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JEE Advanced 2022 Paper 2 Online
Numerical
+3
-1
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In a particular system of units, a physical quantity can be expressed in terms of the electric charge $e$, electron mass $m_{e}$, Planck's constant $h$, and Coulomb's constant $k=\frac{1}{4 \pi \epsilon_{0}}$, where $\epsilon_{0}$ is the permittivity of vacuum. In terms of these physical constants, the dimension of the magnetic field is $[B]=[e]^{\alpha}\left[m_{e}\right]^{\beta}[h]^{\gamma}[k]^{\delta}$. The value of $\alpha+\beta+\gamma+\delta$ is _______.

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2
JEE Advanced 2019 Paper 2 Offline
Numerical
+3
-0
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An optical bench has 1.5 m long scale having four equal divisions in each cm. While measuring the focal length of a convex lens, the lens is kept at 75 cm mark of the scale and the object pin is kept at 45 cm mark. The image of the object pin on the other side of the lens overlaps with image pin that is kept at 135 cm mark. In this experiment, the percentage error in the measurement of the focal length of the lens is ..............
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3
JEE Advanced 2018 Paper 2 Offline
Numerical
+3
-0
A steel wire of diameter $$0.5$$ $$mm$$ and Young's modulus $$2 \times {10^{11}}\,\,N{m^{ - 2}}$$ carries a load of mass $$M.$$ The length of the wire with the load is $$1.0$$ $$m.A$$ vernier scale with $$10$$ divisions is attached to the end of this wire. Next to the steel wire is a reference wire to which a main scale, of least count $$1.0$$ $$mm$$ , is attached. The $$10$$ divisions of the vernier scale correspond to $$9$$ divisions of the main scale. Initially, the zero of vernier scale coincides with the zero of main scale. If the load on the steel wire is increased by $$1.2$$ $$kg,$$ the vernier scale division which coincides with a main scale division is _____________. Take $$g = 10\,m\,{s^{ - 2}}.$$ and $$\pi = 3.2.$$
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4
JEE Advanced 2015 Paper 2 Offline
Numerical
+4
-0
The energy of a system as a function of time t is given as E(t) = $${A^2}\exp \left( { - \alpha t} \right)$$, where $$\alpha = 0.2\,{s^{ - 1}}$$. The measurement of A has an error of 1.25 %. If the error in the measurement of time is 1.50 %, the percentage error in the value of E(t) at t = 5 s is
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