The radii of curvature of the faces of a double convex lens of focal length 12 cm made up of glass (\(\mu=1.5\)) are 10 cm and 'p' cm respectively. The value of p is :

The focal length of a lens depends on

In an electromagnetic wave, the amplitude of magnetic field is \( 1.1 \times 10^{-6} \text{ T} \). What is the amplitude of electric field?

Light of frequency \( \nu \) falls on a metal whose work function is \( h\nu_0 \). Choose the most appropriate condition from the following under which the photoelectric effect will take place.

The total energy of the electron in a hydrogen atom is \( -1.51 \text{ eV} \).
A. Its Kinetic energy is \( -1.51 \text{ eV} \)
B. Its potential energy is \( -3.02 \text{ eV} \)
C. electron is in second excited state
D. The ground state energy of hydrogen atom is 13.6 eV
Choose the correct answer from the options given below:

When a charged particle moves in a uniform magnetic field, its kinetic energy:

In a common emitter amplifier the audio signal voltage across the collector resistance of 2 \( k\Omega \) is 2 V. The current amplification factor is 50. The value of base current is:

Match List-I with List-II

List-I (Equationof Lines)	List-II (Information)
(A) \(\vec{r}=(3 \hat{i}-2 \hat{j}+\hat{k})+\lambda(\hat{j}-2 \hat{k})\)	(I) Direction ratios are \(2,4,-1\)
(B) \(\frac{2-x}{1}=\frac{2 y+1}{4}, z=2\)	(II) Perpendicular to \(2 \hat{i}-\hat{j}+\hat{k}\)
(C) \(\frac{x}{1}=\frac{y-3}{2}=\frac{3-4 z}{2}\)	(III) Passing through the point \((3,-2,1)\)
(D) \(\vec{r}=(3 \hat{i}+2 \hat{j}+\hat{k})+\lambda(2 \hat{i}+\hat{j}-3 \hat{k})\)	(IV) Direction ratios are \(-1,2,0\)

Choose the correct answer from the options given below :

All food chains begin with producers, except -

Match List - I with List - II

List - I	List - II
(A) \(\int_{-\pi / 2}^{\pi / 2} \sin ^5 x d x\)	(I) \(\pi\)
(B) \(\int_{-\pi / 2}^{\pi / 2}\left(x^3+\tan ^3 x+1\right) d x\)	(II) \(\frac{\pi}{12}\)
(C) \(\int_0^{\pi / 2} \frac{\cos ^5 x}{\cos ^5 x+\sin ^5 x} d x\)	(III) \(\frac{\pi}{4}\)
(D) \(\int_1^{\sqrt{3}} \frac{d x}{1+x^2}\)	(IV) 0

Choose the correct answer from the options given below:

Read the following paragraph carefully and answer the given questions.
Certain types of leukocytes (WBC) of our body like polymorpho-nuclear leukocytes (PMNL-neutrophils) and monocytes and natural killer (type of lymphocytes) in the blood as well as macrophages in tissues can phagocytose and destroy microbes. For determining the cause of allergy, the patient is exposed to or injected with very small doses of possible allergens, and the reactions studied. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Heroin, commonly called smack is chemically diacetylmorphine which is a white, odourless, bitter crystalline compound. This is obtained by acetylation of morphine. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal.
Heroin, commonly called smack is chemically __________ which is a white, odourless, bitter crystalline compound.

A 300 turns rectangular coil of length 20 cm and breadth 12 cm is carrying a current of 12 A, when placed in a magnetic field of 6 T. The plane of the coil is making an angle of 60° with the magnetic field. What is the torque acting on the coil?

The probability distribution of a random variable X is given by

X	0	1	2
P(X)	\(1-7 a^2\)	\(\frac{1}{2} a+\frac{1}{4}\)	\(a^2\)

If \(a>0\), then \(P(0<X \leq 2)\) is equal to