NTA JEE Main 25th July 2022 Shift 2

The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are $$1\%$$, $$2\%$$ and $$3\%$$ respectively. The maximum percentage error in the detection of the dissipated heat will be:

A ball is projected from the ground with a speed $$15 \text{ m s}^{-1}$$ at an angle $$\theta$$ with horizontal so that its range and maximum height are equal, then $$\tan \theta$$ will be equal to

For a free body diagram shown in the figure, the four forces are applied in the '$$x$$' and '$$y$$' directions. What additional force must be applied and at what angle with positive $$x$$-axis so that the net acceleration of body is zero?

A bag of sand of mass $$9.8 \text{ kg}$$ is suspended by a rope. A bullet of $$200 \text{ g}$$ travelling with speed $$10 \text{ m s}^{-1}$$ gets embedded in it, then loss of kinetic energy will be

Two billiard balls of mass $$0.05 \text{ kg}$$ each moving in opposite directions with $$10 \text{ m s}^{-1}$$ collide and rebound with the same speed. If the time duration of contact is $$t = 0.005 \text{ s}$$, then what is the force exerted on the ball due to each other?

The length of a seconds pendulum at a height $$h = 2R$$ from earth surface will be: (Given: $$R$$ = Radius of earth and acceleration due to gravity at the surface of earth $$g = \pi^2 \text{ m s}^{-2}$$)

An object is taken to a height above the surface of earth at a distance $$\dfrac{5}{4}R$$ from the centre of the earth. Where radius of earth, $$R = 6400 \text{ km}$$. The percentage decrease in the weight of the object will be

A drop of liquid of density $$\rho$$ is floating half immersed in a liquid of density $$\sigma$$ and surface tension $$7.5 \times 10^{-4} \text{ N cm}^{-1}$$. The radius of drop in cm will be: (Take: $$g = 10 \text{ m s}^{-2}$$)

Let $$\eta_1$$ is the efficiency of an engine at $$T_1 = 447°C$$ and $$T_2 = 147°C$$ while $$\eta_2$$ is the efficiency at $$T_1 = 947°C$$ and $$T_2 = 47°C$$. The ratio $$\dfrac{\eta_1}{\eta_2}$$ will be

Sound travels in a mixture of two moles of helium and $$n$$ moles of hydrogen. If rms speed of gas molecules in the mixture is $$\sqrt{2}$$ times the speed of sound, then the value of $$n$$ will be