NTA JEE Mains 04th April 2024 Shift 1 - Physics

In an experiment to measure focal length (f) of convex lens, the least counts of the measuring scales for the position of object (u) and for the position of image (v) are $$\Delta u$$ and $$\Delta v$$, respectively. The error in the measurement of the focal length of the convex lens will be:

The equation of stationary wave is: $$y = 2a\sin\left(\frac{2\pi nt}{\lambda}\right)\cos\left(\frac{2\pi x}{\lambda}\right)$$. Which of the following is NOT correct:

A body travels 102.5 m in the $$n^{th}$$ second and 115.0 m in the $$(n+2)^{th}$$ second. The acceleration is:

The co-ordinates of a particle moving in x-y plane are given by: $$x = 2 + 4t,\ y = 3t + 8t^2$$. The motion of the particle is:

A wooden block, initially at rest on the ground, is pushed by a force which increases linearly with time t. Which of the following curve best describes acceleration of the block with time:

If a rubber ball falls from a height h and rebounds upto the height of h/2. The percentage loss of total energy of the initial system as well as velocity of ball before it strikes the ground, respectively, are:

A metal wire of uniform mass density having length L and mass M is bent to form a semicircular arc and a particle of mass m is placed at the centre of the arc. The gravitational force on the particle by the wire is:

Given below are two statements: Statement I: When speed of liquid is zero everywhere, pressure difference at any two points depends on equation $$P_1 - P_2 = \rho g(h_2 - h_1)$$. Statement II: In venturi tube shown, $$2gh = v_1^2 - v_2^2$$. Choose the most appropriate answer from the options given below.

The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are 8Ω and 10Ω respectively. After inserting in a hot bath of temperature 400°C, the resistance of platinum wire is:

On Celsius scale the temperature of body increases by 40°C. The increase in temperature on Fahrenheit scale is:

P-T diagram of an ideal gas having three different densities $$\rho_1, \rho_2, \rho_3$$ (in three different cases) is shown in the figure. Which of the following is correct:

An infinitely long positively charged straight thread has a linear charge density $$\lambda\ Cm^{-1}$$. An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of electron as a function of radius of circular path from the wire is:

To measure the internal resistance of a battery, potentiometer is used. For R = 10Ω, the balance point is observed at l = 500 cm and for R = 1Ω the balance point is observed at l = 400 cm. The internal resistance of the battery is approximately:

An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then:

In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to: A. pure inductor. B. pure capacitor. C. pure resistor. D. combination of an inductor and capacitor. Choose the correct answer from the options given below :

The electric field in an electromagnetic wave is given by $$\vec{E} = \hat{i}40\cos\omega(t - z/c)\ NC^{-1}$$. The magnetic field induction of this wave is (in SI unit):

An effective power of a combination of 5 identical convex lenses which are kept in contact along the principal axis is 25D. Focal length of each of the convex lens is:

Which figure shows the correct variation of applied potential difference (V) with photoelectric current (I) at two different intensities of light $$(I_1 < I_2)$$ of same wavelengths:

Which of the following nuclear fragments corresponding to nuclear fission between neutron $$\binom{1}{0}n$$ and uranium isotope $$\left(_{92}^{235}U\right) $$ is correct:

The value of net resistance of the network as shown in the given figure  is:

Two forces $$\vec{F_1}$$ and $$\vec{F_2}$$ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between $$\vec{F_1}$$ and $$\vec{F_2}$$ is $$\cos^{-1}\left(\frac{1}{n}\right)$$. The value of |n| is _____.

A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed $$\upsilon$$. The sphere and the cylinder reaches upto maximum heights $$h_1$$ and $$h_2$$, respectively, above the initial level. The ratio $$h_1 : h_2$$ is $$\frac{n}{10}$$. The value of n is _____.

An elastic spring under tension of 3 N has a length a. Its length is b under tension 2 N. For its length (3a − 2b), the value of tension will be ______ N.

A soap bubble is blown to a diameter of 7 cm. 36960 erg of work is done in blowing it further. If surface tension of soap solution is 40 dyne/cm then the new radius is ______ cm. (Take $$\pi = \frac{22}{7}$$)

An infinite plane sheet of charge having uniform surface charge density $$+\sigma_s\ C/m^2$$ is placed on x−y plane. Another infinitely long line charge having uniform linear charge density $$+\lambda_e\ C/m$$ is placed at z = 4 m plane and parallel to y-axis. If the magnitude values $$|\sigma_s| = 2|\lambda_e|$$, then at point (0, 0, 2), the ratio of magnitudes of electric field values due to sheet charge to that of line charge is $$\pi\sqrt{n} : 1$$. The value of n is _____.

Twelve wires each having resistance 2Ω are joined to form a cube. A battery of emf 6 V is joined across point a and c. The voltage difference between e and f is ______ V.

The magnetic field existing in a region is given by $$\vec{B} = 0.2(1 + 2x)\hat{k}\ T$$. A square loop of edge 50 cm carrying 0.5 A current is placed in x−y plane with its edges parallel to the x−y axes, as shown in figure. The magnitude of the net magnetic force experienced by the loop is ______ mN.

A alternating current at any instant is given by $$i = [6 + \sqrt{56}\sin(100\pi t + \pi/3)]\ A$$. The rms value of the current is ______ A.

Two wavelengths $$\lambda_1$$ and $$\lambda_2$$ are used in Young's double slit experiment. $$\lambda_1 = 450\ nm$$ and $$\lambda_2 = 650\ nm$$. The minimum order of fringe produced by $$\lambda_2$$ which overlaps with the fringe produced by $$\lambda_1$$ is n. The value of n is _____.

A hydrogen atom changes its state from n = 3 to n = 2. Due to recoil, the percentage change in the wavelength of emitted light is approximately $$1 \times 10^{-n}$$. The value of n is _____. [Given Rhc = 13.6 eV, hc = 1242 eVnm, h = 6.6×10⁻³⁴ Js, mass of hydrogen atom = 1.6×10⁻²⁷ kg]