If matrices \(A=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]\) and \(B=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]\), then \(B A\) is equal to:

If \(f(x)=a \log _e|x|+b x^2+x\) has critical points at \(x=-2\) and \(x=1\), then

If \(A=\left[\begin{array}{ll}1 & 2 \\ 4 & 5\end{array}\right]\) then
Match List-I with List-II

List-I	List-II
(A) \(\operatorname{det}(A)\)	(I) \(-\frac{1}{3}\)
(B) \(\operatorname{det}\left(A^{-1}\right)\)	(II) \(- 12\)
(C) \(\operatorname{det}(2 A)\)	(III) \(- 3\)
(D) \(\operatorname{det}\left( 3 A ^T\right)\)	(IV) \(- 27\)

Choose the Correct answer from the options given below :

The sum of the order and degree of the differential equation \(\frac{d^2 y}{d x^2}+\sqrt[3]{\frac{d y}{d x}}+(1+x)=0\) is :

Choose the correct statement about CAGR (compound annual growth rate)?

A parallelogram is constructed on the vectors \(\vec{a}=3 \vec{\alpha}-\vec{\beta}, \vec{b}=\vec{\alpha}+3 \vec{\beta}\). If \(|\vec{\alpha}|=|\vec{\beta}|=2\) and the angle between \(\vec{\alpha}\) and \[\vec{\beta}\] is \(\frac{\pi}{3}\), then length of the diagonal of the parallelogram is:

The rate of change of the area of a circular disc with respect to its circumference when radius is 3 is :

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.
Match List I with List II

LIST I	LIST II
A. Bakelite formaldehyde resin	I. Condensation polymers
B. Melamine formaldehyde resin	II. Phenol and formaldehyde
C. Urea formaldehyde resin	III. Melamine and formaldehyde
D. Bakelite \(\&\) Melamine formaldehyde resin	IV. Unbreakable cups and laminated sheets

Choose the correct answer from the options given below:

In a single slit diffraction experiment, first minima for \( \lambda_1 = 600 \, \text{nm} \) coincides with first maxima for wavelength \( \lambda_2 \). The value of \( \lambda_2 \) is

Some important general properties of the electric field lines are given below:
(A) Field lines start from positive charges and end at negative charges
(B) In a charge-free region, electric field lines can be taken to be continuous curves without any breaks
(C) Electrostatic field lines form closed loops
(D) Two field lines can never cross each other
Choose the correct answer from the options given below:

The value of \(\left|\begin{array}{lll}265 & 240 & 219 \\ 240 & 225 & 198 \\ 219 & 198 & 181\end{array}\right|\) is

Which one of the following is the cathodic reaction in a fuel cell?

The internal resistance of a cell of emf 2 V is 0.1 \( \Omega \). It is connected to an external resistance of 3.9 \( \Omega \). The terminal potential difference across the cell will be