A circular conducting loop is placed in a uniform magnetic field with its plane perpendicular to the field. An emf is induced in the loop if:
A. it is displaced in the same plane in magnetic field
B. it is rotated about its axis
C. it is rotated about a diameter
D. it is converted into square loop in the same plane:
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The wavelength of matter wave depends upon:
A. charge
B. velocity
C. momentum
D. mass
E. charge density
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Identify the incorrect statement(s) among the following:
when a dielectric medium is introduced between the plates of a charged capacitor:
(A) If a plate of dielectric constant k, thickness t is placed between the plates of a charged capacitor of area A and distance d, then the new capacitance will be \( \frac{A\varepsilon_0}{d - t(1 - 1/k)} \)
(B) The electric field between plates of the charged capacitor when the dielectric is introduced will be \( E = (E_0 - E_p) \)
(C) Dielectric constant of the dielectric placed between plates of charged capacitor will be \( k = \frac{E_0}{E_0 - E_p} \)
(D) Dielectric strength of the dielectric is the maximum value of the electric field which may be applied before its breakdown.
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There is a small air bubble inside a glass sphere (\( \mu = 1.5 \)) of radius 10 cm. The bubble is 4.0 cm below the surface and is viewed normally from outside as shown. The apparent depth of the bubble will be

Which of the following is NOT true about a shunt ?

Nichrome element is used in household appliances because of the following characteristics
1. Its melting point is high
2. Its resistivity is large
3. It is tensile
4. It does not oxidize easily by the oxygen of the air when heated
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In a series LCR circuit, \( C = 5 \text{ }\mu\text{F} \) and \( \omega = 1000 \text{ rad/s} \). The value of inductance L for which the current is maximum in this circuit will be :

If \(\int_0^1\left(3 x^2+2 x+5 k\right) d x=0\), then the value of \(k\) is:

The edge lengths of the unit cells in terms of the radius of spheres constituting fcc, bcc \& simple cubic unit cell respectively are:

Match List-I with List-II

List-I (Differential Equation)	List-II (Order and Degree)
(A) \(\left(\frac{d^2 y}{d x^2}\right)^2-e^x\left(\frac{d y}{d x}\right)^4+1=0\)	(I) order \(=1\) and degree \(=2\)
(B) \(\left(\frac{d y}{d x}\right)^2+x y=0\)	(II) order \(=2\) and degree \(=1\)
(C) \(\left(1+\frac{d y}{d x}\right)^{3 / 2}=4\left(\frac{d^2 y}{d x^2}\right)^2\)	(III) order \(=2\) and degree \(=2\)
(D) \(\sqrt{\frac{d^2 y}{d x^2}}+1=\frac{d y}{d x}\)	(IV) order \(=2\) and degree \(=4\)

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The kinetic energy of an \(\alpha\)-particle incident on gold foil is reduced to half of its initial value. How does the distance of closest approach change?

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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A trust invites a deposit of a lump sum amount from an individual so that an annual scholarship of Rs. 5000 is paid. Rate of interest is 5% per annum.
If the scholarship is to start at the end of this year, then the amount needed to deposit to the trust is: