If A and B are invertible matrices of the same order, then \(( AB )^{-1}\) is equal to

If \(x, y, z\) are non-zero numbers, then the inverse of matrix \(\mathrm{A}=\left[\begin{array}{lll}x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z\end{array}\right]\) is

Consider the function \(f(x)=x^3-3 x\). Then Match List-I with List-II:

List-I	List-II
(A) Point of local Maxima	(I) 1
(B) Point of local Minima	(II) -1
(C) Local maximum value	(III) 2
(D) Local minimum value	(IV) - 2

Choose the correct answer from the options given below:

Determinant is unaltered if :

The interval in which the function \(g(x)=x^2 e^{-x}\) is increasing is :

The solution of the differential equation \(\left(x^2+x y\right) d y=\left(x^2+y^2\right) d x\) is

In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is:

In the following hypothetical rate equation :
\(r = k[A]^x [B]^y\)
If the concentration of \([B]\) is kept constant and the concentration of \([A]\) is increased to \(3\) times, the reaction rate increases \(27\) times. The order of reaction with respect to \(A\) is :

The electric charges are distributed in a small volume. The flux of the electric field through a sphere of radius 10 cm surrounding the total charge is 20 Vm. The flux over a concentric sphere of radius 20 cm will be:

Identify the product C in the following sequence of reactions.
\(\text{CH}_3 - \text{CH} = \text{CH} - \text{CH}_3 \xrightarrow{\text{O}_3} \text{A} \xrightarrow{\text{Zn/H}_2\text{O}} \text{B} \xrightarrow{\text{LiAlH}_4} \text{C}\)

Read the passage carefully and answer the questions
The carbonyl group of aldehydes and ketones is highly polar. The positively charged carbon is readily attacked by electron-rich nucleophile and the negatively charged oxygen atom is attacked by an electro-deficient electrophile. Aldehydes and ketones undergo nucleophilic addition reactions in the presence of acid or a base. The mechanism involves attack of a nucleophile on the electron deficient carbonyl carbon to form a tetrahedral intermediate. A new bond is formed between the carbon and oxygen. Protonation of the anion furnished by the reaction medium yields a neutral addition product. The addition product is same whether the reaction is catalyzed by acid or a base. For example in the presence of base aldehydes and ketones react with hydrogen cyanide to form cyanohydrin.
Which of the following reactions is not a nucleophilic addition reaction of aldehydes and ketones?

The plane \(x(1+2 \lambda)+y(2+\lambda)+z(3-\lambda)=0\) passes through the intersection of :

Deficiency disease caused due to deficiency of Vitamin \(K\) is :