The current flowing through a wire as a function of time is given as : \( I = 3t^2 + 2t + 5 \). The charge flowing through any cross-section of the wire in first 2 s is :

Two parallel beams of monochromatic light pass through a long slit of width 0.2 mm one by one. The angular divergence in which most of the light is diffracted for both the beams are \( 2.25 \times 10^{-3} \text{ rad} \) and \( 4.50 \times 10^{-3} \text{ rad} \) respectively. If the wavelength of the first beam is \( \lambda_1 = 3000 \text{ Å} \), then the wavelength of the second beam is:

A system has two charges, \( q_A = 5 \times 10^{-7} \, \text{C} \) and \( q_B = -5 \times 10^{-7} \, \text{C} \), located at points \( A : (0, 0, -10 \, \text{cm}) \) and \( B : (0, 0, +10 \, \text{cm}) \), respectively. Which of the following are true?
(A) The electric field of dipole at point (0, 0, -15 cm) is \( 1.73 \times 10^6 \, \text{NC}^{-1} \)
(B) Electric field intensity is zero at origin (0, 0, 0)
(C) dipole moment \( (p) = 5 \times 10^{-8} \, \text{C-m} \)
(D) direction of the dipole moment is along the negative z- axis
Choose the correct answer from the options given below:

A metal plate is getting heated. It can be because of:
A. An alternating current is passing through the plate.
B. It is placed in a time varying magnitude field.
C. A direct current is passing through the plate.
D. It is placed in a space varying magnitude field, but does not vary with time.
E. It is placed in a time constant magnetic filed.
Choose the correct answer from the options given below:

Donor energy level in 'n' type and acceptor energy level in 'p' type semiconductor are:

The current changes in a coil from 10 A to 2 A in 0.2 s. The induced emf produced is 50 V. The self inductance of the coil is:

A metal cube of side 0.1 m is uniformly charged by 18 \( \mu C \). Its surface charge density will be

Read the following passage carefully and answer the given questions.
Plasmodium, a tiny protozoan is responsible for the disease malaria. 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. Innate immunity consist of four types of barriers. These are – (i) Physical barriers- skin on our body is the main barrier which prevents entry of the micro-organisms. (ii) Physiological barriers- Acid in the stomach, saliva in the mouth, tears from eyes-all prevent microbial growth. (iii) Cellular barriers- 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. (iv) Cytokine barriers- virus-infected cells secrete proteins called interferons which protect non-infected cells from further viral infection. Allergy is due to the release of chemicals like histamine and serotonin from the mast cells. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Drugs like barbiturates, amphetamines, benzodiazepines, and other similar drugs, that are normally used as medicines to help patients cope with mental illnesses like depression and insomnia, are often abused.
Which one of the following drugs or chemicals can not quickly reduce the symptoms of allergy?

Let \(y=138.86+7.64(x-2021)\) be a straight line of best fit by using least square method.

\(YEAR(X)\)	2018	2019	2020	2021	2022	2023	2024
\(PROFIT(y)\)	144	130	126	144	138	156	164

Then the trend value for the year 2024 is :

Read the passage carefully and answer the Questions
Amines are classified as primary \(\left(1^{\circ}\right)\), secondary \(\left(2^{\circ}\right)\) and tertiary \(\left(3^{\circ}\right)\) depending upon the number of hydrogen atoms replaced by alkyl or aryl groups in ammonia molecules. Aliphatic amines are a stronger bases due to \(+I\) effect of an alkyl groups.
Intermolecular hydrogen bonding in primary and secondary amines affects the boiling points of amines. The intermolecular association is more in primary amines than in secondary amines as there are more number of hydrogen atoms available for hydrogen bond formation. Nitro compounds are reduced to amines by passing hydrogen gas in the presence of finely divided nickel, palladium or platinum and also by reduction with metals in an acidic medium. Gabriel synthesis is used for the preparation of primary amines. Primary amines react with nitrous acid to give unstable diazonium-salts which can be used to synthesize a variety of compounds.
The compound having the highest boiling point is

In the depletion region of a diode :
(A) There are no mobile charges
(B) Equal number of holes and electrons exist, making the region neutral
(C) recombination of holes and electrons has taken place
(D) Immobile charged ions exist
(E) There are mobile charges
Choose the correct answer from the options given below :

The cell \(emf\) depends on:

The 'stopping potential' in photoelectric emissions