If a matrix has 24 elements, which of the following cannot be the possible order of the matrix?

A line passes through the point with position vector \(2 \hat{i}-\hat{j}+4 \hat{k}\) and is in the direction of the vector \(\hat{i}+\hat{j}-2 \hat{k}\). The equation of the line in Cartesian form is:

Let L be the set of all lines in a plane and R be the relation on set L defined by \(R=\left\{\left(L_1, L_2\right) : L_1 \perp L_2\right\}\). Then R is
(A) an equivalence Relation
(B) a symmetric Relation
(C) not a transitive Relation
(D) a reflexive Relation
Choose the correct answer from the options given below :

If \(y=(\log x)^{\log x}, x>1\) then \(\frac{d y}{d x}\) is equal to

In a 500 m race, the ratio of speeds of two participants, A and B, is 4 : 5 respectively.
If A has a start of 180 m, then the distance by which A wins is :

The integrating factor of the differential equation \(\frac{d y}{d x}+y \cot x=2 x+x^2 \cot x, x \neq 0\) is

If \(A, B\) and \(C\) are all the corner points of feasible region (bounded) of an LPP with objective function \(Z\) that needs to be maximized such that \(Z_A>Z_B\) and \(Z_C < Z_A\) (Here \(Z_A\) denotes value of \(Z\) at \(A\) ), then which of the following statements is TRUE ?

A light of wavelength of \( \lambda = 6 \times 10^{-7} \text{ m} \) illuminates a single slit of width \( a = 1.2 \text{ mm} \). The screen is at a distance of \( D = 2.4 \text{ m} \) away from the slit. The width of central maximum (\( \beta_0 \)) is

If you place blood cells in a solution containing more than 0.9% (mass/volume) sodium chloride, water will flow out of the cells and they will shrink. Such a solution is called

The correct sequence for product formation according to the Collision theory of chemical reaction is
(A) Proper orientation
(B) Molecules collide with threshold energy
(C) Intermediate formation
(D) Formation of products
Choose the correct answer from the options given below:

A long solenoid is formed by winding 40 turns/cm. The current required to produce a magnetic field of 22 mT inside the solenoid will be (Take \( \mu_0 = 4\pi \times 10^{-7} \, Tm A^{-1} \))

Osmotic pressure measurements are less accurate and difficult to carry out. Therefore, this method is not useful for measuring molecular weights. But it is used to find out molecular weights of polymers eg. plastics, proteins and starch having many monomer units. Knowing the value of osmotic pressure of a given solution, molecular weight of the solute can be calculated using Van't Hoff equation.
In a nearly saturated solution, which of the following statements are correct?
A. If dissolution process is endothermic, solubility increases with increase in temperature.
B. If dissolution process is endothermic, solubility decreases with increase in temperature.
C. If dissolution process is exothermic, solubility decreases with increase in temperature.
D. If dissolution process is exothermic, solubility increases with increase in temperature.
Choose the correct answer from the options given below:

Read the following paragraph and answer the given questions.
Bio-fertilisers are organisms that enrich the nutrient quality of the soil like cyanobacteria, while there are organisms that help to control plant diseases and pests. The very familiar beetle, the ladybird and dragonflies are useful to get rid of aphids and mosquitoes, respectively. An example of microbial biocontrol agents that can be introduced to control butterfly caterpillars is certain bacteria, which are available in sachets in the form of dry spores. These spores are mixed with water and sprayed onto vulnerable plants. Trichoderma species that are very common in the root ecosystem, are very effective biocontrol agents of several plant pathogens.Baculoviruses attack insects and other arthropods. Usage of these viruses is desirable when an ecological sensitive area is being treated.
Which one of the following is not an advantage of Nucleopolyhedrovirus as biocontrol agents?