The electric field amplitude of an electromagnetic wave is \(100 N C ^{-1}\) and its frequency is 50 MHz . What is the magnitude of wave vector \(k\), (given speed of electromagnetic wave is \(3 \times 10^8 m s ^{-1}\) )

In a potentiometer arrangement for comparing emf of two cells, it was found that a cell of emf 1.25 V gives a balance point at 0.35 m length of the wire. On replacing the cell by another cell, the balance point shifted to 0.63 m. The emf of the second cell is :

If electron, deutron, \(\alpha\)-particle and proton have same kinetic energy, which one has the largest deBroglie wavelength.

The current changes in a coil from 10 A to 2 A in 0.2 s. The induced emf produced is 50 V. The self inductance of the coil is:

A battery of emf 10 V and internal resistance \( 3 \, \Omega \) is connected to an external resistor. If the current in the circuit is 0.5 A, then the voltage drop across the external resistor will be

The ratio of the intensity of unpolarised incident light and polarised emergent light is :

To demonstrate the phenomenon of interference, we require two sources, which emit radiation of

If \(\cos^2 y + \sin(xy) = \lambda\), then \(\frac{dy}{dx} =\)

Match List-l with List-ll
Let \(A\) be any invertible square matrix. Then

List-l	List-ll
(A) \(A-A^T\)	(I) \(|A| A^{-1}\)
(B) \(A A^T\)	(II) Skew-symmetric
(C) \(\operatorname{det}\left(A^{-1}\right)\)	(III) Symmetric
(D) \(\operatorname{adj} A\)	(IV) \([\operatorname{det}(A)]^{-1}\)

Choose the correct answer from the options given below :

Answer the question on the basis of passage given below :
Formaldehyde is the first member of the aldehydic series. It is present in green leaves of plants where its presence is supposed to be due to the reaction of \(CO_2\) with water in the presence of sunlight and chlorophyll. Commercially, formaldehyde is obtained by the controlled oxidation of methane in the presence of molybdenum oxide (\(MoO\)) acting as a catalyst. Formaldehyde is a constituent of a number of polymers also called resins. These are non volatile solids or semi solids which are obtained directly from certain plants and can be synthesized in the laboratory.
Question: Formaldehyde on reaction with benzaldehyde in basic medium gets converted to:

The maximum value of \(Z=3 x+4 y\) subject to constraint \(x+y \leq 6, x, y \geq 0\) is:

Question: In the complex ion \(\left[ Fe \left( C _2 O _4\right)_3\right]^{3-}\), the coordination number of Fe is:

The value of \(\int e^x\left[f(x)+f^{\prime}(x)\right] d x\) is :