NTA JEE Mains 21st Jan 2026 Shift 1

A point charge of $$10^{-8}$$ is placed at origin. The work done in moving a point charge $$2 \mu C$$ from point A(4, 4, 2) m to B(2, 2, 1) m is _____J $$\left(\frac{1}{4\pi\epsilon _{0}}=9\times10^{9} \text{in SI units}\right)$$

A conducting circular loop of area $$1.0m^{2}$$ is placed perpendicular to a magnetic field which varies as $$B = \sin(100 t)$$ Tesla. If the resistance of the loop is $$100 \Omega$$, then the average thermal energy dissipated in the loop in one period is _______J.

In an experiment the values of two spring constants were measured as $$k_{1}=(10\pm0.2)N/m\text{ and }k_{2}=(20\pm0.3)N/m$$. lf these springs are connected in parallel, then the percentage error in equivalent spring constant is :

If an alpha particle with energy 7.7 MeV is bombarded on a thin gold foil, the closest distance from nucleus it can reach is ___ m. (Atomic number of gold = 79 and $$\frac{1}{4\pi\epsilon _{0}}=9\times10^{9} \text{in SI units} )$$

Initially a satellite of 100 kg is in a circular orbit of radius $$1.5R_{E}$$ This satellite can be moved to a circular orbit of radius $$3R_{E}$$ by supplying $$\alpha\times10^{6}J$$ of energy The value of $$\alpha$$ is ____. (Take Radius of Earth $$R_{E}=6\times10^{6}m\text{ and }g=10m/s^{2}$$)

Two identical thin rods of mass M kg and length L m are connected as shown in figure. Moment of inertia of the combined rod system about an axis passing through point P and perpendicular to the plane of the rods is $$\frac{x}{12}ML^{2}\text{kg m}^{2}$$. The value of x is ____ .

10 mole of oxygen is heated at constant volume from $$30^{\circ}C  \text{to}  40^{\circ}C$$. The change in the internal energy of the gas is ____ cal (the molecular specific heat of oxygen at constant pressure, $$C_{p}= 7 \text{cal}/\text{mol}.^{\circ}C \text{and} R = 2 \text{cal}./\text{mol}.^{\circ}C).$$

A collimated beam of light of diameter 2 mm is propagating along x-axis. The beam is required to be expanded in a collimated beam of diameter 14 mm using a system of two convex lenses. lf first lens has focal length 40 mm, then the focal length of second lens is ____ mm.

The heat generated in 1 minute between points A and B in the given circuit, when a battery of 9 V with internal resistance of 1Ω is connected across these points is ____ J

In a microscope the objective is having focal length $$f_{0}=2 \text{cm}$$ and eye-piece is having focal length $$f_{e} = 4 \text{cm}$$ The tube length is 32 cm. the magnification produced by this microscope for normal adjustment is _______.