The interval on which the function \(f(x)=x^3+2 x^2-1\) is decreasing, is

Consider the function \(f(x)=\sin x\) in the interval \([\pi, 2 \pi]\), then which of the following statements are correct?
(A) \(x=\frac{3 \pi}{2}\) is its stationary point.
(B) Its maximum value is 1
(C) Its minimum value is -1
(D) It attains its maximum value at \(\pi\) and \(2 \pi\)
Choose the correct answer from the options given below:

Let \(\vec{a}=\hat{i}+\hat{j}, \vec{b}=\hat{i}-\hat{j}\) and \(\vec{c}=\hat{i}+\hat{j}+\hat{k}\). If \(\hat{m}\) is a unit vector perpendicular to both \(\vec{a}\) and \(\vec{b}\), then \(|\vec{c} \cdot \hat{m}|\) is equal to :

If \(y=\frac{1}{x+1}\), then \(\frac{d^2 y}{d x^2}\) at x = 2 is:

Let \(X\) denote the number of hours a student studies on a selected day. The probability distribution of \(X\) is given by (where \(k\) is some unknown constant)
\(P\left(X=x_i\right)=\left\{\begin{array}{ll}0.5, & \text { if } x_i=0 \\k x_i, & \text { if } x_i=1 \\k\left(4-x_i\right), & \text { if } x_i=2 \text { or } 3 \\0, & \text { otherwise }\end{array}\right.\)
Then the value of \(k\) is

Magnetic moment of a thin bar magnet is ' M '. If it is bent into a semicircular form, its new magnetic moment will be

The corner points of the bounded feasible region for an LPP are (0,4), (4, 4), (6, 6), (0, 12).
If the objective function is \(Z=p x+q y, p>0, q>0\) then the condition on p and q so that the maximum of Z occurs at (6, 6) and (0, 12) is

Match List I with List II

LIST I	LIST II
A. Serotonin	I. Antihistamine
B. Phenelzine	II. Antibiotic
C. Terfenadine	III.Tranquilizer
D. Vancomycin	IV. Anti depressant drug

Choose the correct answer from the options given below:

Match List-I (Amino acid) with List-II (Example)

List - I (Amino acid)	List-II (Example)
(A) Basic amino acid	(I) Glycine
(B) Acidic amino acid	(II) Alanine
(C) Neutral amino acid	(III) Aspartic acid
(D) Optically inactive amino acid	(IV) Lysine

Choose the correct answer from the options given below:

Over 95% of all existing transgenic animals are:

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, pressure 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 \(= \text{k}[\text{A}]^x [\text{B}]^y\)
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.
If the temperature is raised by \(10^\circ\text{C}\), then the rate of the reaction increases approximately by:

If \(e^x+e^y=e^{x+y}\), then \(\frac{d y}{d x}=\)

Value of \(\tan ^{-1} 2+\tan ^{-1} 3+\tan ^{-1} 4\) is equal to: