If \(\vec{a}=3 \hat{i}-6 \hat{j}+\hat{k}\) and \(\vec{b}=2 \hat{i}-4 \hat{j}+\lambda \hat{k}\) are such that \(\vec{a} \| \vec{b}\), then \(3 \lambda+2=\)

The equation of the normal to the curve \(y=\frac{x-7}{(x-2)(x-3)}\) at (7,0) is:

Which one of the following options is incorrect?
For a square matrix \(A\) in the matrix equation \(A X=B\).

The differential equation of the family of parabolas \(y^2=4 a x\) where \(a\) is an arbitrary constant is :

The value of \(\tan ^2\left(\sec ^{-1} 2\right)\) is:

The corner points of the feasible region of the LPP: Minimize \(Z=-50 x+20 y\) subject to
\(2 x-y \geq-5,3 x+y \geq 3,2 x-3 y \leq 12\) and \(x, y \geq 0\) are:

If A is a square matrix of order 3 and |A| = 5, then | adj A| is:

If \(y=\log \left[\frac{x^2}{e^2}\right]\) then value of \(\frac{d^2 y}{d x^2}\) is :

Answer the question on basis of passage given below :
Molecular nitrogen is very little reactive chemically. During lightning discharge, atmospheric nitrogen and oxygen combines to form nitric oxide which also combines with oxygen to form nitrogen dioxide. Both NO and \(NO _2\) constitute smog which is very poisonous. It can cause burning sensation in the eyes and adversely affect respiratory system.
Molecular nitrogen is very little reactive since it has -

When light passes from air to glass, then

Let \(f(x)=x|x|\). Then \(f(x)\) is:

Read the following passage carefully and answer the given questions.
Bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus Trichoderma polysporum. Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol. Baculoviruses are pathogens that attack insects and other arthropods. The majority of baculoviruses used as biological control agents are in the genus Nucleopolyhedrovirus. These viruses are excellent candidates for species-specific, narrow spectrum insecticidal applications. They have been shown to have no negative impacts on plants, mammals, birds, fish or even on non-target insects. BOD refers to the amount of the oxygen that would be consumed if all the organic matter in one liter of water were oxidised by bacteria. The sewage water is treated till the BOD is reduced. Cheese, is one of the oldest food items in which microbes were used. Different varieties of cheese are known by their characteristic texture, flavour and taste. For example, the large holes in 'Swiss cheese' are due to production of a large amount of CO₂ by a bacterium named Propionibacterium sharmanii.
Baculoviruses are-

The region where the body of the ovule fuses with funicle is known as: