What is the mathematical expression for potential gradient?

Which of the following is the correct expression for force due to a magnetic field (\( \vec{B} \)) on a straight conductor of length (\( l \)) carrying current \( I \)?

Identify the correct statement(s) among the following:
(A) The time taken by a light wave is \( 5 \times 10^{-9} \text{ s} \) to travel a thickness of 1 cm of glass having refractive index 1.5.
(B) Two similar waves of amplitude 3 mm and 5 mm reach a point in the same phase. The resultant amplitude will be 8 mm.
(C) Two waves of amplitude 2 mm each reach a point with a phase difference of \( \pi/2 \). The resultant amplitude is zero.
(D) If one of the slits is closed in Young's double slit experiment, the interference pattern will disappear.
Choose the correct answer from the options given below :

Which of the following examples are based upon the total internal reflection of light?
(A) Optical fibre
(B) Twinkling of stars
(C) Mirage
(D) Sparkling of diamond
Choose the correct answer from the options given below:

Two capacitors of capacitances \(3 \mu F\) and \(6 \mu F\) are charged to potentials of \(2 V\) and \(3 V\), respectively. Now, if they are connected in parallel, the charge on each of the two capacitors, will be

The de Broglie wavelength of an electron having kinetic energy 56 eV is :

The velocity of light in diamond, glass and water decreases in the following order :

If \(y=38.85+7.64(x-2020)\) is the equation of the straight line trend for the following data:

Year(x)	2017	2018	2019	2020	2021	2022	2023
Profit( Rs. '000) (y)	14	30	26	44	38	56	64

The trend value for the year 2021 by least square method is :

The compound which produce turbidity immediately with Lucas reagent is

Which of the following statement(s) is/are incorrect?
(A) The Kirchhoff's laws are equally applicable in alternating current circuit and direct current circuits.
(B) It is not necessary that the wire stretched on the meter bridge must have a uniform cross-sectional area.
(C) The internal resistance of the cell does not affect the reading of the null point in metre bridge.
(D) Electrical potential has no direction, the electrical potential gradient has a direction.

The correct shape \(\&\) hybridisation for \(XeF_2\) are:

Who popularised the term 'Biodiversity'?

Read the passage carefully and answer the Questions
Aldehydes, carboxylic acids and ketones are widespread in the animal and plant kingdoms.
They play a pivotal role in various biochemical processes of life. Their presence in nature adds fragrance and flavor. These compounds are widely used in food products, pharmaceuticals, paints, resins and other important product industries. These compounds are prepared by various laboratory methods, which mainly include oxidation, formylation, acylation and reduction. Due to the polar nature of the carbonyl group in aldehydes and ketones, they can exhibit different reactions like nucleophilic addition. They do exhibit redox and various condensation reactions which lead to the formation of various important compounds. On the other hand, the carboxylic acids are mainly prepared by oxidation and hydrolysis of different compounds. The carboxylic acid consists of a carbonyl group and the hydroxy group (attached to the carbonyl carbon atom). This makes it possible for the carboxylic acid to participate in various chemical reactions which involve cleavage of the C-OH bond and the O_H bond along with the reactions involving the complete -COOH group.
The products formed when 2,2-Dimethylpropan-1-al is heated with concentrated KOH are :