JEE Main 2000 Previous Year Question Paper with Solutions

Consider two radiations of wavelengths :1. Å2. ÅThe ratio of the energies of these two radiations is ____. (Nearest integer)[JEE Main 8 apr 2026 shift 2]

Which of the following pictorial diagram most correctly represents the molecular orbital between two atoms if the internuclear axis is taken to be in the z -direction ?[JEE Main 4 Apr 2026 Shift 2]

Compound A formed in the following reaction reacts with gives the product . Find out A and B. [30-Jan-2024 Shift 1]

Consider the following reactions : (a) (b) (c) (d) Which of these reaction(s) will not produce Saytzeff product ? [7-Jan-2020 Shift 1]

The final product , formed in the following reaction sequence is: [27-Jan-2024 Shift 2]

Product formed in the above reaction is: [11-Apr-2023 shift 2]

If the solubility product of is , then the solubility of in pure water at is . The value of is _______. (Nearest Integer) [Given : ] [29-Jul-2022-Shift-1]

In the following reaction sequence : The compound is : [Main 9 April 2017]

L-isomer of tetrose gives positive schiff's test and has two chiral carbons. On acetylation. ' ' yields triacetate. ' ' undergoes following reactions ' ' is [11-Apr-2023 shift 1]

The correct structure of product 'A' formed in the following reaction. is [28-Jun-2022-Shift-1]

But-2-yne is reacted separately with one mole of Hydrogen as shown below: Identify the incorrect statements from the options given below: A. is more soluble than . B. The boiling point & melting point

Consider the following reaction: . The correct statement for product is. It is [31-Jan-2023 Shift 1]

Based upon VSEPR theory, match the shape (geometry) of the molecules in List-I with the molecules in List-II and select the most appropriate option. List - I(Shape) List - II(Molecules) (A) T-shaped (

'A' and 'B' respectively are: [27-Jun-2022-Shift-1]

The number of bridged oxygen atoms present in compound B formed from the following reactions is [25-Jun-2022-Shift-2]

Consider the following reactions. Total number of electrons in the π bonds and lone pair of electrons in the product (X) is: [JEE Main 6 Apr 2026 shift 2]

. Red phosphorus is obtained by heating "A" at , and can be converted to "B" by heating at under pressure. and , respectively, are [30-Jun-2022-Shift-1]

The major product formed in the following reaction is Choose the correct answer from the options given below: [11-Apr-2023 shift 2]

Let the line of the shortest distance between the lines and intersect and at and respectively. If is the midpoint of the line segment PQ, then is equal to____ [1-Feb-2024 Shift 1]

Suppose exists and is equal to , where Then, is equal to___ [30-Jun-2022-Shift-1]

A plane is perpendicular to the two planes and , and passes through the point . If the distance of the plane from the point is , then is equal to [25-Jul-2022-Shift-2]

Let the solution curve of the differential equation pass through the origin. Then is equal to [26-Jul-2022-Shift-2]

Let the solution curve of the differential equation pass through the origin. Then is equal to : [30-Jan-2023 Shift 1]

Let C be a curve given by . If P is a pointon C, such that the tangent at P has slope , then a point through which the normal at P passes, is :[Main 10 Apr 2016]

If are the roots of the equation then the equation, whose roots are and , is : [27-Jul-2022-Shift-2]

If is the shortest distance between the lines and is the shortest distance between the lines , then the value of is :__ [30-Jan-2024 Shift 1]

The positive value of the determinant of the matrix A, whose , is____ [27-Jun-2022-Shift-1]

Let . if the function defined as is continuous in the interval , then an ordered pair is :[Main 10 Apr 2016]

Let be a real matrix such that Then, the system has [31-Jan-2024 Shift 2]

Let and . The sum of the prime factors of is equal to [29-Jan-2024 Shift 2]

The largest value of , for which the perpendicular distance of the plane containing the lines and from the point is , is _________. [26-Jul-2022-Shift-2]

Let . If and are respectively the number of points of local minimum and local maximum of in the interval , then is equal to____ [25-Jun-2022-Shift-2]

A plane contains the line of intersection of the plane and . If passes through the point , then the square of distance of the point from the plane is : [6-Apr-2023 shift 2]

If a point satisfying lies on the plane , then is equal to: [31-Jan-2023 Shift 2]

Let be a differentiable function satisfying and . If passes through the point , then is equal to __________. [27-Jul-2022-Shift-2]

If the shortest distance between the lines and is , then the integral value of a is equal to [24-Jun-2022-Shift-1]

Let be differentiable in and . Then the value of ea, such that , is equal to_____ [29-Jan-2024 Shift 2]

Let be the origin, and and be the points on the lines and respectively such that is the shortest distance between the given lines. Then is equal to [29-Jan-2024 Shift 2]

Let be a function defined by : where is the greatest integer less than or equal to . Let be the number of points where is not differentiable and . Then the ordered pair is equal to : [29-Jun-2022-Shif

Let and , then the value of is: [26-Jul-2022-Shift-2]

Let and . If , then equal to [8-Apr-2023 shift 1]

Let y = y(x) be the solution of the differential equation , . If , then the greatest integer less than is ______ .[JEE Main 6 Apr 2026 shift 1]

Let . If and denote the number of points where is not continuous and not differentiable respectively, then is equal to : [1-Feb-2024 Shift 2]

Let the solution curve of the differential equation pass through the points and . Then is equal to [28-Jun-2022-Shift-1]

Let be a plane. Let be another plane which passes through the points and . If the direction ratios of the line of intersection of and be , then the value of is equal to____ [29-Jun-2022-Shift-1]

Let be the adjoint of a matrix and . then is equal to [13-Apr-2023 shift 1]

Consider a triangle whose vertices are and . Let be a point moving on the line and be the centroid of . If the minimum length of is , then is equal to___ [30-Jun-2022-Shift-1]

Let be roots of equation , where . If assumes the minimum possible value, then is equal to : [30-Jan-2024 Shift 1]

The number of distinct real roots of the equation, in the interval is :[Main 9 Apr 2016]

Let the foot of perpendicular from the point on the plane be . If , is a point on plane such that the area of the triangle is , then is equal to _______. [10-Apr-2023 shift 2]

Let the solution curve of the differential equation , intersect the line at and the line at . Then the value of is : [28-Jul-2022-Shift-1]

If the shortest between the lines and is 6 , then the square of sum of all possible values of is [24-Jan-2023 Shift 2]

The distance of the point from the plane parallel to the line of the shortest distance between the lines and is [13-Apr-2023 shift 1]

Let be the angle between the planes and .Let be the line that meets at the point and makes an angle with the normal of . If is the angle between and then is equal to _______. [31-Jan-2023 Shift 1]

If the solution curve of the differential equation , which passes through the point (1, 1) and intersects the line at the point , then value of is equal to : [25-Jun-2022-Shift-1]

Let a curve pass through the point and the area of the region under this curve, above the -axis and between the abscissae 3 and be . If this curve also passes through the point in the first quadrant,

Let the matrix and the matrix . If for all , then is equal to : [28-Jul-2022-Shift-1]

Consider the function. Where denotes the greatest integer less than or equal to . If denotes the set of all ordered pairs such that is continuous at , then the number of elements in is : [27-Jan-2024

Let . Then which of the following statements are true? is a point of local minima of is a point of inflection of is increasing for [29-Jul-2022-Shift-1]

Let the line meet the plane at the point . If the angle between the line and the plane is , then is equal to _______. [11-Apr-2023 shift 2]

Let the lines intersect at the point . If a plane passes through and is parallel to both the lines and , then the value of is equal to [25-Jun-2022-Shift-1]

Let be a differentiable function such that and and let for . Then is equal to : [28-Jun-2022-Shift-2]

If the shortest distance between the lines and is , then the sum of all possible value of is : [24-Jun-2022-Shift-2]

Let and is odd .Let and .If , then is equal to : ion: [24-Jun-2022-Shift-1]

Let be two functions defined by and . Then the value of is equal to [31-Jan-2024 Shift 2]

The point represented by in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from there units in the south-westwards direction. Then its new position in the Argand plane is

Let be defined as If is continuous everywhere in and is the number of points where is NOT differential then equals : [1-Feb-2024 Shift 1]

Let be a thrice differentiable function in . Let the tangents to the curve at (1, and make angles and , respectively with positive -axis. If where are integers, then the value of equals [30-Jan-2024 S

If is a matrix satisfying the equation , where I is identity matrix, thenordered pair (a, b) is equal to :[Main 2015]

Let be a non-zero matrix, where . For a square matrix , let trace (M) denote the sum of all the diagonal entries of M. Then, among the statements:(I) Trace (II) If , then has exactly one non-zero entr

Consider the function defined by . Consider the statements(I) The curve intersects the -axis exactly at one point(II) The curve intersects the -axis at Then [29-Jan-2024 Shift 1]

Let and be prime numbers and let Then the sum of the maximum values of and , such that and divide , is ________. [29-Jul-2022-Shift-1]

Let the equation of plane passing through the line of intersection of the planes and be . For , if the distance of this plane from the point is , then is equal to [13-Apr-2023 shift 1]

Let and where the inverse trigonometric functions take principal values. Then, the equation whose roots are and is : [30-Jun-2022-Shift-1]

Let the sets A and B denote the domain and range respectively of the function , where denotes the smallest integer greater than or equal to . Then among the statements : and(S2) : [6-Apr-2023 shift 2]

Let the shortest distance between the lines and be . If lies on , then which of the following is NOT possible? [31-Jan-2023 Shift 1]

Let a function be defined by then, is [28-Jun-2022-Shift-1]

If denotes the greatest integer , then the number of points, at which the function is not differentiable in the open interval , is ________. [29-Jul-2022-Shift-2]

Let and be two points on the line at a distance from the point . Then the square of the area of the triangle is _________. [26-Jul-2022-Shift-1]

Consider the matrix .Given below are two statements :Statement I: is the inverse of the matrix .Statement II: .In the light of the above statements, choose the correct answer from the options given be

Let be the line in -plane with and intercepts and respectively, and be the line in -plane with and intercepts and respectively. If is the shortest distance between the line and , then is equal to____

Let be positive consecutive terms of an arithmetic progression. If is its common difference, then : is [6-Apr-2023 shift 1]

Let and , be the two sets of observations. If and are their respective means and is the variance of all the observations in , then is equal to _______. [29-Jan-2023 Shift 2]

Let and be positive real numbers such that the function is differentiable for all . Then is equal to ________. [8-Apr-2023 shift 2]

Let a line pass through the origin and be perpendicular to the lines and .If is the point of intersection of and , and is the foot of perpendicular from on , then is equal to ______. [11-Apr-2023 shif

Let be the roots of the equation and be the roots of the equation . Then the roots of the equation are : [28-Jul-2022-Shift-2]

Let and , where α is a real number. If the largest possible value of α is p, then the circle 320, intersects the co-ordinate axes at[JEE Main 4 Apr 2026 Shift 2]

Let . Let , be the solution curve of the differential equation . If the sum of abscissas of all the points of intersection of the curve with the curve is , then is equal to____ [26-Jun-2022-Shift-1]

Let A be a matrix such that If , then is equal to :[JEE Main 5 Apr 2026 Shift 1]

Let the co-ordinates of one vertex of be and the other two vertices lie on the line . For , if the area of is 21 sq. units and the line segment has length units, then is equal to _______. [29-Jan-2023

The number of points where the function [t] denotes the greatest integer , is discontinuous is [24-Jun-2022-Shift-1]

Let and . If , then the number of elements in the set is equal to [25-Jul-2022-Shift-1]

Let for Some . Then is equal to .[JEE Main 6 Apr 2026 shift 1]

Let y = y(x) be the solution of the differential equation They equal to:[JEE Main 8 apr 2026 shift 2]

Let be a differentiable function defined on such that and .Then is equal to___ [24-Jan-2023 Shift 2]

If the eqation of the plane containing the line and perpendicular to the plane is ax+by , then is equal to [8-Apr-2023 shift 1]

Let be the three A.P. with the same common difference and having their first terms as , respectively. Let a, b, c be the terms of , respectively such that If , then the sum of first 20 terms of an AP

At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by .If the firm employee 25 more workers,then the

Let and .If , then the value of is :[JEE Main 6 Apr 2026 shift 2]

The square of the distance of the point of intersection of the line , and from the origin is :[JEE Main 5 Apr 2026 Shift 1]

For and , let the angle between the plane and the line +1 be . If the distance of the point from the plane is , then is equal to [8-Apr-2023 shift 2]

If two distinct point lie on the line of intersection of the planes and and where the point is , then the area of the triangle is equal to [28-Jun-2022-Shift-1]

Let , . If a respectively are the maximum and the minimum values of , then [1-Feb-2023 Shift 1]

Let and Be three lines such that is perpendicular to and is perpendicular to both and . Then the point which lies on is [30-Jan-2024 Shift 2]

A vector in the first octant is inclined to the axis at , to the -axis at and to the z-axis at an acute angle. If a plane passing through the points and , is normal to , then [30-Jan-2023 Shift 2]

If and and ,then K is equal to[Main 2014]

Let a line pass through the origin and be perpendicular to the lines and , is the point on at a distance of from the point of intersection of and , then is equal to _____.[JEE Main 8 apr 2026 shift 2]

Let be the roots of the equation and be the roots of the equation . If , then is equal to___ [27-Jun-2022-Shift-2]

Let be the sum of the numbers appeared when two fair dice are rolled and let the probability that are in geometric progression be . Then the value of is [25-Jan-2023 Shift 2]

The slope of the tangent to a curve at any point on it is . If passes through the points and , then is equal to : [25-Jul-2022-Shift-1]

If and , where are two roots of the equation , then is equal to :[JEE Main 4 Apr 2026 Shift 2]

If is the solution of the differential equation such that and , then is equal to _______ [13-Apr-2023 shift 2]

Let be a singular matrix. Let . If M and m are respectively the maximum and the minimum values of f in [1, α] then is equal to :[JEE Main 6 Apr 2026 shift 2]

The plane intersects the line segment joining the points and at the point in the ratio and the distance of the point from the origin is . If and is the point then is equal to : [29-Jan-2023 Shift 2]

Let and be two real roots of the equation . , where and are real numbers. If , then a value of λ is ; [7-Jan-2020 Shift 1]

Let the plane contain the line of intersection of two planes and If the plane passes through the point , then the value of is equal to [28-Jun-2022-Shift-1]

The number of points, at which the function , is not differentiable, is _____ .[JEE Main 4 Apr 2026 Shift 1]

If the length of the perpendicular drawn from the point on the line is units and is the image of the point in this line, then is equal to : [27-Jul-2022-Shift-2]

Let and be opposite vertices of a parallelogram if the diagonal then the area of the parallelogram is equal to [30-Jan-2024 Shift 1]

Consider a matrix , where are three distinct natural numbers. If , then the number of such 3 - tuples is _________. [27-Jul-2022-Shift-2]

Let be a real matrix such that and If and I is an identity matrix of order 3 , then the system has : [25-Jun-2022-Shift-1]

Let and . If det(B) = 66, then det(adj (A))equals:[JEE Main 8 apr 2026 shift 2]

The line of shortest distance between the lines and makes an angle of with the plane . If the image of the point in the plane is , then is equal to [25-Jul-2022-Shift-1]

Let and If , then is equal to___ [26-Jun-2022-Shift-2]

Let M be a matrix such that and . If , then equals :[JEE Main 5 April 2026 Shift 2]

Let α be a root of the equation and the matrix , then the matrix is equal to: [7-Jan-2020 Shift 1]

Let be the roots of the equation such that . Let be integers not divisible by 3 and be a natural number such that . Then is equal to____ [29-Jan-2024 Shift 2]

Let and be three given vectors. Let be a vector in the plane of and whose projection on is . If , then is equal to : [26-Jun-2022-Shift-2]

Let a function be defined as : where . If is continuous at , then which of the following statements is NOT true? [27-Jul-2022-Shift-1]

Let be the solution curve of the differential equation passing through the point . Then is equal to: [28-Jul-2022-Shift-2]

Let . If for some then is equal to [25-Jul-2022-Shift-2]

Let be the plane passing through the intersection of the planes and , and the point . Let the position vectors of the points and be and respectively. Then the points [25-Jun-2022-Shift-2]

Let be a root of the equation where are distinct real numbers such that the matrix is singular. Then the value of is [24-Jan-2023 Shift 1]

Let and . Then the absolute value of the sum of all values of for which is : [30-Jun-2022-Shift-1]

Let be the set of all values of , for which the shortest distance between the lines and is 13 . Then is equal to [15-Apr-2023 shift 1]

If the points of intersection of two distinct conics and lie on the curve , then times the area of the rectangle formed by the intersection points is__ [29-Jan-2024 Shift 1]

Let and Then the ratio of the area of to the area of is [29-Jan-2023 Shift 1]

Let a smooth curve be such that the slope of the tangent at any point on it is directly proportional to . If the curve passes through the points and , then is equal to [25-Jul-2022-Shift-2]

Let . Then the sum of all elements of the matrix is equal to :[JEE Main 4 Apr 2026 Shift 1]

Let , where , are column matrices, and , If and is the sum of all the diagonal elements of , then is equal to [27-Jan-2024 Shift 1]

The shortest distance between the lines and , is :[JEE Main 4 Apr 2026 Shift 2]

Let be the mirror image of the point with respect to the plane . Let be a plane passing through the point and contains the line . Then, which of the following points lies on ? [29-Jun-2022-Shift-2]

Let and . Let in be maximum and minimum at and respectively. If , where are integers, then equals______ [1-Feb-2024 Shift 1]

Let be defined as where and [t] denotes greatest integer less than or equal to . Then, which of the following statements is true? [28-Jun-2022-Shift-1]

Let be the greatest integer . Then the number of points in the interval , where the function is discontinuous, is _______. [12-Apr-2023 shift 1]

If denotes the number of solutions of and , where , then the distance of the point from the line is____ [31-Jan-2024 Shift 1]

Let . Then the sum of the squares of all the values of , for which , is [27-Jun-2022-Shift-2]

Let , where . If and the positive value of a belongs to the interval , where , then is equal to ______. [11-Apr-2023 shift 1]

If is defined by , and , then k is equal to:[JEE Main 5 April 2026 Shift 2]

If the lines and are co-planar, then the distance of the plane containing these two lines from the point is : [26-Jun-2022-Shift-2]

The set of all values of , for which the matrix is invertible, is [29-Jan-2023 Shift 2]

Let . Let attains minimum and maximum values, respectively, at and . If , where and are integers, then the value of is equal to_____ [29-Jun-2022-Shift-1]

Let the image of the point in the line , be . If , is the point on L such that the distance of S from the foot of perpendicular from the point P on L is , then is equal to :[JEE Main 6 Apr 2026 shift

Let be the set of all values of for which the system of linear equations has non-trivial solution. Then is equal to [8-Apr-2023 shift 2]

Let and , where . If , then the inverse of the matrix is [25-Jan-2023 Shift 2]

Let and where , be three vectors. If the projection of on is and , then the value of is equal to: [29-Jun-2022-Shift-1]

A mixture of hydrogen and oxygen has volume , temperature , pressure and mass . The ratio of number of moles of hydrogen to number of moles of oxy in the mixture will be:[Take gas constant [27-Jun-202

Given below are two statements:Statement I : Electromagnetic waves are not deflected by electric and magnetic field.Statement II : The amplitude of electric field and the magnetic field in electromagn

The refractive index of an equilateral prism is . The angle of emergence under minimum deviation position of prism, in degree, is_____ [30-Jun-2022-Shift-1]

For an electromagnetic wave propagating through vacuum, , and represent propagation vector, electric field and angular frequency, respectively. The magnetic field associated with this wave is represen

As shown in the figure, after passing through the medium 1 . The speed of light in medium 2 will be: ( ) Given [28-Jul-2022-Shift-1]

An electron of mass m is moving in an electric field , with an initial velocity . If , its de Broglie wavelength at time t is _________. (e = charge of electron)[JEE Main 5 Apr 2026 Shift 1]

The vector is rotated through a right angle, passing through the -axis in its way and the resulting vector is . Then the projection of on is [25-Jan-2023 Shift 1]

Let a vector be coplanar with the vectors and . If the vector also satisfies the conditions and , then the value of is equal to : [30-Jun-2022-Shift-1]

The distance of the point form the line passing through the point and perpendicular to the lines and is [31-Jan-2024 Shift 1]

Let and be three non zero vectors such that and . If be a vector such that , then is equal to [25-Jan-2023 Shift 1]

Let and be two unit vectors such that . If is the angle between and , then among the statements : (S2) : The projection of on is [24-Jun-2022-Shift-2]

Let be the set of all for which the angle between the vectors and is acute. Then is equal to : [28-Jul-2022-Shift-2]

A ray of light is incident from air on a glass plate having thickness and refractive index . Lateral displacement (given ) [25-Jan-2023 Shift 1].

Let . If is a vector such that and , then is equal to____ [25-Jun-2022-Shift-2]

Let . Let a vector be such that the angle between and is and , If , then the value of is equal to [30-Jan-2024 Shift 2]

Let be a triangle such that and . Consider the statements : Then [25-Jul-2022-Shift-1]

The ratio of wavelengths of proton and deuteron accelerated by potential and is . Then the ratio of to will be : [25-Jul-2022-Shift-2]

Let and be two vectors. Let and . If , then the value of is [30-Jan-2023 Shift 2]

Let and the angle between the vectors and be . Then is equal to [13-Apr-2023 shift 2]

Let and be three non-zero non-coplanar vectors. Let the position vectors of four points , and be , and respectively. If , and are coplanar, then is :Official Ans. by NTA [29-Jan-2023 Shift 1]

Let be three points whose position vectors respectively are If is the smallest positive integer for which are noncollinear, then the length of the median, in , through is : [29-Jun-2022-Shift-2]

Magnetic field in a plane electromagnetic wave is given by T Expression for corresponding electric field will be : Where c is speed of light.[Main 8 April 2017]

Let and be two vectors, such that . Then the projection of on is equal to [27-Jul-2022-Shift-1]

Let and be the vectors along the diagonals of a parallelogram having area . Let the angle between and be acute, , and . If , then an angle between and is [27-Jun-2022-Shift-2]

The plane be taken as the boundary between two transparent media and . in has a refractive index of and with has a refractive index of . A ray of light travelling in along the direction given by the v

Let be the angle between the vectors and , where ,3 and . Then is equal to__ [25-Jun-2022-Shift-1]

A 60 HP electric motor lifts an elevator havinga maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N,the speed of the elevator at full load is close to:(1 HP = 74

A small bulb is placed at the bottom of a tank containing water to a depth of m. The refractive index of water is . The area of the surface of water through which light from the bulb can emerge out is

Let be a non-zero vector parallel to the line of intersection of the two places described by and . If is the angle between the vector and the vector and , then ordered pair is equal to : [11-Apr-2023

Let and be two vectors such that and . If , then the angle between and is equal to : [30-Jan-2024 Shift 1]

Let and be vectors such that . If , then is equal to _______. [8-Apr-2023 shift 1]

Let and be two vectors such that and . Then is equal to _______. [29-Jul-2022-Shift-2]

Let , and and be two nonzero vectors such that and . Consider the following two statement:(A) for all .(B) and are always parallel [31-Jan-2023 Shift 1]

Let a vector , has magnitude 9. Let a vector be such that for every , the vector is perpendicular to the vector . Then the value of is equal to: [28-Jul-2022-Shift-1]

A velocity selector consists of electric field and magnetic field with . The value of required for an electron of energy moving along the positive -axis to pass undeflected is : (Given, mass of electr

Let be the origin and the position vector of the point be . If the position vectors of the and are and respectively, then the projection of the vector on a vector perpendicular to the vectors and is :

Let and , Let -be a vector which is perpendicular to both , and , and . The -is equal to [10-Apr-2023 shift 2]

Let : and be there vectors. If is a vector such that, and . Then is equal to [31-Jan-2023 Shift 2]

A magnetic field vector in an electromagnetic wave is represented by, . Its associated electric field vector is _______.[JEE Main 4 Apr 2026 Shift 2]

Consider a light ray travelling in air is incident into a medium of refractive index . The incident angle is twice that of refracting angle. Then, the angle of incidence will be : [27-Jun-2022-Shift-1

and are the impact parameters corresponding to scattering angles and respectively, when an particle is approaching a gold nucleus. For , the value of will be_____ [29-Jun-2022-Shift-1]

A series L,R circuit connected with an ac source has a power factor of . If the source of emf is changed to t)V, the new power factor of the circuit will be : [30-Jan-2024 Shift 1]

Let be three coplanar concurrent vectors such that angles between any two of them is same. If the product of their magnitudes is 14 and , then is equal to: [29-Jul-2022-Shift-2]

Let and , where is the origin. If is the parallelogram with adjacent sides and , then is equal to [29-Jan-2024 Shift 2]

Let for a triangle , If and the area of the triangle is , then is equal to [13-Apr-2023 shift 2]

Let and be three non-zero vectors such that and are non-collinear .if is collinear with is collinear with and , then is equal to [29-Jan-2024 Shift 1]

Let and . Let be a vector such that and . Then is equal to [12-Apr-2023 shift 1]

The distance of the Sun from earth is and its angular diameter is (2000) s when observed from the earth. The diameter of the Sun will be : [27-Jun-2022-Shift-2]

A monochromatic beam of light has a frequency Hz and is propagating along the direction .It is polarized along th direction. The acceptable form for the magnetic field is :[Main 15 April 2018 S1]

Let be three non-coplanar vectors such that and If , then is equal to________. [27-Jul-2022-Shift-2]

Let and be two vectors such that and . Then is equal to [30-Jan-2024 Shift 2]

Let and be three unit vectors such that . If is not parallel to , then the angle between and is :[Main 2016]

Let and be three given vectors. If is a vector such that and , then is equal to : [1-Feb-2023 Shift 2]

Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance is used to measure the potential difference across resistor, the reading of the voltmeter will b

Let , and be a vector such that . If the minimum value of the scalar triple product is , and where and are coprime natural numbers, then is equal to _______. [1-Feb-2023 Shift 1]

Let and be three zero vectors such that no two no them are collinear and .If θ is the angle between vectors and ,then a value of sin θ is :[Main 2015]

If the vector is written as the sum of a vector ,parallel to and a vector , perpendicular to then is equal to:[Main 9 April 2017]

Let and , where . If the area of the parallelogram whose adjacent sides are represented by the vectors and is , then the value of is equal to : [28-Jun-2022-Shift-2]

A water heater of power is used to heat water. The specific heat capacity of water is . The efficiency of heater is . Time required to heat of water from to is _______ s.(Assume that the specific heat

A plane electromagnetic wave of frequency propagates in free space along -direction. At a particular space and time, . What is at this point? [11-Apr-2023 shift 2]

A ray of light is incident at an angle of incidence on the glass slab of refractive index . After refraction, the light ray emerges out from other parallel faces and lateral shift between incident ray

Given below are two statements: Statement I : A time varying electric field is a source of changing magnetic field and vice-versa. Thus a disturbance in electric or magnetic field creates EM waves. St

In the given figure, the face ACA CAC of the equilateral prism is immersed in a liquid of refractive index ' n '. For incident angle at the side ACA CAC, the refracteel light beam just grazes along fa

Let .If , then is equal to [30-Jan-2023 Shift 2]

Let and .Let be a vector such that and the angle between and be 30°.Then is eqaula to :[Main 2017]

An electron (mass ) with an initial velocity ( ) is moving in an electric field ( ) where is constant. If at de Broglie wavelength is , then its de Broglie wavelength after time is given by [27-Jul-20

Let the vectors and be coplanar. If the vectors and are also coplanar, then is equal to [8-Apr-2023 shift 2]

If are three non-zero vectors and is a unit vector perpendicular to such that and , then is equal to : [30-Jan-2023 Shift 1]

A plane electromagnetic wave of frequency travels in free space along the X-direction. At a particular point (in space and time) . The value of magnetic field at this point is : [29-Jan-2024 Shift 2]

Match List I with List II : A. Gauss'sLaw inElectrostat ics I. B. Faraday'sLaw II. C. Gauss'sLaw inMagnetism III. D. Ampere-MaxwellLaw IV. Choose the correct answer from the options given below : [25-

Let and be three vectors. If a vectors satisfies and , then is equal to [31-Jan-2024 Shift 1]

Let and be three vectors such that . If the angle between the vector and the vector is , then the greatest integer less than or equal to is : [1-Feb-2024 Shift 2]

If the maximum load carried by an elevator is ( Passengers - elevator), which is moving up with a uniform speed of and the frictional force acting on it is , then the maximum power used by the motor i

The electric field in an electromagnetic wave is given as where and are angular frequency and velocity of electromagnetic wave respectively. the energy contained in a volume of will be (Given ) [11-Ap

Let and . If a vector satisfies and , then is equal to - [13-Apr-2023 shift 1]

Let the vectors and be such that for . Then, the setof all values of is : [28-Jul-2022-Shift-1]

Let be three vectors such that and .If the angle between and is , then is equal to _________. [31-Jan-2023 Shift 2]

Let and and is a vector such that and projection of on is 1 , then the projection of on equals : [29-Jan-2023 Shift 2]

Let and be a vector such that and . Then is equal to____ [31-Jan-2024 Shift 2]

An electromagnetic wave travels in free space along the x-direction. At a particular point in space and time, is associated with this wave. The value of corresponding electric field at this point is _

An arc of a circle subtends a right angle at its centre . The mid point of the arc is . If and , then are the roots of the equation : [10-Apr-2023 shift 1]

If the vectors and are coplanar and the projection of on the vector is units, then the sum of all possible values of is equal to [29-Jan-2023 Shift 1]

Let and . Let be a vector satisfying . If and are non-parallel, then the value of is: [29-Jul-2022-Shift-1]

Let a unit vector make angles and with the vectors and respectively. If , then is equal to [29-Jan-2024 Shift 2]

The refractive index of a transparent liquid filled in an equilateral hollow prism is . The angle of minimum deviation for the liquid will be ________. [15-Apr-2023 shift 1]

Let and . Let be parallel to and be perpendicular to . If , then the value of is [24-Jan-2023 Shift 2]