The resistivity of a wire depends on :
(A) its length
(B) its area of cross-section
(C) its temperature
(D) nature of material
(E) voltage applied across it
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The electron in a hydrogen atom emits wavelengths \( \lambda_1, \lambda_2, \lambda_3, \lambda_4 \) in the following transitions (A), (B), (C), and (D), respectively. Arrange the transitions in the increasing order of emitted wavelengths:
(A) n = 3 to n = 2
(B) n = 4 to n = 3
(C) n = 4 to n = 2
(D) n = 2 to n = 1
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Two batteries of emf 5 V with internal resistance 2 \( \Omega \) and 6 V with internal resistance 3 \( \Omega \) are connected in series with an external resistor. If the current in the circuit is 0.5 A, then the resistance of the resistor is

The given figure shows two magnetized needles and a magnet P with their magnetic moments, shown with the arrow sign. Which of the following statements are correct in respect of this configuration?

(A) \(Q_1\) is in stable equilibrium
(B) \(Q_2\) is in unstable equilibrium
(C) \(Q_1\) is in unstable equilibrium
(D) \(Q_2\) is in stable equilibrium
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In a diffraction pattern due to a narrow slit of width a, alternate dark and bright fringe pattern is obtained on a screen kept at distance D from the slit. Choose the correct option.
(A) The angular width of central maximum is given by 2D/a, linear width is given by 2D\lambda/a
(B) When the size of aperture, a is quite large, the diffraction effect is negligible,
(C) For light of smaller wavelength, angular width of central maximum increases, while linear width decreases,
(D) Angular width of central maximum does not decrease while linear width decreases on decreasing distance of screen from slit.
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A circular loop of 20 turns carries a current of 5.0 A. If the magnetic field at the centre of the loop is 1.57 mT, the radius of the loop would be :

A moving coil galvanometer has a resistance of 40 \( \Omega \). It gives a full scale deflection with a current of 2 mA. How is to be modified to convert it to a voltmeter of 5 V range?

If the matrix \(\begin{bmatrix} 3 & a+b & 4 \\ 2 & 0 & -1 \\ a-b & c & 5 \end{bmatrix}\) is symmetric, then the value of a, b and c is given by:

A \( 14.0 \, \mu\text{F} \) capacitor is connected to a 220 V, 50 Hz source. The value of peak current in the circuit is (Given: \( \pi = \frac{22}{7} \) and \( \sqrt{2} = 1.414 \)):

A Linear Programming Problem (LPP) consists of which of the following components?
(A) Decision variables
(B) The graphical compliment
(C) The objective function
(D) The linear constraints
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Other than absorption of phosphorus from soil, Glomus gives other benefits to plants like:
A. Addition of organic matter to the soil.
B. Resistance to root borne pathogens.
C. Tolerance to salinity
D. Increase in soil fertility
E. Tolerance to drought
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The area bounded by the curve \(y=4+3 x-x^2\) and the \(x\)-axis is equal to

Match List-l with List-ll

List-l (Differential Equation)	List-ll (Order and degree of differential equation)
(A) \(\frac{d^2 y}{d x^2}+2\left(\frac{d y}{d x}\right)^2=e^{\frac{d y}{d x}}+1\)	(I) Order = 1, Degree = 2
(B) \(\left(\frac{d^2 y}{d x^2}\right)^2+4\left(\frac{d y}{d x}\right)^3=e^y-1\)	(II) Order = 2, Degree = 1
(C) \(3\left(\frac{d y}{d x}\right)+4 y+e^y=\frac{d x}{d y}\)	(III) Order = 2 , Degree = 2
(D) \(\frac{d^2 y}{d x^2}+3\left(\frac{d y}{d x}\right)=\left(e^y+\frac{d y}{d x}\right)^2\)	(IV) Order = 2, Degree = Not defined

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