The maximum value of \(y=x^3-3 x\) is :

\(\int_0^2|x-1| d x=\)

If \(P(A)=\frac{3}{10}, P(B)=\frac{2}{5}\) and \(P(A \cup B)=\frac{3}{5}\), then the value of \(P(B \mid A)+P(A \mid B)\) is :

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:

Which of the following statements is incorrect?

If the lines \(\frac{1-x}{3}=\frac{3 y-6}{k}=\frac{3-z}{-2}\) and \(\frac{1-x}{2 k}=\frac{y-5}{3}=\frac{6-z}{5}\) are perpendicular, then \(k\) is equal to :

The maximum profit that a company can make if the profit function is
\(P(x)=41+24 x-18 x^2\) is :

Let \(X\) denotes the number of heads in a simultaneous toss of three coins, then \(P(0< X< 3)\) is

A charge moving _________ to the direction of the magnetic field does not experience any magnetic Lorentz force.
(A) parallel
(B) perpendicular
(C) antiparallel
(D) at any acute angle
Choose the correct answer from the options given below:

Which one of the following ligands forms a chelate?

Which one of the following diagnostic techniques is based on the principle of antigen-antibody interaction?

Let \(y=138.86+7.64(x-2021)\) be a straight line of best fit by using least square method.

\(YEAR(X)\)	2018	2019	2020	2021	2022	2023	2024
\(PROFIT(y)\)	144	130	126	144	138	156	164

Then the trend value for the year 2024 is :

Read the Passage carefully and answer the Questions
Kinetic studies not only help us to determine the rate of a chemical reaction but also describe the conditions by which the reaction rates can be altered.
The factors such as concentration, temperature, preasure and catalyst affect the rate of a reaction.
The speed of a reaction or the rate of a reaction can be defined as the change in concentration of a reactant or product in unit time.
Rate \(=k|A|^a[B]^y\)
Here \(k\) is the rate constant
\(x+y\) gives the overall order of a reaction, whereas \(x\) and \(y\) represent the order with respect to the reactants \(A\) and \(B\), respectively.
Table: Initial rate of formation of NO₂

S.No.	Initial [NO]/mol L-1	Initial [O2]/mol L-1	Initial rate of formation of [NO2]/mol L-1s-1
1.	0.30	0.30	0.096
2.	0.60	0.30	0.384
3.	0.30	0.60	0.192
4.	0.60	0.60	0.768

Based on the above observations, the rate of formation of NO₂ can be represented as