Two Polaroids are placed in such a way that their axes make an angle of 60° with each other. If an unpolarized light is incident on a system of these Polaroids, the fraction of transmitted light to the incident light will be

In an electromagnetic wave, if \(\vec{B}\) and \(\vec{E}\) represent the magnetic field and electric field respectively, then the direction of propagation of the electromagnetic wave is along the direction of:

A particle of mass m and charge q is placed at rest in a uniform electric field E and then released. The kinetic energy attained by the particle after moving a distance y is:

A proton and an alpha particle accelerated through different potential differences have the same de-Broglie wavelength. The ratio of their respective accelerating potentials is

The storage battery of a car has an emf of 10 V. If the internal resistance of the battery is \( 0.2 \Omega \), then the maximum current that can be drawn from the battery is

A plano convex lens is made of material having refractive index 1.8. If the radius of curvature of the curved surface is 80 cm, then focal length of the lens is :

An infinite plane sheet of charge density \(10^{-8} \text{ C m}^{-2}\) is held in air. In this situation, the distance between two equipotential surfaces, whose potential difference is 10 V, will be (Given: Permittivity of vacuum\(\epsilon_0 \approx 8.85 \times 10^{-12} F / m\))

The acute angle between the lines \(\vec{r}=(4 \hat{i}-\hat{j})+\lambda(2 \hat{i}+\hat{j}-3 \hat{k})\) and \(\frac{x-1}{1}=\frac{y+1}{-3}=\frac{z-2}{2}\) is

match List - I with List - II

List - I (function)	List - II (inceasing on the interval)
(A) f(x) = -\(x^2\) - 2x + 1	(I) \((-\infty,-1)\)
(B) f(x) = \(x^2\) + 1	(II) \((1, \infty)\)
(C) f(x) = \(x^2\) - 2x + 3	(III) \((-\infty, 0)\)
(D) f(x) = \(- x^2\)	(IV) \((0, \infty)\)

Choose the correct answert from the option given below :

The objective function of an LPP is \(Z=a x+b y\). If the maximum value of the objective function is 180 , which occurs at two points \((15,15)\) and \((0,20)\), then which one of the following is true?

Read the following passage carefully and answer the given questions.
Cancerous cells just continue to divide giving rise to masses of cells called tumors. Benign tumors normally remain confined to their original location and do not spread to other parts of the body and cause little damage. The malignant tumors, on the other hand are a mass of proliferating cells called neoplastic or tumor cells. Transformation of normal cells into cancerous neoplastic cells may be induced by physical, chemical or biological agents. Ionising radiations like X-rays and gamma rays and non-ionizing radiations like UV cause cancer. Cancer-causing viruses are called oncogenic viruses which have viral oncogenes. The substances to which an immune response is produced are called allergens. The antibodies produced to these are of IgE type. Common examples of allergens are mites in dust, pollens, animal dander, etc. The primary lymphoid organs are bone marrow and thymus. The secondary lymphoid organs provide the sites for interaction of lymphocytes with the antigen, which then proliferate to become effector cells.
Which one of the following antibodies are produced in response to the allergens?

Acidified potassium dichromate oxidises iodides to \(\underline{X}\), sulphides to \(\underline{Y}\) and tin (II) to \(\underline{Z}\). \(X\), \(Y\) and \(Z\) respectively are:

Central Limit Theorem implies that as the size of the sample increases, the distribution approaches: