If \(f(x)=x^2-4 x+13, x \in R\), then which of the following are correct?
(A) \(x=2\) is a stationary point of \(f(x)\).
(B) \(f ( x )\) is increasing function on (2, \(\infty)\) .
(C) \(f ( x )\) have maxima at \(x =2\).
(D) \(f ( 2 )= 9\).
Choose the correct answer from the options given below :

The solution of the differential equation \(\frac{d y}{d x}=\frac{3 e^{2 x}+3 e^{4 x}}{e^x+e^{-x}}\) is:

The rise in prices before Christmas is an example of

Sum of the minor and the cofactor of the element 6 in the determinant \(\left|\begin{array}{lll}2 & 3 & 1 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right|\) is :

Match List I with List II

LIST I	LIST II
A. \(\left( \frac{dy}{dx} \right)^2 + \frac{dy}{dx} + 5 = 0\)	I. order 3, degree 1
B. \(xy \frac{d^2y}{dx^2} + x \left( \frac{dy}{dx} \right)^2 - y \frac{dy}{dx} = 0\)	II. order 2, degree 2
C. \(\left( \frac{d^2y}{dx^2} \right)^2 + \frac{dy}{dx} = 0\)	III. order 2, degree 1
D. \(\frac{d^3y}{dx^3} + 2\frac{d^2y}{dx^2} + \frac{dy}{dx} = 0\)	IV. order 1, degree 2

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The average salary per head of the entire staff of a small factory including managers and technicians is Rs. 5750.
The average salary per head of a manager is Rs. 20000
and that of a technician is Rs. 5000.
If there are 4 managers, then the number of technicians in the factory is :

If \(A=\left[\begin{array}{lll}1 & 2 & 1 \\ 2 & 3 & 1 \\ 0 & 0 & 1\end{array}\right]\), then \(\left|\operatorname{adj}\left(3 A^T\right)\right|^2\) is equal to

If the price of a machinery costing ₹ 25000 is expected to have a useful life of 4 years and a scrap value of ₹ 5000 . Then the annual depreciation by linear method is:

A bar magnet of magnetic moment 3 J/T lies aligned with the directions of a uniform magnetic field of 0.2 T. The amount of work, required so as to align its magnetic moment opposite to the field direction is :

Read the passage carefully and answer the questions
Amines are considered as derivatives of ammonia obtained by replacement of hydrogen atoms with alkyl or aryl groups. In nature they occur among proteins, vitamins, alkaloids and hormones. These can be primary, secondary or tertiary depending on the number of hydrogen groups replaced. They can be prepared from nitro compounds, alkyl halides, nitriles, amides etc. Due to unshared pair of electrons they behave as Lewis bases. Influence of the number of hydrogen atoms at nitrogen atom is displayed in physical properties such as solubility, boiling point and chemical reactions including basicity. Basic character of amines is expressed in terms of their \(K_b\) and \(p K_b\) values. Three classes of amines can be distinguished with p-toluene sulphonyl chloride which reacts with primary and secondary ddu amines. Amino group when attached to benzene ring behaves as an activating and ortho para directing group.
Which of the following reaction is not given by aniline?

According to Arrhenius equation \(k=A e^{-\frac{E_a}{R T}}\). If In k vs 1/T graph plotted, what will be the intercept of this plot?

Match List-I with List-II

List-I	List-II
(A) D	(I) Loss of blood clotting
(B) C	(II) Rickets
(C) \(B_6\)	(III) Scurvy
(D) K	(IV) Convulsions

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When a ray of light enters from denser medium to rarer medium, its velocity is doubled. The critical angle for total internal reflection will be :