $x_2 = 5 \cos(\omega t)$, find the value of $\omega$ for which the energies of both particles are equal.

A particle travels in a straight line with uniform acceleration. If the particle's average speed is u for the entire motion, what is the maximum possible speed at the midpoint of the path?

A ball of mass 3kg is suspended from a bar of the same mass with a light inextensible cord. Initially the system is held at rest as shown. Determine the tension in the string immediately after the system is released. The incline is fixed and frictionless.

Two identical simple pendulums, A and B, are set into motion such that A has twice the kinetic energy of B. Assuming their amplitudes are small, what is the ratio of the amplitude of A to the amplitude of B?

A point source of light emits uniformly in all directions. At a distance of 2 meters from the source, the intensity of the light is $I$. What will be the intensity at a distance of 4 meters from the source?