A. Transformers can not be used to step up DC.
B. The frequency of output across the secondary is always equal to the frequency of input across the primary.
C. The output power of a transformer may be increased to a value which is more than the input power.
D. Transformation ratio is equal to turns ratio.
E. In a step up transformer, secondary current is less than primary current.
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Arrange the wavelengths of the following radiations in the decreasing order: \( \lambda_{visible}, \lambda_{X-rays}, \lambda_{radiowaves}, \lambda_{\gamma-rays} \)

A wire of resistance 4 \( \Omega \) is used to make a coil of radius 7 cm. The wire has a diameter of 1.4 mm and the resistivity of its material is \( \rho = 2 \times 10^{-7} \, \Omega \, m \). The number of turns in the coil will be

Match List-I with List-II

List- I	List- II
(A) For a series LC circuit	(I) Currents in L and C are 180° out of phase
(B) For a parallel LC circuit	(II) Power Factor=0
(C) For a purely capacitive circuit	(III) Voltage across L and C are 180° out of phase
(D) For a series LCR circuit at resonance	(IV) Reactance is zero

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The capacitance of a capacitor becomes \(\frac{7}{6}\) times its original value if a dielectric slab of thickness \(t=\frac{2}{3} d\) is introduced between the plates, where \(d\) is the separation between the plates. The dielectric constant of the slab is:

The optical length of an astronomical telescope with magnifying power of 10 for normal adjustment is 55 cm. What is the focal length of the objective ?

A concave lens and a convex mirror both are dipped in an oil of refractive index 1.2. The focal length of:

If the cash equivalent of a perpetuity of ₹ 1200 payable at end of each half year is ₹ 96,000, the annual rate of interest compounded half yearly is :

Read the passage carefully and answer the questions:
The degeneracy of the \(d\) orbitals has been removed due to ligand electron-metal electron repulsions in the octahedral complex to yield three orbitals of lower energy, \(t_2\), set and two orbitals of higher energy, \(e_g\) set. This splitting of the degenerate levels due to the presence of ligands in a definite geometry is termed as crystal field splitting and the energy separation is denoted by \(\Delta_0\). Thus energy of the two \(e_g\) orbitals will increase by \((3 / 5) \Delta_0\) and that of three \(t_{2 g}\) will decrease by \((2 / 5) \Delta_0\). The crystal field splitting \(\Delta_{\circ}\) depends upon the field produced by the ligand and charge on the metal ion. Some ligands are able to produce strong fields, in which case the splitting will be large, whereas others produce weak fields and consequently result in small splitting of \(d\) orbitals. Relative magnitude of crystal field splitting energy \(\Delta_0\) and pairing energy, \(P\) (energy required for electron pairing in a single orbital) determine the formation of low spin ( \(\Delta_{\circ}>P\) ) or high spin ( \(\Delta_{\circ}<P\) ) complex. In tetrahedral coordination entity formation, the d-orbital splitting is inverted and is smaller as compared to the octahedral field splitting. The crystal field theory attributes the colour of the complex to \(d-d\) transition of the electron. The colour of the coordination compounds depends on the crystal field splitting. In the absence of ligand, crystal field splitting does not occur and hence the substance is colourless.
What will be the crystal field splitting energy for tetrahedral \(\left[ CoCl _4\right]^{2-}\) if its value for octahedral \(\left[ CoCl _6\right]^{4-}\) is \(18,000 cm^{-1}\) ?

The complex \([\text{Co(NH}_3)_4(\text{NO}_2)_2]\text{Cl}\) exhibits :
A. Coordination isomerism
B. Linkage isomerism
C. Solvate isomerism
D. Ionisation isomerism
E. Geometrical isomerism
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Match List - I with List - II. If \(A=\left|\begin{array}{ccc}3 & -2 & 3 \\ 2 & 1 & -1 \\ 4 & -3 & 2\end{array}\right|\)

List - I	List - II
(A) \(M_{23}\)	(I) -17
(B) \(A_{32}+a_{13}\)	(II) -1
(C) \(A\) (Determinant value)	(III) 0
(D) \(a_{13} A_{12}+a_{23} A_{22}+a_{33} A_{32}\)	(IV) 12

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For which value of \(k\), the given system of linear equations is inconsistent?
\(3 x+6 y+3 z=4\)
\(x+k y+2 z=6\)
\(z=7\)

If A is a square matrix such that \(A^2=A\) and I is the identity matrix of the same order as A, then \((I+A)^2-3 A\) is equal to