If \(A\) is an invertible matrix of order 2 , then \(\operatorname{det}\left((\operatorname{adj} A)^{-1}\right)\) is equal to

If \(A\) and \(B\) are independent events and \(P(A)=\frac{1}{2}, P(B)=\frac{1}{3}\) then
Match List-I with List-II

List-I	List-II
(A) \(P(A \cap B)\)	(I) \(\frac{1}{2}\)
(B) \(P(\bar{A}) P(B)+P(A) P(\bar{B})\)	(II) \(\frac{1}{3}\)
(C) \(P(A \mid B)+P(B \mid A)\)	(III) \(\frac{1}{6}\)
(D) \(P(\overline{A \cap B})\)	(IV) \(\frac{5}{6}\)

Choose the correct answer from the options given below :

The solution set of the inequality \(3 x+5 y<15\) is :

If \(|\vec{a}|=3\) and \(|\vec{b}|=4\), then a value of \(\lambda\) for which \(\vec{a}+\lambda \vec{b}\) and \(\vec{a}-\lambda \vec{b}\) are perpendicular is :

The area of the region bounded by parabola \(x^2=4 y\), straight line \(x=2\) and \(x\)-axis, is

If \(\left|\begin{array}{ccc}x-2 & 1 & 2 \\ 1 & 2 x & 1 \\ -1 & 1 & 1\end{array}\right|=3\) then the values of x are:

If \(A=\left[\begin{array}{cc}3 & 1 \\ 2 & -3\end{array}\right]\) be such that \(A^{-1}=K A\), then the value of \(K\) is :

The rupturing of RBCs is associated with release of a toxic substance known as:-

The linear charge density of an infinite line charge producing a uniform electric field of \(9 \times 10^6 N / C\) at a distance of 2 cm is :
(Take permittivity of vacuum \(\epsilon_0=8.85 \times 10^{-12} C ^2 N^{-1} m^{-2}\) )

Which of the following statement is \text{\textbf\{incorrect\}?}

Read the passage carefully and answer the Questions
Carboxylic acids are the earliest organic compounds isolated from nature. These are also known as organic acids but are weaker acids as compared to mineral acids. However, they are more acidic than alcohols and phenols because of greater resonance stabilization of the parent acid and its conjugate base. The acidic strength is determined by the \(K _a\), which is called the acidity constant. The greater the value of \(K _a\), the greater the tendency of the acid to ionize and hence the stronger the acid. The acidic strength of the saturated aliphatic carboxylic acid depends upon the inductive effect and its position with respect to - COOH groups. Electron-donating substituents tend to decrease whereas electron -withdrawing substituents tend to increase the acidic strength. The acidic strength of the aromatic carboxylic acid, on the other hand depends upon both the inductive effect and the resonance effect of the substituents.
How can we express the (acidity constant) \(K_{ a }\) of RCOOH ?

The area (in sq. units) bounded by the parabola \(y^2=4 a x\), its latus rectum and the \(x\)-axis in the first quadrant is:

Answer the question on the basis of passage given below:
Second period elements of p-Block differs from the rest of their group members due to their small atomic size, high electronegativity, high ionization enthalpy and absence of d-orbitals. The elements from the second period like C, N, O have unique property of forming \(p \pi-p \pi\) multiple bonds whereas other heavier elements of p-block form \(d \pi-p \pi\) multiple bonds. This changes the properties of second period elements to great extent. Also the single bond strength of the p-block elements with their own atoms gets affected by their atomic size and presence of lone pairs.
Inert pair effect also affects the properties of the p-Block elements especially for those elements which are present from 4th period onward and this happens due to poor screening effect of inner (n-1)d subshell electrons.
Catenation tendency of Nitrogen is weaker than Phosphorus, because