Set A has 3 elements and the set B has 4 elements. Then the number of injective mappings that can be defined from A to B 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:

A relation \(R\) in the set \(A=\{1,2,3,4\}\) is given by \(R=\{(1,1),(2,2),(1,2),(2,3),(3,4),(4,4),(1,3),(2,4),(1,4)\}\) is

If the cash equivalent of a perpetuity of ₹ 1200 payable at end of each half year is ₹ 96,000, the annual rate of interest compounded half yearly is :

The corner points of the bounded feasible region for an LPP are (0, 20), (3, 12), (6,8), (0, 15).
The objective function is \(Z=a x+\beta y\), where \(a, \beta>0\).
If the maximum of Z occurs at the corner points (3, 12) and (6,8), then the relationship between \(a\) and \(\beta\) is:

If A = \(\left[\begin{array}{ccc}0 & 1 & -3 \\ -1 & 0 & 5 \\ 3 & -5 & 0\end{array}\right]\), then the value of \(\left|A^{2025}\right|\) is

If \(f: R \rightarrow R\) is defined by f(x) = sin x + x then f(f(x)) is:

The Medical Termination of Pregnancy (Amendment) Act, 2017 was enacted by the government of India with the intension of __________.

The value of the definite integral \(I=\int_{-1}^1 \frac{1}{1+\sqrt{e^x}} d x\) is :

When strong magnetic field is applied on a stationary electron, the electron :

If \(A\) is any event associated with sample space and If \(E_1, E_2, E_3\) are mutually exclusive and exhaustive events. Then which of the following are true?
(A) \(P(A)=P\left(E_1\right) P\left(E_1 \mid A\right)+P\left(E_2\right) P\left(E_2 \mid A\right)+P\left(E_3\right) P\left(E_3 \mid A\right)\)
(B) \(P(A)=P\left(A \mid E_1\right) P\left(E_1\right)+P\left(A \mid E_2\right) P\left(E_2\right)+P\left(A \mid E_3\right) P\left(E_3\right)\)
(C) \(P\left(E_i \mid A\right)=\frac{P\left(A \mid E_i\right) P\left(E_i\right)}{\sum_{i=1}^3 P\left(A \mid E_i\right) P\left(E_i\right)}, i=1,2,3\)
(D) \(P\left(A \mid E_i\right)=\frac{P\left(E_i \mid A\right) P\left(E_i\right)}{\sum_{i=1}^3 P\left(E_i \mid A\right) P\left(E_i\right)}, i=1,2,3\)
Choose the correct answer from the options given below:

Amines are reactive in nature, mainly due to difference in electronegativity between Nitrogen and Hydrogen and, due to lone pair of electrons on Nitrogen. Amines behave like nucleophiles and as good lewis bases and there are various reactions to support this. Different degree of amines differ in their reactivity due to steric hinderance and electronic effects. Aromatic amines are less basic due to + R effect, hence have higher pkb value than aliphatic amines. Basic strength of amines also depends on stability of corresponding conjugate acid in aqueous medium.
Which of the following will be having lowest \(p K_b\) in gaseous medium?

The IUPAC name for the following complex compound
\(\text{K[Au(Br)(ONO) (SO}_4\text{)(NH}_3\text{)]}\) is