NTA JEE Main 9th April 2017 Online

A physical quantity $$P$$ is described by the relation $$P = a^{\frac{1}{2}} b^2 c^3 d^{-4}$$. If the relative errors in the measurement of $$a, b, c$$ and $$d$$ respectively, are 2%, 1%, 3% and 5%. Then the relative error in $$P$$ will be:

A car is standing 200 m behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration 2 m s$$^{-2}$$ and the car has acceleration 4 m s$$^{-2}$$. The car will catch up with the bus after time:

A conical pendulum of length $$l$$ makes an angle $$\theta = 45^\circ$$ with respect to Z-axis and moves in a circle in the XY plane. The radius of the circle is 0.4 m and its center is vertically below O. The speed of the pendulum, in its circular path, will be - (Take $$g = 10$$ m s$$^{-2}$$)

The machine as shown has 2 rods of length 1 m connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has a roller that rolls along the floor in a slot. As the roller goes back and forth, a 2 kg weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a:

Two particles $$A$$ and $$B$$ of equal mass $$M$$ are moving with the same speed $$v$$ as shown in figure. They collide completely inelastic and move as a single particle $$C$$. The angle $$\theta$$ that the path of $$C$$ makes with the X-axis is given by-

A circular hole of radius $$\frac{R}{4}$$ is made in a thin uniform disc having mass and radius $$R$$, as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point O and perpendicular to the plane of the disc is-

The mass density of a spherical body is given by $$\rho(r) = \frac{k}{r}$$ for $$r \le R$$ and $$\rho(r) = 0$$ for $$r > R$$, where $$r$$ is the distance from the center. The correct graph that describes qualitatively the acceleration, $$a$$ of a test particle as a function of $$r$$ is:

Two tubes of radii $$r_1$$ and $$r_2$$ and lengths $$l_1$$ and $$l_2$$, respectively, are connected in series and a liquid flows through each of them in stream line conditions. $$P_1$$ and $$P_2$$ are pressure differences across the two tubes. If $$P_2$$ is $$4P_1$$ and $$l_2$$ is $$\frac{l_1}{4}$$ then the radius $$r_2$$ will be equal to:

A steel rail of length 5 m and area of cross section 40 cm$$^2$$ is prevented from expanding along its length while the temperature rises by 10°C. If coefficient of linear expansion and Young's modulus of steel are $$1.2 \times 10^{-5}$$ K$$^{-1}$$ and $$2 \times 10^{11}$$ N m$$^{-2}$$ respectively, the force developed in the rail is approximately:

For the $$P - V$$ diagram given for an ideal gas

Out of the following which one correctly represents the $$T - P$$ diagram?