NTA JEE Mains 23rd Jan 2026 Shift 1

The de Broglie wavelength of an oxygen molecule at $$27^{\circ}C\text{ is }x\times10^{-12}m$$. The value of x is (take Planck's constant $$=6.63\times10^{-34}J.s$$, Boltzmann constant $$=1.38\times10^{-23}J/K$$, mass of oxygen molecule $$=5.31\times10^{-26}kg$$)

A simple pendulum of string length 30 cm performs 20 oscillations in 10 s. The length of the string required for the pendulum to perfo rm 40 oscillations in the same time duration is _________cm. [Assume that the mass of the pendulum remains same.]

A small bob A of mass m is attached to a massless rigid rod of length 1 m pivoted at point P and kept at an angle of 60° with vertical as shown in figure. At distance of 1 m below point P, an identical bob B is kept at rest on a smooth horizontal surface that extends to a circular track of radius R as shown in figure. If bob B just manages to complete the circular path of radius R upto a point Q after being hit elastically by bob A, then radius R is ____ m.

A wire of uniform resistance AΩ/m is bent into a circle of radius r and another piece of wire with length 2r is connected between points A and B (AOB) as shown in figure. The equivalent resistance between points A and B is ____Ω .

Two point charges 2q and q are placed at vertex A and centre of face CDEF of the cube as shown in figure. The electric flux passing through the cube is :

In a screw gauge, the zero of the circular scale lies 3 divisions above the horizontal pitch line when their metallic studs are brought in contact. Using this instrument thickness of a sheet is measured. If pitch scale reading is 1 mm and the circular scale reading is 51 then the correct thickness of the sheet is_____ mm.
[Assume least count is 0.01 mm]

Four persons measure the length of a rod as 20.00 cm, 19.75 cm, 17.01 cm and 18.25cm. The relative error in the measurement of average length of the rod is :

Consider light travelling from a medium A to medium B separated by a plane interface. If the light undergoes total internal reflection during its travel from medium A to B and the speed of light in media A and B are $$2.4\times10^{8}m/s\text{ and }2.7\times10^{8}m/s$$ respecti vely, then the value of critical angle is :

An object is projected with kinetic energy K from a point A at an angle 60° with the horizontal The ratio of the difference in kinetic energies at points B and C to that at point A (see figure), in the absence of air friction is :

Matd1 List - I with List - II.
atd1 List - I with List - II.
List - I List - II
Relation Law
A. $$\oint\overrightarrow{E}.\overrightarrow{dl}=-\frac{d}{dt}\oint\overrightarrow{B}.\overrightarrow{da}$$ I. Ampere's circuital law
B. $$\oint\overrightarrow{B}.\overrightarrow{dl}=\mu_{\circ}\left(I+\epsilon_{\circ}\frac{d\phi_{E}}{dt}\right)$$ II. Faraday's laws of electromagnetic induction
C. $$\oint\overrightarrow{E}.\overrightarrow{da}=\frac{1}{\epsilon_{\circ}}\int_{v}^{} \rho dv$$ III. Ampere - Maxwell law
D. $$\oint\overrightarrow{B}.\overrightarrow{dl}=\mu_{\circ}I$$ IV. Gauss's law of electrostatics
Choose the correct answer from the options given below :