NTA JEE Mains 22nd Jan 2025 Shift 1

A bob of mass m is suspended at a point O by a light string of length l and left to perform vertical motion (circular) as shown in figure. Initially, by applying horizontal velocity $$v_o$$ at the point ' A ', the string becomes slack when, the bob reaches at the point ' D '. The ratio of the kinetic energy of the bob at the points B and C is

________.

Given is a thin convex lens of glass (refractive index $$\mu$$) and each side having radius of curvature R. One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that the image gets formed on the object itself ?

Which of the following circuits represents a forward biased diode?

Choose the correct answer from the options given below :

Sliding contact of a potentiometer is in the middle of the potentiometer wire having resistance $$R_p = 1 \Omega$$ as shown in the figure. An external resistance of $$R_e = 2 \Omega$$ is connected via the sliding contact. The electric current in the circuit is :

A small point of mass m is placed at a distance 2R from the centre 'O' of a big uniform solid sphere of mass M and radius R . The gravitational force on ' m ' due to M is $$F_1$$. A spherical part of radius R/3 is removed from the big sphere as shown in the figure and the gravitational force on m due to remaining part of M is found to be $$F_2$$ . The value of ratio $$F_1 : F_2$$ is

A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities $$\rho_1$$ and $$\rho_2$$, respectively. The frequency of $$9^{th}$$ harmonic of closed tube is identical with $$4^{th}$$ harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is $$\rho_1 : \rho_2=1:16$$, then the length of the open tube is :

If B is magnetic field and $$\mu_o$$ is permeability of free space, then the dimensions of $$(B/\mu_o)$$ is

A line charge of length $$\frac{'a'}{2}$$is kept at the center of an edge BC of a cube ABCDEFGH having edge length 'a' as shown in the figure. If the density of line charge is $$\lambda C$$ per unit length, then the total electric flux through

all the faces of the cube will be . (Take, $$\epsilon _o$$ as the free space permittivity)

Given below are two statements : Statement I : In a vernier callipers, one vernier scale division is always smaller than one main scale division. Statement II : The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions. In the light of the above statements, choose the correct answer from the options given below.

The work functions of cesium (Cs) and lithium (Li) metals are 1.9 eV and 2.5 eV , respectively. If we incident a light of wavelength 550 nm on these two metal surfaces, then photo-electric effect is possible for the case of