In a nuclear fission reaction given below, the three neutrons are released. The value of x and y are\( {}_{0}^{1}n + {}_{92}^{235}U \rightarrow {}_{56}^{x}Ba + {}_{y}^{89}Kr + 3{}_{0}^{1}n \)

Match List-I with List-II

List-I (Electric Field)	List-II (Expression)
(A) Field due to an infinitely long straight uniformly charged wire	(I) \(\sigma\left(2 \varepsilon_0\right)^{-1}\)
(B) Field due to a uniformly charged thin spherical shell (inside the shell)	(II)\(q\left(4 \pi \varepsilon_0 r^2\right)^{-1}\)
(C) Field due to a uniformly charged infinite plane sheet	(III) \(\lambda\left(2 \pi \varepsilon_0 r\right)^{-1}\)
(D) Field due to a uniformly charged thin spherical shell (outside the shell)	(IV) zero

Choose the correct answer from the options given below:

The ratio of the Nuclear density of the gold isotope \(^{197}_{79}\text{Au}\) and the silver isotope \(^{107}_{47}\text{Ag}\) is :

If we double the number of turns of coil in a moving coil galvanometer, its voltage sensitivity will :

An electromagnet has stored 540 J of magnetic energy when a current of 6 A exists in its coil. What is the value of average emf induced, if the current is reduced to zero in 0.54s?

Consider a permanent dipole of dipole moment P in a non-uniform electric field E. Which of the following option is correct?

An electron moves with a velocity of \( 1200 \, \text{m s}^{-1} \) in a magnetic field of 0.4 T at an angle of 30\(^\circ\). What will be the approximate radius of its path? (Take \( e/m \) of electron \( = 1.76 \times 10^{11} \, \text{C kg}^{-1} \))

Typical embryo sac at maturity is:

On simplifying \(\cot \left(2 \tan ^{-1} x\right)\) where \(|x|<1\), we get:

Ethanol is treated with concentrated sulphuric acid. The product formed is :

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.

For the linear programming problem,
Minimize (Z) =60x + 30y
subject to : \(2 x - y \geq-5 ; 3 x + y \geq 3 ; 2 x -3 y \leq 12; x , y \geq 0\)
the optimal value of \(z\) is

In the context of humans, which one of the following groups will have 46 chromosomes: