\(I=\int a^{5 x+3} d x\) is :

If \(\sin ^{-1} x+\sin ^{-1} y=\frac{2 \pi}{3}\), then the value of \(\cos ^{-1} x+\cos ^{-1} y\) 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 \(\left|\begin{array}{ccc}x+4 & 2 x & 2 x \\ 2 x & x+4 & 2 x \\ 2 x & 2 x & x+4\end{array}\right|=k(x-4)^2\), then value of \(k\) is :

The sale of ice creams is higher in summer than in winter is an example of:

Which of the following statements are correct about the "Central Limit Theorem"?
(A) The sampling distribution of the sample mean approaches the normal distribution as the sample size gets larger.
(B) A sample size of 30 or more is considered to be sufficient to hold the "Central Limit Theorem".
(C) As the sample size becomes larger, the prediction of characteristics of the population becomes more accurate.
(D) The sampling distribution of the sample mean approaches bell shaped curveas the sample size gets larger.
Choose the correct answer from the options given below :

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

During forward bias in a p-n junction :

Identify A and B in the following reaction.

If \(A=\left[\begin{array}{ccc}2 & 1 & 3 \\ 4 & -3 & 5\end{array}\right]\) and \(B=\left[\begin{array}{cc}-2 & 3 \\ 4 & -5 \\ 1 & 2\end{array}\right]\), then which of the following statements are TRUE?
(A) AB is defined
(B) AB and BA both are defined and \(A B=I\), where I is an identity matrix of order 2
(C) BA is defined
(D) AB and BA both are defined and \(A B=B A\)
Choose the text correct answer from the options given below :

Inlet pipe A can fill a tank in 30 minutes and outlet pipes B and C can empty the tank in 2 hours each. If all three pipes operate together, the tank will be filled in

The activation energy for a reaction at a temperature \(T\) K was found to be \(2.303 RT\) J/mol.
The ratio of the rate constant to Arrhenius factor is:

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.
Carbylamine reaction is used as a test for