Choose the correct sets with respective observations: (1) \( \text{CuSO}_4 \) (acidified with acetic acid) + \( K_2\text{Fe(CN)}_6 \) (neutralized with NaOH) → Blue precipitate (2) \( 2\text{CuSO}_4 \) + \( K_2\text{Fe(CN)}_6 \) → Blue precipitate (3) \( 4\text{FeCl}_3 \) + \( 3\text{K}_4\text{Fe(CN)}_6 \) → \( \frac{1}{2}K_4\text{Fe(CN)}_6 \) (4) \( 37\text{Cl}_2 \) + \( 2\text{KFe(CN)}_6 \) → 6KC1 In the light of the above options, choose the correct set:
Given below are two statements: Statement I: Vanillin will react with NaOH and also with Tollen’s reagent. Statement II: Vanillin will undergo self-aldol condensation very easily. In the light of the above statements, choose the most appropriate answer from the options given below:
Designate whether each of the following compounds is aromatic or not aromatic.
A point charge $ +q $ is placed at the origin. A second point charge $ +9q $ is placed at $ (d, 0, 0) $ in Cartesian coordinate system. The point in between them where the electric field vanishes is:
Match List-I with List-II.
A small bob of mass 100 mg and charge +10 µC is connected to an insulating string of length 1 m. It is brought near to an infinitely long non-conducting sheet of charge density \( \sigma \) as shown in figure. If the string subtends an angle of 45° with the sheet at equilibrium, the charge density of sheet will be :
A particle is subjected to simple harmonic motions as: $ x_1 = \sqrt{7} \sin 5t \, \text{cm} $ $ x_2 = 2 \sqrt{7} \sin \left( 5t + \frac{\pi}{3} \right) \, \text{cm} $ where $ x $ is displacement and $ t $ is time in seconds. The maximum acceleration of the particle is $ x \times 10^{-2} \, \text{m/s}^2 $. The value of $ x $ is:
The relationship between the magnetic susceptibility $ \chi $ and the magnetic permeability $ \mu $ is given by: $ \mu_0 $ is the permeability of free space and $ \mu_r $ is relative permeability.
A square Lamina OABC of length 10 cm is pivoted at \( O \). Forces act at Lamina as shown in figure. If Lamina remains stationary, then the magnitude of \( F \) is:
A slanted object AB is placed on one side of convex lens as shown in the diagram. The image is formed on the opposite side. Angle made by the image with principal axis is:
Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density \( +\sigma \) and \( -\sigma \). The force experienced by a point charge \( +q \) placed at the mid point between the plates will be:
A wheel of radius $ 0.2 \, \text{m} $ rotates freely about its center when a string that is wrapped over its rim is pulled by a force of $ 10 \, \text{N} $. The established torque produces an angular acceleration of $ 2 \, \text{rad/s}^2 $. Moment of inertia of the wheel is............. kg m².
A steel wire of length 2 m and Young's modulus \( 2.0 \times 10^{11} \, \text{N/m}^2 \) is stretched by a force. If Poisson's ratio and transverse strain for the wire are \( 0.2 \) and \( 10^{-3} \) respectively, then the elastic potential energy density of the wire is \( \times 10^6\), in SI units .
Match List-I with List-II: List-I List-II
A body of mass 1kg is suspended with the help of two strings making angles as shown in the figure. Magnitude of tensions $ T_1 $ and $ T_2 $, respectively, are (in N):
