JEE Main 2021 Physics Paper: 31 Aug, Shift 1

In an ac circuit, an inductor, a capacitor and a resistor are connected in series with XL = R = XC. Impedance of this circuit is:

A capacitor of 50 $\mu$F is connected in a circuit as shown in figure. The charge on the upper plate of the capacitor is ______________$\mu$C.

A square shaped wire with resistance of each side 3$\Omega$ is bent to form a complete circle. The resistance between two diametrically opposite points of the circle in unit of $\Omega$ will be ___________.

The voltage drop across 15$\Omega$ resistance in the given figure will be ______________ V.

Consider a galvanometer shunted with 5$\Omega$ resistance and 2% of current passes through it. What is the resistance of the given galvanometer?

A moving proton and electron have the same de-Broglie wavelength. If K and P denote the K.E. and momentum respectively. Then choose the correct option:

A small square loop of side 'a' and one turn is placed inside a larger square loop of side b and one turn (b >> a). The two loops are coplanar with their centres coinciding. If a current I is passed in the square loop of side 'b', then the coefficient of mutual inductance between the two loops is:

The electric field in an electromagnetic wave is given by E = (50 NC${}^{-1}$) sin$\omega$ (t $-$ x/c) The energy contained in a cylinder of volume V is 5.5 $\times$ 10$-$12 J. The value of V is _____________ cm3. (given $\varepsilon$0 = 8.8 $\times$ 10$-$12C2N$-1\,\text{m}-$2)

Two particles A and B having charges 20$\mu$C and $-5\mu$C respectively are held fixed with a separation of 5 cm. At what position a third charged particle should be placed so that it does not experience a net electric force?

When a rubber ball is taken to a depth of __________m in deep sea, its volume decreases by 0.5%. (The bulk modulus of rubber = 9.8 $\times$ 108 Nm${}^{-2}$, Density of sea water = 103 kgm${}^{-3}$, g = 9.8 m/s2)

The masses and radii of the earth and moon are (M1, R1) and (M2, R2) respectively. Their centres are at a distance 'r' apart. Find the minimum escape velocity for a particle of mass 'm' to be projected from the middle of these two masses:

A car is moving on a plane inclined at 30$^\circ$ to the horizontal with an acceleration of 10 ms${}^{-2}$ parallel to the plane upward. A bob is suspended by a string from the roof of the car. The angle in degrees which the string makes with the vertical is ______________. (Take g = 10 ms${}^{-2}$)

When a rubber ball is taken to a depth of __________m in deep sea, its volume decreases by 0.5%. (The bulk modulus of rubber = 9.8 $\times$ 108 Nm−2, Density of sea water = 103 kgm−3, g = 9.8 m/s2)

A uniform heavy rod of weight 10 kg ms−2, cross-sectional area 100 cm2 and length 20 cm is hanging from a fixed support. Young modulus of the material of the rod is 2 $\times$ 1011 Nm−2. Neglecting the lateral contraction, find the elongation of rod due to its own weight.

A coil having N turns is wound tightly in the form of a spiral with inner and outer radii 'a' and 'b' respectively. Find the magnetic field at centre, when a current I passes through coil:

A sample of a radioactive nucleus A disintegrates to another radioactive nucleus B, which in turn disintegrates to some other stable nucleus C. Plot of a graph showing the variation of number of atoms of nucleus B versus time is:

(Assume that at t = 0, there are no B atoms in the sample)

A particle of mass 1 kg is hanging from a spring of force constant 100 Nm${}^{-1}$. The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period T. The time when the kinetic energy and potential energy of the system will become equal, is $\frac{T}{x}$. The value of x is _____________.

A helicopter is flying horizontally with a speed 'v' at an altitude 'h' has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped?

Two plane mirrors M1 and M2 are at right angle to each other shown. A point source 'P' is placed at 'a' and '2a' meter away from M1 and M2 respectively. The shortest distance between the images thus formed is: (Take $\sqrt{5}$ = 2.3)

An object is placed at the focus of concave lens having focal length f. What is the magnification and distance of the image from the optical centre of the lens?

Angular momentum of a single particle moving with constant speed along circular path:

In the following logic circuit the sequence of the inputs A, B are (0, 0), (0, 1), (1, 0) and (1, 1). The output Y for this sequence will be:

Choose the correct waveform that can represent the voltage across R of the following circuit, assuming the diode is ideal one:

For an ideal gas the instantaneous change in pressure 'p' with volume 'v' is given by the equation $\frac{dp}{dv} = -ap$. If p = p0 at v =0 is the given boundary condition, then the maximum temperature one mole of gas can attain is: (Here R is the gas constant)

A reversible engine has an efficiency of $\frac{1}{4}$. If the temperature of the sink is reduced by 58$^\circ$C, its efficiency becomes double. Calculate the temperature of the sink:

Which of the following equations is dimensionally incorrect?

Where t = time, h = height, s = surface tension, $\theta$ = angle, $\rho$ = density, a, r = radius, g = acceleration due to gravity, v = volume, p = pressure, W = work done, $\Gamma$ = torque, $\epsilon$ = permittivity, E = electric field, J = current density, L = length.

Match List - I with List - II.

Choose the most appropriate answer from the options given below:

A wire having a linear mass density 9.0 $\times$ 10$-$4 kg/m is stretched between two rigid supports with a tension of 900 N. The wire resonates at a frequency of 500 Hz. The next higher frequency at which the same wire resonates is 550 Hz. The length of the wire is ____________ m.

A block moving horizontally on a smooth surface with a speed of 40 ms${}^{-1}$ splits into two equal parts. If one of the parts moves at 60 ms${}^{-1}$ in the same direction, then the fractional change in the kinetic energy will be x: 4 where x = ___________.