Identify the correct statement(s).
(A) In any lens, the optical centre is always at the centre of the lens.
(B) In a lens, if the curvature of its two surfaces is equal, the optical centre is at the centre of the lens.
(C) A light ray passing through the optical centre of a lens never shifts from the direction of the incident ray.
(D) A ray of light incident perpendicularly on a lens passes through its focus after refraction.
Choose the correct answer from the following given options.

An unpolarized light of intensity \(I_0\) is passed through a polariser and is incident on an analyser making an angle of \((\pi/6) \text{ rad}\) with that of the polariser. The intensity of the light transmitted from the analyzer is

The instantaneous magnetic flux linked with a coil is given by \(\phi = (15t^3 - 100t^2 + 40)\) Wb. The emf induced in the coil at time \(t = 1\) s is :

An electron of mass \( 9.1 \times 10^{-31} \text{ kg} \) carrying charge \( 1.6 \times 10^{-19} \text{ C} \), is moving horizontally with a speed of \( 4 \times 10^6 \text{ m/s} \) in a uniform magnetic field of magnitude \( 8 \times 10^{-4} \text{ T} \) acting vertically upward. The radius of its circular path is,

The electric field in a region is \( \vec{E} = (6\hat{i} + 3\hat{j} + 5\hat{k}) \text{ N/C} \).
The electric flux due to this electric field through an area of \( 100 \text{ cm}^2 \) lying in the X-Y plane is :

The shortest wavelength in the Balmer series of a hydrogen atom is (Given: \(R=1.1 \times 10^7 m^{-1}\) )

When a potential difference is applied across a copper wire, the drift velocity of the electrons is v. If the same potential difference is applied across another copper wire of the same length but twice the diameter, the drift velocity of electrons will be

The rate law for a reaction between substance P \& Q is given by
Rate = k[P]^x [Q]^y
If concentration of P is doubled and concentration of Q is halved, the ratio of the new rate to the earlier rate of reaction will be : 

In a double slit experiment using light of wavelength 450 nm, the angular width of a fringe formed on a distant screen is 0.15°. The spacing between the two slits is

Interval in which the function \(f\) given by \(f(x)=\tan x-4 x, x \in\left(0, \frac{\pi}{2}\right)\) is strictly decreasing 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?

Match List-I with List-II

List-I	List-II
(A) The equation of the line passing through the points \((-1,0,2)\) and \((3,4,6)\) is	(I) \(\vec{r}=(-\hat{i}+2 \hat{k})+\lambda(4 \hat{i}+4 \hat{j}+4 \hat{k})\)
(B) The vector equation of the line \(\frac{x-1}{2}=\frac{y+1}{3}=\frac{4-z}{5}\) is	(II) \(\vec{r}=(\hat{i}+3 \hat{j}+2 \hat{k})+\lambda(2 \hat{i}+\hat{j}+3 \hat{k})\)
(C) The equation of the line passing through \((1,3,2)\) and parallel to \(\frac{x+1}{2}=\frac{y-1}{1}=\frac{z+1}{3}\) is	(III) \(\vec{r}=(-\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(2 \hat{i}+\hat{j}+4 \hat{k})\)
(D) The equation of the line along \(2 \hat{i}+\hat{j}+4 \hat{k}\) and passing through \((-1,2,3)\) is	(IV) \(\vec{r}=(\hat{i}-\hat{j}+4 \hat{k})+\lambda(2 \hat{i}+3 \hat{j}-5 \hat{k})\)

where \(\lambda\) is an arbitrary constant.
Choose the correct answer from the options given below:

The association of Glomus with roots of higher plants is known as ___________ .