NTA JEE Mains 30th Jan 2024 Shift 1

The displacement and the increase in the velocity of a moving particle in the time interval of $$t$$ to $$(t + 1)$$ s are $$125 \text{ m}$$ and $$50 \text{ m s}^{-1}$$, respectively. The distance travelled by the particle in $$(t + 2)^{th}$$ s is __________ m.

Consider a disc of mass $$5 \text{ kg}$$, radius $$2 \text{ m}$$, rotating with angular velocity of $$10 \text{ rad s}^{-1}$$ about an axis perpendicular to the plane of rotation. An identical disc is kept gently over the rotating disc along the same axis. The energy dissipated so that both the discs continue to rotate together without slipping is _________ J.

Each of three blocks $$P$$, $$Q$$ and $$R$$ shown in figure has a mass of $$3 \text{ kg}$$. Each of the wire $$A$$ and $$B$$ has cross-sectional area $$0.005 \text{ cm}^2$$ and Young's modulus $$2 \times 10^{11} \text{ N m}^{-2}$$. Neglecting friction, the longitudinal strain on wire $$B$$ is $$\_\_\_\_ \times 10^{-4}$$. (Take $$g = 10 \text{ m s}^{-2}$$)

In a closed organ pipe, the frequency of fundamental note is $$30 \text{ Hz}$$. A certain amount of water is now poured in the organ pipe so that the fundamental frequency is increased to $$110 \text{ Hz}$$. If the organ pipe has a cross-sectional area of $$2 \text{ cm}^2$$, the amount of water poured in the organ tube is ________ g. (Take speed of sound in air is $$330 \text{ m s}^{-1}$$)

A capacitor of capacitance $$C$$ and potential $$V$$ has energy $$E$$. It is connected to another capacitor of capacitance $$2C$$ and potential $$2V$$. Then the loss of energy is $$\frac{x}{3}E$$, where $$x$$ is ______.

Two cells are connected in opposition as shown. Cell $$E_1$$ is of $$8 \text{ V}$$ emf and $$2 \text{ } \Omega$$ internal resistance; the cell $$E_2$$ is of $$2 \text{ V}$$ emf and $$4 \text{ } \Omega$$ internal resistance. The terminal potential difference of cell $$E_2$$ is ______ V.

A ceiling fan having $$3$$ blades of length $$80 \text{ cm}$$ each is rotating with an angular velocity of $$1200 \text{ rpm}$$. The magnetic field of earth in that region is $$0.5 \text{ G}$$ and angle of dip is $$30°$$. The emf induced across the blades is $$N\pi \times 10^{-5} \text{ V}$$. The value of $$N$$ is ______.

The horizontal component of earth's magnetic field at a place is $$3.5 \times 10^{-5} \text{ T}$$. A very long straight conductor carrying current of $$\sqrt{2} \text{ A}$$ in the direction from South east to North West is placed. The force per unit length experienced by the conductor is ________ $$\times 10^{-6} \text{ N m}^{-1}$$.

The distance between object and its two times magnified real image as produced by a convex lens is $$45 \text{ cm}$$. The focal length of the lens used is ________ cm.

An electron of hydrogen atom on an excited state is having energy $$E_n = -0.85 \text{ eV}$$. The maximum number of allowed transitions to lower energy level is _______.