If \(A=\left[\begin{array}{l}-2 \\ -1 \\ -4\end{array}\right], B=\left[\begin{array}{lll}-1 & 2 & 3\end{array}\right]\), then the value of \(A^{\prime} B^{\prime}\) is

If the line \(\vec{r}=(\hat{i}+\hat{j}+\hat{k})+\lambda(2 \hat{i}+\hat{j}+2 \hat{k})\)
is parallel to the plane \(\vec{r} \cdot(3 \hat{i}-2 \hat{j}+a \hat{k})=11\), then \(a\) is equal to :

The equation of tangent to the curve given by \(x=a \sin ^3 t, y=b \cos ^3 t\) at a point where \(t=\frac{\pi}{2}\) is :

The area of the region bounded by the curves \(y=x^2+2\) and the \(x\)-axis, between \(x=0\) and \(x=3\) in the first quadrant is :

If \(A\) and \(B\) are two events such that \(P(A \mid B)=P(B \mid A)\), and \(A \cap B \neq \emptyset\), then :

The order of the differential equation \(\left[1+\left(\frac{d y}{d x}\right)^2\right]^2=\left(\frac{d^3 y}{d x^3}\right)\) is:

If the points P, Q, R with position vectors \(5 \hat{i}+\lambda \hat{j}, 20 \hat{i}-\hat{j}\) and \(15 \hat{i}- 6\hat{j}\) respectively are colinear, then the value of \(\lambda\) is

Arrange the following electromagnetic waves in the increasing order of their energy:
(A) infrared rays
(B) AM radio waves
(C) y - rays
(D) Microwaves
Choose the correct answer from the options given below:

If \(\left[\begin{array}{cc}x-y & t \\ 2 x-y & w\end{array}\right]=\left[\begin{array}{cc}-1 & 2 \\ 0 & 1\end{array}\right]\), then \(2 x+y+3 t+w\) is equal to

Read the passage carefully and answer the questions.
Amines are considered to be derivatives of ammonia obtained by replacement of hydrogen atoms with alkyl or aryl groups. They are usually prepared from nitro compounds, halides, amides, imides etc. The presence of hydrogen bonding influences its physical properties. In alkylamines, a combination of electron releasing steric and hydrogen bonding factors influences the stability of substituted ammonium cations in protic polar solvents and thus affects the basic nature of amines. Alkyl amines are found to be stronger bases than ammonia which is more basic than water. Primary and secondary amines are engaged in intermolecular association due to hydrogen bonding. This intermolecular association is more in primary amines than in secondary amines. Tertiary amines do not have intermoleulcar association due to the absenceof hydrogen atom available for hydrogen bonding. Thus, the boiling point of amines depends on hydrogen bonding. In aromatic amines, electron releasing and withdrawing groups increase and decrease their basic character. Aryl diazonium salts usually obtained from arylamine undergo replacement of the diazonium group with a variety of nucleophile. Their coupling reaction of aryl diazonium salts with phenol or arylamine results in formation of dyes.
Complete the reaction by giving the final product:
Chloroethane + ethanolic (NaCN) + LiAlH\(_4\) \(\rightarrow\) ?

If \(A=\left[\begin{array}{ccc}\cos \theta & \sin \theta & 0 \\ -\sin \theta & \cos \theta & 0 \\ 0 & 0 & 1\end{array}\right]\) and B is a square matrix of order 3, then |AB| is equal to:

In coordinate compound \([Cr(NH_3)_6][Co(CN)_6]\)
what type of isomerism arises?

Question based on following passage: Adsorption is the process of attracting and retaining the adsorbate molecules on the surface of adsorbent. It is of two types i.e. Physisrption and chemisorption. To increase the rate of reaction, the substance called 'catalyst' is added. Promotors enhance the activity of catalyst while poison decrease the catalyst activity. Solutions may be true solution, suspension and colloids. Colloids are heterogenous but quite stable. On the basis of nature of interaction, colloids may be Lyophilic or Lyophobic. On the basis of type of dispersed phase particles, there may be multimolecular colloids, macromlecular colloids and associated colloids. The congulation of colloids may be done by boiling, dialysis or by mixing oppositely charged sols.
The Characteristic of physical adsorption is that it is :