NTA JEE Mains 1st Feb 2024 Shift 1

Two identical capacitors have same capacitance $$C$$. One of them is charged to the potential $$V$$ and other to the potential $$2V$$. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is :

The reading in the ideal voltmeter $$V$$ shown in the given circuit diagram is: 

A galvanometer has a resistance of $$50\ \Omega$$ and it allows maximum current of $$5$$ mA. It can be converted into voltmeter to measure upto $$100$$ V by connecting in series a resistor of resistance.

A parallel plate capacitor has a capacitance $$C = 200$$ pF. It is connected to $$230$$ V ac supply with an angular frequency $$300$$ rad s$$^{-1}$$. The rms value of conduction current in the circuit and displacement current in the capacitor respectively are :

In series LCR circuit, the capacitance is changed from $$C$$ to $$4C$$. To keep the resonance frequency unchanged, the new inductance should be :

A monochromatic light of wavelength $$6000\ \mathring{A}$$ is incident on the single slit of width $$0.01$$ mm. If the diffraction pattern is formed at the focus of the convex lens of focal length $$20$$ cm, the linear width of the central maximum is :

The de Broglie wavelengths of a proton and an $$\alpha$$ particle are $$\lambda$$ and $$2\lambda$$ respectively. The ratio of the velocities of proton and $$\alpha$$ particle will be :

The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly :

In the given circuit if the power rating of Zener diode is $$10$$ mW, the value of series resistance $$R_s$$ to regulate the input unregulated supply is: 

$$10$$ divisions on the main scale of a Vernier calliper coincide with $$11$$ divisions on the Vernier scale. If each division on the main scale is of $$5$$ units, the least count of the instrument is :