Question 1 :
Two resistances of 400 Ω and 800 Ω connected in series with a 6 volt battery of negligible internal resistance. A voltmeter of resistance 10,000Ω is used to measure the potential difference across 400 Ω. The error in the measurement of potential difference in volts approximately is
Question 2 :
The density of wood is 0.5 g cm<sup>-3</sup> in cgs system of units. The corresponding value in SI units is-
Question 4 :
A sample of gas is at 0°C. To what temperature it must be raised in order to double the r.m.s. speed of the molecule-
Question 5 : The velocity of a particle is given by v = a + <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75c571b5f89758f2d4e454' height='37' width='15' > + ct<sup>2</sup><br>The unit of b will be
Question 6 :
The value of {tex} n {/tex} so that vectors {tex} 2 \hat { i } + 3 \hat { j } - 2 \hat { k } , 5 \hat { i } + n \hat { j } + \hat { k } {/tex} and {tex} - \hat { i } + 2 \hat { j } + 3 \hat { k } {/tex} may be coplanar, will be
Question 7 : What is the final reading of callipers as shown -<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75c65b4389b1556ddef620' height='97' width='176' >
Question 8 : Dimensional formula <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75c5cfb5f89758f2d4e4bb' height='17' width='48' > does not represent the physical quantity -
Question 9 :
{tex}Assertion:{/tex} Specific gravity of a fluid is a dimensionless quantity
<br>{tex}Reason: {/tex} It is the ratio of density of fluid to density of water.
Question 10 :
A screw gauge with a pitch of {tex} 0.5mm{/tex} and a circular scale with 50 divisions is made to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the 45th division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is {tex} 0.5mm {/tex} and the 25th division coincides with the main scale line.
Question 12 :
Pitch of a screw gauge is 0.5 mm and its least count is 0.01 mm. Calculate no. of divisions on its head scale.
Question 13 :
Given {tex} \vec { A } = 2 \hat { i } + p \hat { j } + q \hat { k } {/tex} and {tex} \vec { B } = 5 \hat { i } + 7 \hat { j } + 3 \hat { k } . {/tex} If {tex} \vec { A } \| \vec { B } , {/tex} then the values of {tex} p {/tex} and {tex} q {/tex} are, respectively,
Question 14 :
If velocity, force and time are taken to be fundamental quantities find dimensions formula for (a) mass
Question 17 : Match the Column I with Column II <table><tr><th>Column I Physical quantity</th> <th>Column II Name of unit</th> </tr><tr><td>(A) Conductance</td> <td>(p) Gray</td> </tr> <tr><td>(B) Magnetic induction </td> <td>(q) Lumen</td> </tr> <tr><td>(C) Absorbed dose</td> <td>(r) Tesla</td> </tr> <tr><td>(D) Luminous flux</td> <td>(s) Siemens</td></tr></table>
Question 18 :
Which of the following physical quantities has same unit in all the three system of units?
Question 19 :
The dimensional formula of kinetic energy is the same as that of -
Question 20 :
Which of the rectangular pair may be the components of a 13 N force?
Question 21 :
Calculate the area of the triangle determined by the two vectors {tex} \vec { A } = 3 \hat { i } + 4 \hat { j } {/tex} and {tex} \vec { B } = - 3 \hat { i } + 7 \hat { j } {/tex}
Question 23 :
Dimensions of one or more pairs are same. Identify the pairs-
Question 24 :
Which of the following relation cannot be derived using dimensional analysis (Neglect value of constant) -
Question 26 :
The equation of a wave is y = a sin (At - Bx + C), where A, B and C are constants. The dimensions of A, B and C are respectively
Question 27 :
If L and R denote inductance and resistance, respectively, then the dimension of L/R is -
Question 28 :
Two rods with lengths 20.123 cm and 18.1 cm are placed side by side. The difference in their lengths is
Question 29 :
Error in the measurement of radius of sphere is 2{tex} \% {/tex}. Then error in the calculation of volume will be
Question 31 :
The dimensions of h/e (h = Planck's constant and e = electronic charge) are same as that of :
Question 32 :
Taking into account the significant figures, what is the value of 9.99 m + 0.0099 m
Question 33 :
Energy due to position of a particle is given by, {tex} U = \frac { \alpha \sqrt { y } } { y + \beta } , {/tex} where {tex} \alpha {/tex} and {tex} \beta {/tex} are constants, {tex} y {/tex} is distance. The dimensions of {tex} ( \alpha \times \beta ) {/tex} are
Question 34 :
The projection of a vector {tex} \vec { r } = 3 \hat { i } + \hat { j } + 2 \hat { k } {/tex} on the {tex} x - y {/tex} plane has magnitude
Question 35 :
The angles which the vector {tex} \vec { A } = 3 \hat { i } + 6 \hat { j } + 2 \hat { k } {/tex} makes with the co-ordinate axes are
Question 36 :
The component of vector {tex} \vec { A } = 2 \hat { i } + 3 \hat { j } {/tex} along the vector {tex} \hat { i } + \hat { j } {/tex} is
Question 37 :
Unit vector parallel to the resultant of vectors {tex} \vec { A } = 4 \hat { i } - 3 \hat { j } {/tex} and {tex} \vec { B } = 8 \hat { i } + 8 \hat { j } {/tex} will be
Question 38 : In the given relation P = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75c5f3491ec95800697483' height='40' width='41' >, where P is power, x is distance and t is time, the dimensions of 'a' will be -
Question 40 : A block of mass {tex} m {/tex} is connected to three springs, each of spring constant {tex} k {/tex} as shown in Fig. 1.26. The block is pulled by {tex} x {/tex} in the direction of {tex} C . {/tex} Find resultant spring constant.<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5d5809e541fcca588ca358b7"><br>
Question 41 :
A scientist performs an experiment and takes 50 readings. He repeats the same experiment and now takes 200 readings. By doing so:
Question 42 :
{tex}\mathbf {Assertion}{/tex} : : Mass, length and time are fundamental physical quantities. <br>{tex}\mathbf {Reason}{/tex} : They are independent of each other.
Question 43 :
The {tex} ( x , y , z ) {/tex} co-ordinates of two points {tex} A {/tex} and {tex} B {/tex} are given respectively as {tex} ( 0,3 , - 1 ) {/tex} and {tex} ( - 2,6,4 ) . {/tex} The displacement vector from {tex} A {/tex} to {tex} B {/tex} is given by
Question 45 :
Two forces {tex} \vec { F } _ { 1 } = 500 \mathrm { N } {/tex} due east and {tex} \vec { F } _ { 2 } = 250 \mathrm { N } {/tex} due north have their common initial point. {tex} \vec { F } _ { 2 } - \vec { F } _ { 1 } {/tex} is
Question 48 :
On a long horizontally moving belt, a child runs to and fro with a speed 9 km h<sup>-1</sup> (with respect to the belt) between his father and mother located 50 m apart on the moving belt. The belt moves with a speed of 4 km h<sup>-1</sup>.
For an observer on a stationary platform outside, what is the time taken by the child to go from father to mother and back to father is
Question 49 :
{tex} \begin{array} { l l } { \text { Assertion } } & {: \text { A body can have acceleration even if its velocity is } } \\ { } & { \text { zero at a given instant of time. } } \\ { \text { Reason } } & {: \text { A body is momentarily at rest when it reverses its } } \\ { } & { \text { direction of motion. } } \end{array} {/tex}
Question 50 :
A stone is dropped from a height {tex} h {/tex}. Simultaneously, another stone is thrown up from the ground which reaches a height 4 h. The two stones cross each other after time
Question 51 :
A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed again by 5 steps forward and 3 steps backward, and so on. Each step is 1{tex} \mathrm { m } {/tex} long and requires 1{tex} \mathrm { s } {/tex} . How long will it take for the drunkard to fall in a pit 13{tex} \mathrm { m } {/tex} away from the start.
Question 52 : In Fig. the position time graph of a particle of mass 0.1 kg is shown. Find the impulse at t = 2sec. <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5ec3b93894199c6b82bee788' class="uploaded-image" /> <br>
Question 53 :
A cat wants to catch a rat. The cat follows the path whose equation is x + y = 0, but the rat follows the path whose equation is$x^{2}+ y^{2} = 4$. The coordinates of possible points of catching the rat are?
Question 54 :
A body falls freely from the top of a tower. It covers {tex} 36 \% {/tex} of the total height in the last second before striking the ground level. The height of the tower is
Question 55 :
A body is thrown vertically upwards. If air resistance is to be taken into account, then the time during which the body rises is
Question 56 : A small body of mass {tex} m {/tex} slides down from the top of a hemisphere of radius {tex} r . {/tex} The surface of block and hemisphere are frictionless. The height at which the body lose contact with the surface of the sphere is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5dc4f1d54548337453d213ed"><br>
Question 57 :
Journey in a train is adventurous particularly when you have a seat. The girl sitting near window ate a banana and dropped the peel from the window. Her co-passenger looking through the window found that it dropped vertically down and touched the ground in $0.2s$. After sometime she requested her sister sitting on the upper berth to drop a chocolate bar.The sister dropped the bar, but it fell in front of the girl instead of reaching her hand. She was angry but the co-passenger calmed her by saying that she dropped exactly in line of your hand but as the train is accelerating it did not reach you and fell in front of you. An observer standing outside the train finds the banana peel moving<br/>
Question 58 :
A ring of radius r and mass per unit length m rotates with an angular velocity ωin free space. The tension in the ring is
Question 59 :
A circular track of radius 300 m is banked at an angle π/12 radian. If the coefficient of friction between wheel of a vehicle and road is 0.2, the maximum safe speed of vehicle is
Question 60 :
A point particle starting from rest has a velocity that increases linearly with time such that $v=pt$ where $p=4m/s^2$. The distance covered in the first $2$ sec will be?
Question 61 : STATEMENT-1: For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.<div> <br/>STATEMENT-2: If the observer and the object are moving at velocities $\vec{\mathrm{V}}_{1}$ and $\vec{\mathrm{V}}_{2}$ respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is $\vec{\mathrm{V}}_{2}-\vec{\mathrm{V}}_{1}$. <br/></div>
Question 62 :
A force of 10 N act on a body of mass 5 kg what is displacement after 2 second when particle is initially at rest.<br/>
Question 63 :
A projectile is fired vertically upwards with an initial velocity {tex} u {/tex} . After an interval of {tex} T {/tex} seconds a second projectile is fired vertically upwards, also with initial velocity {tex} u {/tex} . The correct statement is
Question 64 :
A car starts from rest moving along a line, first with acceleration a= $2 m/s^{2}$ , then uniformly and finally decelerating at the same rate and comes to rest. The total time of motion is $10$ sec. The average speed during this time is $3.2 m/s$. How long does the car move uniformly?(in seconds)
Question 65 :
The friction of the air causes vertical retardation equal to one tenth of the acceleration due to gravity (Take g = 10 ms<sup>-2</sup>). The time of flight will be decreased by
Question 66 :
Two trains A and B of length 400m each are moving on two parallel tracks with a uniform speed of {tex}72 km \ h^{-1}{/tex} in the same direction, with A ahead of B. The driver of B decides to overtake A and accelerates by {tex}1 m/s^{2}{/tex}. If after 50 s, the guard of B just brushes past the driver of A, what was the original distance between them?
Question 67 : A 2m wide truck is moving with a uniform speed {tex}v_{0} = 8 m/s{/tex} along a straight horizontal road. A pedestrian starts to cross the road with a uniform speed v when the truck is 4m away from him. The minimum value of v so that he can cross the road safely is <br> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5d5804db40fda93533ee5b47" />
Question 68 :
A cannon on a level plane is aimed at an angle $\theta $ above the horizontal and a shell is fired with a muzzle velocity $v_0$ towards a vertical cliff a distance $D$ away.Then the height from the bottom at which the shell strikes the side wall of the cliff is
Question 69 :
A cannon on a level plane is aimed at an angle {tex} \theta {/tex} above the horizontal and a shell is fired with a muzzle velocity {tex} v _ { 0 } {/tex} towards a vertical cliff a distance {tex} D {/tex} away. Then the height from the bottom at which the shell strikes the side walls of the cliff is
Question 70 :
A stone tied to the end of a string 80{tex} \mathrm { cm } {/tex} long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25{tex} \mathrm { s } {/tex} , what is the magnitude of acceleration of the stone?
Question 71 : Displacement {tex} ( s ) {/tex} versus time {tex} ( t ) {/tex} graphs of two parti- cles moving in a straight line along {tex} x {/tex} -axis are shown below. Which of following statement is incorrect.<br><img style='object-fit:contain' src="https://data-screenshots.sgp1.digitaloceanspaces.com/5d5801e815497266f6799b2b.jpg" />
Question 72 : A cyclist starts from centre O of a circular park of radius 1 km and moves along the path OPRQO as shown in figure. If he maintains constant speed of 10 m s<sup>-1</sup>, what is his acceleration at point R?<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75e33c491ec95800697c9f' height='89' width='85' >
Question 73 : <p>The displacement of a particle moving in a straight line is described by the relation, $s = 6 + 12t - 2t^2$.Here $s$ is in metre and $t$ in second. The distance covered by the particle in first 5 s is</p>
Question 74 : The displacement-time graph of motion of a particle is shown in the figure. The ratio of the magnitudes of the speeds during the first two seconds and the next four seconds is:<br><img style='object-fit:contain' src="https://data-screenshots.sgp1.digitaloceanspaces.com/5ea41b2c1318b26b1c13db48.jpg" />
Question 75 : Figure shows a hemisphere and a supported rod. Hemisphere is moving right with a uniform velocity <em>v</em><sub>2</sub> and the end of rod which is in contact with ground is moving left with a velocity <em>v</em><sub>1</sub>. The rate at which the angle θ is decreasing will be <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16bd9d1da6d070c2abf87c"/>
Question 76 :
The acceleration of a particle is increasing linearly with time t as βt. If the particle starts from origin with initial velocity u, the distance travelled by it in t second is
Question 77 :
A particle is moving in a straight line and passes through a point {tex} O {/tex} with a velocity of {tex} 6 \mathrm { ms } ^ { - 1 } {/tex}. The particle moves with a constant retardation of {tex} 2 \mathrm { ms } ^ { - 2 } {/tex} for {tex} 4 s {/tex} and there after moves with constant velocity. How long after leaving {tex} O {/tex} does the particle return to {tex} \mathrm { O } {/tex}
Question 78 :
P is a variable point in the square formed by the lines $x = \pm 1\,and\,y = \pm 1$.P moves such. that its distance from the origin is loss than its distance from any side of square. The area traced by the point P is
Question 79 :
The velocity vector of a particle moving in the xy plane is given by v=ti +xj. If initially , the particle was at origin then the equation of trajectory of the projectile is:
Question 80 :
The ceiling of a long hall is 25{tex} \mathrm { m } {/tex} high. What is the maximum horizontal distance that a ball thrown with a speed of 40{tex} \mathrm { ms } ^ { - 1 } {/tex} can go without hitting the ceiling of the hall?
Question 81 :
A man standing on the roof of a house of height {tex} h {/tex} throws one particle vertically downwards and another particle horizontally with the same velocity {tex} u . {/tex} The ratio of their velocities when they reach the earth's surface will be
Question 82 :
A particle is moving on a circular path with constant speed v. What is the change in its velocity after it has described an angle of 60<sup>0</sup>?
Question 83 :
For a given velocity of projection from a point on the inclined plane, the maximum range down the plane is three times the maximum range up the incline. Then, the angle of inclination of the inclined plane is
Question 84 :
Relation to another coordinate system $\mathrm{S}_{2}$ (denoted by double primes) having an acceleration $-\overline{\mathrm{g}}$, and coincident with the original coordinate system $\mathrm{S}_{0}$ at $\mathrm{t}=0$, the equation of the object becomes<br/>
Question 85 :
A cannon shell is fired straight up from the ground at an initial speed of $225 m/s$. After how much time is the shell at a height of $6.20 * 10^{2} m$ above the ground and moving downward?<br>
Question 86 :
{tex}\mathrm {Assertion} \quad {/tex} :Distance-time graph of the motion of a body having uniformly accelerated motion is a straight line inclined to the time axis.<br> {tex}\mathrm {Reason} \quad {/tex} :Distance travelled by a body having uniformly accelerated motion is directly proportional to the square of the time taken.
Question 87 :
A car travels on a circular road of radius $\dfrac{7}{22}$ km. When it covers a distance of $2 km$ on the road, what will be its displacement?
Question 88 :
A body starts from rest with uniform acceleration. If its velocity after {tex} n {/tex} second is {tex} v , {/tex} then its displacement in the last two seconds is
Question 89 : A given shaped glass tube having uniform area of cross - section is filled with water and is mounted on a rotatable shaft as shown in fig. If the tube is rotated with a constant angular velocity ω, then <br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75e5dc491ec95800697f20' height='167' width='219' >
Question 90 :
Two trains one of length {tex} 100 \mathrm { m } {/tex} and another of length {tex} 125 \mathrm { m } , {/tex} are moving in mutually opposite directions along parallel lines, meet each other, each with speed {tex} 10 \mathrm { m } / \mathrm { s } {/tex}. If their acceleration are {tex} 0.3 \mathrm { m } / \mathrm { s } ^ { 2 } {/tex} and {tex} 0.2 \mathrm { m } / \mathrm { s } ^ { 2 } {/tex} respectively, then the time they take to pass each other will be
