The value of the integral \(I=\int \frac{(\log x)^3}{x} d x\) is :

A metallic wire of uniform area of cross section has a resistance \(R\), resistivity \(\rho\) and power rating P at V volts. The wire is uniformly stretched to reduce the radius to half the original radius. The values of resistance, resistivity and power rating at V volts are now denoted by \(R ^{\prime}, \square\) ' and \(P ^{\prime}\) respectively. The corresponding values are correctly related as ___________ . Fill in the blank with the correct answer from the options given below

Let A be a square matrix of order n, then which of the following are TRUE?
(A) \(|\operatorname{adj} A|=|A|^{n-1}\)
(B) \(|A \cdot \operatorname{adj} A|=|A|^n\)
(C) A. (adj A) = |A|
(D) |KA| = K|A|
(E) \(\left|A^{-1}\right|=\frac{1}{|A|},|A| \neq 0\)
Choose the correct answert from the option given below :

Assuming the same rate of change continues for the following data :

Year(X)	2019	2020	2021	2022	2023
Profit in Percentage (y)	38	40	65	72	69

The equation of the straight line trend using the least square method is :

The value of the determinant \(D=\) equation \(\left|\begin{array}{lll}x & a & a+x \\ y & b & b+y \\ z & c & c+z\end{array}\right|\) is:

If the lines \(\frac{x-1}{-3} = \frac{y-2}{2\lambda} = \frac{z-3}{2}\) and \(\frac{x-1}{3\lambda} = \frac{y-1}{2} = \frac{z-6}{-5}\) are perpendicular. Then the value of \(\lambda\) is:

The value of the integral \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos ^2 x d x\) is:

Progestasert and LNG-20 are examples of:

The radius of spherical balloon is decreasing at the rate of \(0.1 cm / sec\), the rate at which its volume is decreasing, when its radius is 0.5 cm is:

The IUPAC name of allylamine is.

Match List-I with List-II:

List-I (Physical quantity)	List-II (Unit)
(A) Magnetic moment	(I) N A\(^{-2}\)
(B) Magnetic field strength	(II) N m rad\(^{-1}\)
(C) Torsion constant	(III) A m\(^{-1}\)
(D) Magnetic permeability	(IV) A m\(^2\)

choose the correct answer from the options given below:

If \(\left(t_1, y_1\right),\left(t_2, y_2\right)\),...,\(\left(t_n, y_n\right)\) denote the time series and \(y_t\) are the trend values of the variables \(y\), then

The electric field and magnetic field of a plane electromagnetic wave propagating in vacuum are expressed as
\(E_x=E_0 \sin (k z-\omega t)\)
\(B_y=B_0 \sin (k z-\omega t)\)
Which of the following statements are correct?
(A). The wave is propagating along the z- direction.
(B). The electric field Ex and magnetic field By are perpendicular to each other and perpendicular to the z direction.
(C) The electric and magnetic fields Ex and By are perpendicular to each other, and parallel to the direction of propagation.
(D) k is related to the wave length À of the wave by the usual equation \(k = A / 2 Tt\)
Choose the correct answer from the options given below: