Physics · JEE Main

Mathematics in Physics

121 practice questions with a worked solution for each. Tap an option to see instantly if you are right.

95MCQ26Numerical9With diagram
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  1. 1A vector has magnitude same as that of A⃗=3j^+4j^\vec{A}=3\hat{j}+4\hat{j} and is parallel to B⃗=4i^+3j^\vec{B}=4\hat{i}+3\hat{j}. The xx and yy components of this vector in first quadrant are xx and 33 respectively where x=x=____.JEE Main/Numerical/Medium/Fundamentals of Vectors
  2. 2Two vectors X⃗\vec{X} and Y⃗\vec{Y} have equal magnitude. The magnitude of (X⃗−Y⃗)(\vec{X}-\vec{Y}) is nn times the magnitude of (X⃗+Y⃗)(\vec{X}+\vec{Y}). The angle between X⃗\vec{X} and Y⃗\vec{Y} is :JEE Main/MCQ/Medium/Fundamentals of Vectors
  3. 3A particle is moving with a velocity v⃗=K(yi^+xj^),\vec{v}=K\left(y\hat{i}+x\hat{j}\right), where KK is a constant.

    The general equation for its path is:    JEE Main/MCQ/Medium/Fundamentals of Vectors
  4. 4Two particles are located at equal distance from origin. The position vectors of those are represented by Aˉ=2i^+3nj^+2k^\bar{A}=2 \hat{i}+3 n \hat{j}+2 \hat{k} and Bˉ=2i^−2j^+4pk^\bar{B}=2 \hat{i}-2 \hat{j}+4 p \hat{k}, respectively. If both the vectors are at right angle to each other, the value of n−1\mathrm{n}^{-1} is _____ .JEE Main/Numerical/Medium/Addition and Subtraction of Vectors
  5. 5The resultant of two vectors A⃗\vec{A} and B⃗\vec{B} is perpendicular to A⃗\vec{A} and its magnitude is half that of B⃗\vec{B}. The angle between vectors A⃗\vec{A} and B⃗\vec{B} is ______ ∘\circ.JEE Main/Numerical/Medium/Addition and Subtraction of Vectors
  6. 6If a⃗\vec{a} and b⃗\vec{b} makes an angle cos⁡−1(59)\cos ^{-1}\left(\frac{5}{9}\right) with each other, then ∣a⃗+b⃗∣=2∣a⃗−b⃗∣|\vec{a}+\vec{b}|=\sqrt{2}|\vec{a}-\vec{b}| for ∣a⃗∣=n∣b⃗∣|\vec{a}|=n|\vec{b}| The integer value of n\mathrm{n} is ____JEE Main/Numerical/Medium/Addition and Subtraction of Vectors
  7. 7Three vectors OP→,OQ→\overrightarrow{\mathrm{OP}}, \overrightarrow{\mathrm{OQ}} and OR→\overrightarrow{\mathrm{OR}} each of magnitude A\mathrm{A} are acting as shown in figure. The resultant of the three vectors is Ax\mathrm{A} \sqrt{x}. The value of xx is ________ .
    JEE Main/Numerical/Medium/Addition and Subtraction of Vectors/With diagram
  8. 8The angle between vector Q⃗\vec{Q} and the resultant of (2Q⃗+2P⃗)(2 \vec{Q}+2 \vec{P}) and (2Q⃗−2P⃗)(2 \vec{Q}-2 \vec{P}) is :JEE Main/MCQ/Medium/Addition and Subtraction of Vectors
  9. 9Two forces Fˉ1\bar{F}_1 and Fˉ2\bar{F}_2 are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between F⃗1\vec{F}_1 and F⃗2\vec{F}_2 is cos⁡−1(1n)\cos ^{-1}\left(\frac{1}{n}\right). The value of ∣n∣|n| is _____.JEE Main/Numerical/Medium/Addition and Subtraction of Vectors
  10. 10If two vectors A⃗\vec{A} and B⃗\vec{B} having equal magnitude RR are inclined at an angle θ\theta, thenJEE Main/MCQ/Medium/Addition and Subtraction of Vectors
  11. 11A vector in x−yx-y plane makes an angle of 30o{30}^{o} with yy-axis. The magnitude of yy-component of vector is 232\sqrt{3}. The magnitude of xx-component of the vector will be :JEE Main/MCQ/Medium/Addition and Subtraction of Vectors
  12. 12Three forces F1=10N,F2=8N,F3=6N{F}_{1}=10N,{F}_{2}=8N,{F}_{3}=6N are acting on a particle of mass 5kg5kg. The forces F2{F}_{2} and F3{F}_{3} are applied perpendicularly so that particle remains at rest. If the force F1{F}_{1} is removed, then the acceleration of the particle isJEE Main/MCQ/Medium/Addition and Subtraction of Vectors
  13. 13When vector A⃗=2i^+3j^+2k^\vec{A}=2\hat{i}+3\hat{j}+2\hat{k} is subtracted from vector B⃗\vec{B}, it gives a vector equal to 2j^2\hat{j}. Then the magnitude of vector B⃗\vec{B} will be:JEE Main/MCQ/Medium/Addition and Subtraction of Vectors
  14. 14Two forces having magnitude AA and A2\dfrac{A}{2} are perpendicular to each other. The magnitude of their resultant is:JEE Main/MCQ/Medium/Addition and Subtraction of Vectors
  15. 15A body is moving with constant speed, in a circle of radius 10m10m. The body completes one revolution in 4s4s. At the end of 3rd3rd second, the displacement of body (in mm) from its starting point is:JEE Main/MCQ/Medium/Addition and Subtraction of Vectors
  16. 16A person moved from AA to BB on a circular path as shown in figure. If the distance travelled by him is 60m60m, then the magnitude of displacement would be : (Given cos⁡135∘=−0.7\cos 135^{\circ}=-0.7)
    JEE Main/MCQ/Medium/Addition and Subtraction of Vectors/With diagram
  17. 17Two vectors A⃗\vec{A} and B⃗\vec{B} have equal magnitudes. If magnitude of A⃗+B⃗\vec{A}+\vec{B} is equal to two times the magnitude of A⃗−B⃗\vec{A}-\vec{B}, then the angle between A⃗\vec{A} and B⃗\vec{B} will beJEE Main/MCQ/Medium/Addition and Subtraction of Vectors
  18. 18Which of the following relations is true for two unit vector A^\hat{A} and B^\hat{B} making an angle θ\theta to each other?JEE Main/MCQ/Medium/Addition and Subtraction of Vectors
  19. 19Statement-I : Two forces (P⃗+Q⃗)\left(\vec{P}+\vec{Q}\right) and (P⃗−Q⃗)\left(\vec{P}-\vec{Q}\right) where P⃗⊥Q⃗,\vec{P}\perp \vec{Q}, when act at an angle θ1{\theta }_{1} each other, the magnitude of their resultant is 3(P2+Q2),\sqrt{3\left({P}^{2}+{Q}^{2}\right)}, when they act at an angle θ2,{\theta }_{2}, the magnitude of their resultant becomes 2(P2+Q2).\sqrt{2\left({P}^{2}+{Q}^{2}\right)}. This is possible only when θ1<θ2.{\theta }_{1}\lt {\theta }_{2}.
    Statement-II : In the situation given above.
    θ1=60∘{\theta }_{1}=60^{\circ} and θ2=90∘{\theta }_{2}=90^{\circ}
    In the light of the above statement, choose the most appropriate answer from the options given below :    JEE Main/MCQ/Medium/Addition and Subtraction of Vectors
  20. 20Statement I: If three forces F⃗1,F⃗2{\vec{F}}_{1},{\vec{F}}_{2} and F⃗3{\vec{F}}_{3} are represented by three sides of a triangle and F1⃗+F2⃗=−F⃗3,\vec{{F}_{1}}+\vec{{F}_{2}}=-{\vec{F}}_{3}, then these three forces are concurrent forces and satisfy the condition for equilibrium.
    Statement II: A triangle made up of three forces     F1⃗,F2⃗\vec{{F}_{1}},\vec{{F}_{2}} and F3⃗\vec{{F}_{3}} as its sides were taken in the same order, satisfies the condition for translatory equilibrium.
    In the light of the above statements, choose the most appropriate answer from the options given below:    JEE Main/MCQ/Medium/Addition and Subtraction of Vectors
  21. 21The resultant of these forces OP⃗,OQ⃗,OR⃗,OS⃗\vec{OP},\vec{OQ},\vec{OR},\vec{OS} and OT⃗\vec{OT} is approximately ______N.N.
    [Take     3=1.7,2=1.4\sqrt{3}=1.7,\sqrt{2}=1.4 Given i^\hat{i} and j^\hat{j} unit vectors along x,yx,y axis]
    JEE Main/MCQ/Medium/Addition and Subtraction of Vectors/With diagram
  22. 22The angle between vector (A⃗)(\vec{A}) and (A⃗−B⃗)(\vec{A}-\vec{B}) is :
    JEE Main/MCQ/Medium/Addition and Subtraction of Vectors/With diagram
  23. 23The magnitude of vectors OA⃗,OB⃗\vec{OA},\vec{OB} and OC⃗\vec{OC} in the given figure are equal. The direction of OA⃗+OB⃗−OC⃗\vec{OA}+\vec{OB}-\vec{OC} with x−x-axis will be:
    JEE Main/MCQ/Medium/Addition and Subtraction of Vectors/With diagram
  24. 24AssertionA:AssertionA: If A,B,C,DA,B,C,D are four points on a semi-circular arc with a centre at OO such that ∣AB⃗∣=∣BC⃗∣=∣CD⃗∣.|\vec{AB}|=|\vec{BC}|=|\vec{CD}|. Then, AB⃗+AC⃗+AD⃗=4AO⃗+OB⃗+OC⃗\vec{AB}+\vec{AC}+\vec{AD}=4\vec{AO}+\vec{OB}+\vec{OC}
    ReasonR:ReasonR: Polygon law of vector addition yields AB⃗+BC⃗+CD⃗+AD⃗=2AO⃗\vec{AB}+\vec{BC}+\vec{CD}+\vec{AD}=2\vec{AO}

    In the light of the above statements, choose the most appropriate answer from the options given below.    JEE Main/MCQ/Medium/Addition and Subtraction of Vectors/With diagram
  25. 25Match List I with List II. List I List II (a) C⃗−A⃗−B⃗=0\vec{C}-\vec{A}-\vec{B}=0 (i) (b) A⃗−C⃗−B⃗=0\vec{A}-\vec{C}-\vec{B}=0 (ii) (c) B⃗−A⃗−C⃗=0\vec{B}-\vec{A}-\vec{C}=0 (iii) (d) A⃗+B⃗=−C⃗\vec{A}+\vec{B}=-\vec{C} (iv) Choose the correct answer from the options given below:JEE Main/MCQ/Medium/Addition and Subtraction of Vectors/With diagram
  26. 26Three particles P,QP,Q and RR are moving along the vectors A⃗=i^+j^,B⃗=j^+k^\vec{A}=\hat{i}+\hat{j},\vec{B}=\hat{j}+\hat{k} and C⃗=−i^+j^\vec{C}=-\hat{i}+\hat{j}, respectively. They strike on a point and start to move in different directions. Now particle PP is moving normal to the plane which contains vector A⃗\vec{A} and B⃗.\vec{B}. Similarly particle QQ is moving normal to the plane which contains vector A⃗\vec{A} and C⃗.\vec{C}. The angle between the direction of motion of PP and QQ is cos⁡−1(1x).{\cos }^{-1}\left(\dfrac{1}{\sqrt{x}}\right). Then the value of xx is ..JEE Main/Numerical/Medium/Addition and Subtraction of Vectors
  27. 27Two vectors P⃗\vec{P} and Q⃗\vec{Q} have equal magnitudes. If the magnitude of P⃗+Q⃗\vec{P}+\vec{Q} is nn times the magnitude of P⃗−Q⃗,\vec{P}-\vec{Q}, then angle between P⃗\vec{P} and Q⃗\vec{Q} isJEE Main/MCQ/Medium/Addition and Subtraction of Vectors
  28. 28If A⃗\vec{A} and B⃗\vec{B} are two vectors satisfying the relation A⃗⋅B⃗=∣A⃗×B⃗∣\vec{A}\cdot \vec{B}=|\vec{A}\times \vec{B}|. Then the value of ∣A⃗−B⃗∣|\vec{A}-\vec{B}| will be:JEE Main/MCQ/Medium/Addition and Subtraction of Vectors
  29. 29If P⃗×Q⃗=Q⃗×P⃗\vec{P}\times \vec{Q}=\vec{Q}\times \vec{P}, the angle between P⃗\vec{P} and Q⃗\vec{Q} is θ(0∘<θ<360∘)\theta \left(0^{\circ}\lt \theta \lt 360^{\circ}\right). The value of θ\theta will be ___∘^{\circ}.JEE Main/Numerical/Medium/Addition and Subtraction of Vectors
  30. 30In an octagon ABCDEFGHABCDEFGH of equal side, what is the sum of AB⃗+AC⃗+AD⃗+AE⃗+AF⃗+AG⃗+AH⃗,\vec{AB}+\vec{AC}+\vec{AD}+\vec{AE}+\vec{AF}+\vec{AG}+\vec{AH}, if, AO⃗=2i^+3j^−4k^\vec{AO}=2\hat{i}+3\hat{j}-4\hat{k}
    JEE Main/MCQ/Medium/Addition and Subtraction of Vectors/With diagram
  31. 31The sum of two forces P⃗\vec{P} and Q⃗\vec{Q} is R⃗\vec{R} such that ∣R⃗∣=∣P⃗∣\left|\vec{R}\right|=\left|\vec{P}\right|. Find the angle between resultant of 2P⃗2\vec{P} and Q⃗\vec{Q} and Q⃗\vec{Q} , ________JEE Main/Numerical/Medium/Addition and Subtraction of Vectors
  32. 32Ship AA is sailing towards north-east with velocity) v⃗=30i^+50j^kmh−1\vec{v}=30\hat{i}+50\hat{j}km{h}^{-1} where i^\hat{i} points east and j^,\hat{j}, north. The ship BB is at a distance of 80km80km east and 150km150km north of Ship AA and is sailing towards the west at 10kmh−1.10km{h}^{-1}. AA will be at the minimum distance from BB in:JEE Main/MCQ/Medium/Addition and Subtraction of Vectors
  33. 33A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle 60o{60}^{o} with ground level, but he finds the aeroplane right vertically above his position. If vv is the speed of sound, speed of the plane is:JEE Main/MCQ/Medium/Addition and Subtraction of Vectors
  34. 34A particle moves from the point (2.0i^+4.0j^)m,(2.0 \hat{i}+4.0 \hat{j}) \mathrm{m}, at t=0\mathrm{t}=0,

    with an initial velocity     (5.0i^+4.0j^)ms−1.(5.0 \hat{i}+4.0 \hat{j}) \mathrm{ms}^{-1} . It is acted upon by a constant force which produces a constant acceleration

    (4.0i^+4.0j^)ms−2.(4.0 \hat{i}+4.0 \hat{j}) \mathrm{ms}^{-2} . What is the distance of the particle

    from the origin at time     2 s?2 \mathrm{~s} ?    JEE Main/MCQ/Medium/Addition and Subtraction of Vectors
  35. 35Two forces PP and QQ, of magnitude 2F2F and 3F3F, respectively, are at an angle θ\theta with each other. If the force QQ is doubled, then their resultant also gets doubled. Then, the angle θ\theta is:JEE Main/MCQ/Medium/Addition and Subtraction of Vectors
  36. 36In the cube of side 'a' shown in the figure, the vector from the central point of the face ABODABOD to the central point of the face BEFOBEFO will be:

    JEE Main/MCQ/Medium/Addition and Subtraction of Vectors/With diagram
  37. 37The position co-ordinates of a particle moving in a 3D3D coordinate system is given by

    x=acos⁡⁡ωtx=a\cos ⁡\omega t

    y=asin⁡⁡ωty=a\sin ⁡\omega t

    and     z=aωtz=a\omega t

    The speed of the particle is:    JEE Main/MCQ/Medium/Addition and Subtraction of Vectors
  38. 38A vector A⃗\vec{A} is rotated by a small angle ∆θ∆\theta radians (∆θ≪1)\left(∆\theta ≪1\right) to get a new vector B⃗\vec{B} . In that case ∣B⃗−A⃗∣\left|\vec{B}-\vec{A}\right| is :JEE Main/MCQ/Medium/Addition and Subtraction of Vectors
  39. 39A particle is moving eastwards with a velocity of 5 m/s5 \mathrm{~m} / \mathrm{s} in 10 seconds the velocity changes to 5 m/s5 \mathrm{~m} / \mathrm{s} northwards. The average acceleration in this time isJEE Main/MCQ/Medium/Addition and Subtraction of Vectors
  40. 40Two forces are such that the sum of their magnitudes is 18 N18 \mathrm{~N} and their resultant is 12 N12 \mathrm{~N} which is perpendicular to the smaller force. Then the magnitudes of the forces areJEE Main/MCQ/Medium/Addition and Subtraction of Vectors
  41. 41For three vectors A⃗=(−xi^−6j^−2k^),B⃗=(−i^+4j^+3k^)\vec{A}=(-x \hat{i}-6 \hat{j}-2 \hat{k}), \vec{B}=(-\hat{i}+4 \hat{j}+3 \hat{k}) and C⃗=(−8i^−j^+3k^)\vec{C}=(-8 \hat{i}-\hat{j}+3 \hat{k}), if A⃗⋅(B⃗×C⃗)=0\vec{A} \cdot(\vec{B} \times \vec{C})=0, then value of xx is _________JEE Main/Numerical/Medium/Multiplication of Vectors
  42. 42A particle moves in x−yx-y plane under the influence of a force F⃗\vec{F} such that its linear momentum is p→(t)=i^cos⁡(kt)−j^sin⁡(kt)\overrightarrow{\mathrm{p}}(\mathrm{t})=\hat{i} \cos (\mathrm{kt})-\hat{j} \sin (\mathrm{kt}). If k\mathrm{k} is constant, the angle between F→\overrightarrow{\mathrm{F}} and p→\overrightarrow{\mathrm{p}} will be :JEE Main/MCQ/Medium/Multiplication of Vectors
  43. 43If P⃗=3i^+3j^+2k^\vec{P}=3\hat{i}+\sqrt{3}\hat{j}+2\hat{k} and Q⃗=4i^+3j^+2.5k^\vec{Q}=4\hat{i}+\sqrt{3}\hat{j}+2.5\hat{k} then, the unit vector in the direction of P⃗×Q⃗\vec{P}\times \vec{Q} is 1x(3i^+j^−23k^)\dfrac{1}{x}(\sqrt{3}\hat{i}+\hat{j}-2\sqrt{3}\hat{k}). The value of xx isJEE Main/Numerical/Medium/Multiplication of Vectors
  44. 44If two vectors P⃗=i^+2mj^+mk^\vec{P}=\hat{i}+2m\hat{j}+m\hat{k} and Q⃗=4i^−2j^+mk^\vec{Q}=4\hat{i}-2\hat{j}+m\hat{k} are perpendicular to each other. Then, the value of mm will beJEE Main/MCQ/Medium/Multiplication of Vectors
  45. 45Vectors ai^+bj^+k^a\hat{i}+b\hat{j}+\hat{k} and 2i^−3j^+4k^2\hat{i}-3\hat{j}+4\hat{k} are perpendicular to each other when 3a+2b=73a+2b=7, the ratio of aa to bb is x2\dfrac{x}{2}. The value of xx is _____.JEE Main/Numerical/Medium/Multiplication of Vectors
  46. 46If the projection of 2i^+4j^−2k^2\hat{i}+4\hat{j}-2\hat{k} on i^+2j^+αk^\hat{i}+2\hat{j}+\alpha \hat{k} is zero. Then, the value of α\alpha will beJEE Main/Numerical/Medium/Multiplication of Vectors
  47. 47If A⃗=(2i^+3j^−k^)m\vec{A}=\left(2\hat{i}+3\hat{j}-\hat{k}\right)m and B⃗=(i^+2j^+2k^)m\vec{B}=\left(\hat{i}+2\hat{j}+2\hat{k}\right)m. The magnitude of component of vector A⃗\vec{A} along vector B⃗\vec{B} will be _____ mm.JEE Main/Numerical/Medium/Multiplication of Vectors
  48. 48A⃗\vec{A} is a vector quantity such that ∣A⃗∣=\left|\vec{A}\right|= non-zero constant. Which of the following expression is true for A⃗\vec{A}?JEE Main/MCQ/Medium/Multiplication of Vectors
  49. 49What will be the projection of vector A⃗=i^+j^+k^\vec{A}=\hat{i}+\hat{j}+\hat{k} on vector B⃗=i^+j^?\vec{B}=\hat{i}+\hat{j}?JEE Main/MCQ/Medium/Multiplication of Vectors
  50. 50Let ∣A1⃗∣=3,∣A2⃗∣=5\left|\vec{{A}_{1}}\right|=3,\left|\vec{{A}_{2}}\right|=5 and ∣A1⃗+A2⃗∣=5.\left|\vec{{A}_{1}}+\vec{{A}_{2}}\right|=5. The value of (2A1⃗+3A2⃗)∙(3A1⃗−2A2⃗)\left(2\vec{{A}_{1}}+3\vec{{A}_{2}}\right)∙\left(3\vec{{A}_{1}}-2\vec{{A}_{2}}\right) is:JEE Main/MCQ/Medium/Multiplication of Vectors
  51. 51Two vectors A⃗\vec{A} and B⃗\vec{B} have equal magnitudes. The magnitude of (A⃗+B⃗)\left(\vec{A}+\vec{B}\right) is ' nn ' times the magnitude of (A⃗−B⃗)\left(\vec{A}-\vec{B}\right) . The angle between A⃗\vec{A} and B⃗\vec{B} is:JEE Main/MCQ/Medium/Multiplication of Vectors
  52. 52Let A⃗=(i^+j^)andB⃗=(2i^−j^)\vec{A}=\left(\hat{i}+\hat{j}\right)and\vec{B}=(2\hat{i}-\hat{j}) . The magnitude of a coplanar vector C⃗\vec{C} such that A⃗.C⃗=B⃗.C⃗=A⃗.B⃗\vec{A}.\vec{C}=\vec{B}.\vec{C}=\vec{A}.\vec{B} is given by:JEE Main/MCQ/Medium/Multiplication of Vectors
  53. 53If A⃗×B⃗=B⃗×A⃗\vec{A} \times \vec{B}=\vec{B} \times \vec{A}, then the angle between AA and BB isJEE Main/MCQ/Medium/Multiplication of Vectors
  54. 54The density ρ\rho of a uniform cylinder is determined by measuring its mass mm, length ll and diameter dd. The measured values of mm, ll and dd are 97.42±0.0297.42 \pm 0.02 g, 8.35±0.058.35 \pm 0.05 mm and 20.20±0.0220.20 \pm 0.02 mm, respectively. Calculated percentage fractional error in ρ\rho is _______.JEE Main/MCQ/Medium/Errors of Measurement
  55. 55Four persons measure the length of a rod as 20.00 cm,19.75 cm,17.01 cm20.00 \mathrm{~cm}, 19.75 \mathrm{~cm}, 17.01 \mathrm{~cm} and 18.25 cm. The relative error in the measurement of average length of the rod is :JEE Main/MCQ/Medium/Errors of Measurement
  56. 56In an experiment the values of two spring constants were measured as k1=(10±0.2)N/mk_{1}=(10 \pm 0.2) \mathrm{N} / \mathrm{m} and k2=(20±0.3)N/mk_{2}=(20 \pm 0.3) \mathrm{N} / \mathrm{m}. If these springs are connected in parallel, then the percentage error in equivalent spring constant is :JEE Main/MCQ/Medium/Errors of Measurement
  57. 57A quantity Q is formulated as X−2Y+32Z−25⋅X,Y\mathrm{X}^{-2} \mathrm{Y}^{+\frac{3}{2}} \mathrm{Z}^{-\frac{2}{5}} \cdot \mathrm{X}, \mathrm{Y} and Z are independent parameters which have fractional errors of 0.1,0.20.1,0.2 and 0.5 , respectively in measurement. The maximum fractional error of Q isJEE Main/MCQ/Medium/Errors of Measurement
  58. 58A physical quantity C is related to four other quantities p,q,r\mathrm{p}, \mathrm{q}, \mathrm{r} and s as follows C=pq2r3 s\mathrm{C}=\frac{\mathrm{pq}^2}{\mathrm{r}^3 \sqrt{\mathrm{~s}}}
    The percentage errors in the measurement of     p,q,r\mathrm{p}, \mathrm{q}, \mathrm{r} and s are 1%,2%3%1 \%, 2 \% 3 \% and 2%2 \% respectively.
    The percentage error in the measurement of C will be _____    %\%.    JEE Main/Numerical/Medium/Errors of Measurement
  59. 59A physical quantity QQ is related to four observables a,b,c,da, b, c, d as follows :
    Q=ab4 cd\mathrm{Q}=\frac{\mathrm{ab}{ }^4}{\mathrm{~cd}}

    where,     a=(60±3)Pa;b=(20±0.1)m;c=(40±0.2)Nsm−2\mathrm{a}=(60 \pm 3) \mathrm{Pa} ; \mathrm{b}=(20 \pm 0.1) \mathrm{m} ; \mathrm{c}=(40 \pm 0.2) \mathrm{Nsm}^{-2} and d=(50±0.1)m\mathrm{d}=(50 \pm 0.1) \mathrm{m}, then the percentage error in Q is x1000\frac{x}{1000}, where x=x= ________ .    JEE Main/Numerical/Medium/Errors of Measurement
  60. 60The energy of a system is given as E(t)=α3e−βt\mathrm{E}(\mathrm{t})=\alpha^3 \mathrm{e}^{-\beta t}, where t is the time and β=0.3 s−1\beta=0.3 \mathrm{~s}^{-1}. The errors in the measurement of α\alpha and tt are 1.2%1.2 \% and 1.6%1.6 \%, respectively. At t=5 st=5 \mathrm{~s}, maximum percentage error in the energy is :JEE Main/MCQ/Medium/Errors of Measurement
  61. 61The maximum percentage error in the measurment of density of a wire is [Given, mass of wire =(0.60±0.003)g=(0.60 \pm 0.003) \mathrm{g}
    radius of wire     =(0.50±0.01)cm=(0.50 \pm 0.01) \mathrm{cm}
    length of wire     =(10.00±0.05)cm]=(10.00 \pm 0.05) \mathrm{cm}]    JEE Main/MCQ/Medium/Errors of Measurement
  62. 62Young's modulus is determined by the equation given by Y=49000mldyncm2\mathrm{Y}=49000 \frac{\mathrm{m}}{\mathrm{l}} \frac{\mathrm{dyn}}{\mathrm{cm}^2} where MM is the mass and ll is the extension of wire used in the experiment. Now error in Young modules (Y)(Y) is estimated by taking data from M−lM-l plot in graph paper. The smallest scale divisions are 5 g5 \mathrm{~g} and 0.02 cm0.02 \mathrm{~cm} along load axis and extension axis respectively. If the value of MM and ll are 500 g500 \mathrm{~g} and 2 cm2 \mathrm{~cm} respectively then percentage error of YY is :JEE Main/MCQ/Medium/Errors of Measurement
  63. 63In an expression a×10ba \times 10^{\mathrm{b}};JEE Main/MCQ/Medium/Errors of Measurement
  64. 64To find the spring constant (k)(k) of a spring experimentally, a student commits 2%2 \% positive error in the measurement of time and 1%1 \% negative error in measurement of mass. The percentage error in determining value of kk is :JEE Main/MCQ/Medium/Errors of Measurement
  65. 65Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as 4.62 s,4.632 s,4.6 s4.62 \mathrm{~s}, 4.632 \mathrm{~s}, 4.6 \mathrm{~s} and 4.64 s4.64 \mathrm{~s}. The arithmetic mean of these readings in correct significant figure is :JEE Main/MCQ/Medium/Errors of Measurement
  66. 66In an experiment to measure focal length (f)(f) of convex lens, the least counts of the measuring scales for the position of object (u)(\mathrm{u}) and for the position of image (v)(\mathrm{v}) are Δu\Delta \mathrm{u} and Δv\Delta \mathrm{v}, respectively. The error in the measurement of the focal length of the convex lens will be:JEE Main/MCQ/Medium/Errors of Measurement
  67. 67Match List - I with List - II. List - I (Number) List - II (Signficant figure) (A) 10011001 (I) 33 (B) 010.1010.1 (II) 44 (C) 100.100100.100 (III) 55 (D) 0.00100100.0010010 (IV) 66 Choose the correct answer from the options given below:JEE Main/MCQ/Medium/Errors of Measurement
  68. 68The radius (r)\left(r\right), length (l)\left(l\right) and resistance (R)\left(R\right) of a metal wire was measured in the laboratory as
    r=(0.35±0.05)cmr=\left(0.35\pm 0.05\right)cm, R=(100±10)ohmR=\left(100\pm 10\right)ohm, l=(15±0.2)cml=\left(15\pm 0.2\right)cm
    The percentage error in resistivity of the material of the wire is :    JEE Main/MCQ/Medium/Errors of Measurement
  69. 69If the percentage errors in measuring the length and the diameter of a wire are 0.10.1% each. The percentage error in measuring its resistance will be:JEE Main/MCQ/Medium/Errors of Measurement
  70. 70A physical quantity QQ is found to depend on quantities a,b,ca,b,c by the relation Q=a4b3c2Q=\dfrac{{a}^{4}{b}^{3}}{{c}^{2}}. The percentage error in a,ba,b and cc are 33%,4% and 55% respectively. Then, the percentage error in QQ is:JEE Main/MCQ/Medium/Errors of Measurement
  71. 71The resistance R=VIR=\dfrac{V}{I}, where V=(200±5)VV=(200\pm 5)V and I=(20±0.2)AI=(20\pm 0.2)A, the percentage error in the measurement of RR is :JEE Main/MCQ/Medium/Errors of Measurement
  72. 72A physical quantity PP is given as P=a2b3cdP=\dfrac{{a}^{2}{b}^{3}}{c\sqrt{d}}. The percentage error in the measurement of a,b,ca,b,c and dd are 11%,2%,3% and 44% respectively. The percentage error in the measurement of quantity PP will beJEE Main/MCQ/Medium/Errors of Measurement
  73. 73A cylindrical wire of mass(0.4±0.01)g(0.4\pm 0.01)g has length (8±0.04)cm(8\pm 0.04)cm and radius (6±0.03)mm(6\pm 0.03)mm. The maximum error in its density will beJEE Main/MCQ/Medium/Errors of Measurement
  74. 74The length of a metallic wire is increased by 2020% and its area of cross-section is reduced by 44%. The percentage change in resistance of the metallic wire is ________.JEE Main/Numerical/Medium/Errors of Measurement
  75. 75Two resistance are given as R1=(10±0.5)Ω{R}_{1}=(10\pm 0.5)\Omega and R2=(15±0.5)Ω.{R}_{2}=(15\pm 0.5)\Omega . The percentage error in the measurement of equivalent resistance when they are connected in parallel isJEE Main/MCQ/Medium/Errors of Measurement
  76. 76In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as 5.25mm5.25mm and apparent thickness of the glass slab at 5.00mm5.00mm. Travelling microscope has 2020 divisions in one cmcm on main scale and 5050 divisions on Vernier scale is equal to 4949 divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is x10×10−3\dfrac{x}{10}\times {10}^{-3}, where xx is ______JEE Main/Numerical/Medium/Errors of Measurement
  77. 77In an experiment to find acceleration due to gravity (g)\left(g\right) using simple pendulum, time period of 0.5s0.5s is measured from time of 100100 oscillation with a watch of 1s1s resolution. If measured value of length is 10cm10cm known to 1mm1mm accuracy. The accuracy in the determination of gg is found to be xx%. The value of xx isJEE Main/Numerical/Medium/Errors of Measurement
  78. 78A torque meter is calibrated to reference standards of mass, length and time each with 55% accuracy. After calibration, the measured torque with this torque meter will have net accuracy ofJEE Main/MCQ/Medium/Errors of Measurement
  79. 79In an experiment of determine the Young's modulus of wire of a length exactly 1m1m, the extension in the length of the wire is measured as 0.4mm0.4mm with an uncertainty of ±0.02mm\pm 0.02mm when a load of 1kg1kg is applied. The diameter of the wire is measured as 0.4mm0.4mm with an uncertainty of ±0.01mm\pm 0.01mm. The error in the measurement of Young's modulus (ΔY)\left(\Delta Y\right) is found to be x×1010Nm−2x\times {10}^{10}N{m}^{-2}. The value of xx is _____ .JEE Main/Numerical/Medium/Errors of Measurement
  80. 80The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are 11%,2% and 33% respectively. The maximum percentage error in the detection of the dissipated heat will be:JEE Main/MCQ/Medium/Errors of Measurement
  81. 81The distance of the Sun from earth is 1.5×1011m1.5\times {10}^{11}m and its angular diameter is 2000′′2000'' when observed from the earth. The diameter of the Sun will beJEE Main/MCQ/Medium/Errors of Measurement
  82. 82A silver wire has a mass (0.6±0.006)g\left(0.6\pm 0.006\right)g, radius (0.5±0.005)mm\left(0.5\pm 0.005\right)mm and length (4±0.04)cm\left(4\pm 0.04\right)cm. The maximum percentage error in the measurement of its density will beJEE Main/MCQ/Medium/Errors of Measurement
  83. 83For z=a2x3y12z={a}^{2}{x}^{3}{y}^{\dfrac{1}{2}}, where 'aa' is a constant. If percentage error in measurement of 'xx' and 'yy' are 44%and 1212%, respectively, then the percentage error for 'zz' will be _____%.JEE Main/Numerical/Medium/Errors of Measurement
  84. 84If Z=A2B3C4Z=\dfrac{{A}^{2}{B}^{3}}{{C}^{4}}, then the relative error in ZZ will beJEE Main/MCQ/Medium/Errors of Measurement
  85. 85A student determined Young's Modulus of elasticity using the formula Y=MgL34bd3δ.Y=\dfrac{Mg{L}^{3}}{4{bd}^{3}\delta }. The value of gg is taken to be 9.8ms−29.8m{s}^{-2} without any significant error, his observations are as following. Physical Quantity Least count of the Equipment used for measurement Observed Value Mass (M)(M) 1g1g 2kg2kg Length of bar (L)(L) 1mm1mm 1m1m Breadth of bar (b)(b) 0.1mm0.1mm 4cm4cm Thickness of bar (d)(d) 0.01mm0.01mm 0.4cm0.4cm Depression (δ)(\delta ) 0.01mm0.01mm 5mm5mm Then the fractional error in the measurement of YY is :JEE Main/MCQ/Medium/Errors of Measurement
  86. 86The acceleration due to gravity is found up to an accuracy of 44% on a planet. The energy supplied to a simple pendulum of known mass mm to undertake oscillations of time period TT is being estimated. If time period is measured to an accuracy of 33%, the accuracy to which EE is known as ________%JEE Main/Numerical/Medium/Errors of Measurement
  87. 87If the length of the pendulum in pendulum clock increases by 0.10.1%, then the error in time per day is:JEE Main/MCQ/Medium/Errors of Measurement
  88. 88A physical quantity yy is represented by the formula y=m2r−4gxl−32y={m}^{2}{r}^{-4}{g}^{x}{l}^{-\dfrac{3}{2}} If the percentage errors found in y,m,r,ly,m,r,l and gg are 18,1,0.5,418,1,0.5,4 and pp respectively, then find the value of xx and pp.JEE Main/MCQ/Medium/Errors of Measurement
  89. 89Three students S1,S2{S}_{1},{S}_{2} and S3{S}_{3} perform an experiment for determining the acceleration due to gravity (g)(g) using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table. Student No. Length of pendulum
    (cm)(cm) Number of oscillations
    (n)(n) Total time for
    nn oscillations Time
    period
    (s)(s) 1.1. 64.064.0 88 128.0128.0 16.016.0 2.2. 64.064.0 44 64.064.0 16.016.0 3.3. 20.020.0 44 36.036.0 9.09.0 (Least count of length =0.1m=0.1m, least count for time =0.1s=0.1s)
    If     E1,E2{E}_{1},{E}_{2} and E3{E}_{3} are the percentage errors in gg for students 1,21,2 and 33, respectively, then the minimum percentage error is obtained by student no ..    JEE Main/Numerical/Medium/Errors of Measurement
  90. 90The radius of a sphere is measured to be (7.50±0.85)cm(7.50\pm 0.85)cm. Suppose the percentage error in its volume is xx. The value of xx, to the nearest xx, is ___ .JEE Main/Numerical/Medium/Errors of Measurement
  91. 91The time period of a simple pendulum is given by T=2πlg.T=2\pi \sqrt{\dfrac{l}{g}}. The measured value of the length of the pendulum is 10cm10cm known to a 1mm1mm accuracy. The time for 200200 oscillations of the pendulum is found to be 100100 second using a clock of 1s1s resolution. The percentage accuracy in the determination of gg using this pendulum is x.x. The value of xx to the nearest integer is:-JEE Main/MCQ/Medium/Errors of Measurement
  92. 92In order to determine the Young's Modulus of a wire of radius 0.2cm0.2cm (measured using a scale of least count =0.001cm=0.001cm) and length 1m1m (measured using a scale of least count =1mm=1mm), a weight of mass 1kg1kg (measured using a scale of least count =1g=1g ) was hanged to get the elongation of 0.5cm0.5cm (measured using a scale of least count 0.001cm0.001cm). What will be the fractional error in the value of Young's Modulus determined by this experiment?JEE Main/MCQ/Medium/Errors of Measurement
  93. 93The resistance R=VIR=\dfrac{V}{I}, where V=(50±2)VV=\left(50\pm 2\right)V and I=(20±0.2)AI=\left(20\pm 0.2\right)A. The percentage error in RR is xx %. The value of xx to the nearest integer is ________.JEE Main/Numerical/Medium/Errors of Measurement
  94. 94A wire of 1Ω1\Omega has a length of 1m1m. It is stretched till its length increases by 2525%. The percentage change in resistance to the nearest integer is :JEE Main/MCQ/Medium/Errors of Measurement
  95. 95The period of oscillation of a simple pendulum is T=2πLg.T=2\pi \sqrt{\dfrac{L}{g}}. Measured value of LL is 1.0m1.0m from meter scale having a minimum division of 1mm1mm and time of one complete oscillation is 1.95s1.95s measured from stopwatch of 0.01s0.01s resolution. The percentage error in the determination of ′g′'g' will be:JEE Main/MCQ/Medium/Errors of Measurement
  96. 96The density of a solid metal sphere is diameter. The maximum error in the density of the sphere is (x100)\left(\dfrac{x}{100}\right)%. If the relative errors in measuring the mass and the diameter are 6.06.0% and 1.51.5% respectively, the value of xx is −-JEE Main/Numerical/Medium/Errors of Measurement
  97. 97A physical quantity z depends on four observables a,b,ca,b,c and dd, as z=a2b2/3cd3.z=\dfrac{{a}^{2}{b}^{2/3}}{\sqrt{c}{d}^{3}}. The percentage of error in the measurement of a,b,ca,b,c and dd are 22%,1.5%,4% and 2.52.5% respectively. The percentage of error in zz is :JEE Main/MCQ/Medium/Errors of Measurement
  98. 98For the four sets of three measured physical quantities as given below. Which of the following options is correct?
    (i)\left(i\right) A1=24.36,B1=0.0724,C1=256.2{A}_{1}=24.36,{B}_{1}=0.0724,{C}_{1}=256.2
    (ii)\left(ii\right) A2=24.44,B2=16.082,C2=240.2{A}_{2}=24.44,{B}_{2}=16.082,{C}_{2}=240.2
    (iii)\left(iii\right) A3=25.2,B3=19.2812,C3=236.183{A}_{3}=25.2,{B}_{3}=19.2812,{C}_{3}=236.183
    (iv)\left(iv\right) A4=25,B4=236.191,C4=19.5{A}_{4}=25,{B}_{4}=236.191,{C}_{4}=19.5    JEE Main/MCQ/Medium/Errors of Measurement
  99. 99A simple pendulum is being used to determine the value of gravitational acceleration gg at a certain place. The length of the pendulum is 25.0cm25.0cm and a stopwatch with 1s1s resolution measures the time taken for 4040 oscillations to be 50s50s. The accuracy in gg is:JEE Main/MCQ/Medium/Errors of Measurement
  100. 100The area of a square is 5.29cm2.5.29c{m}^{2}. The area of 77 such squares taking into account the significant figures is:JEE Main/MCQ/Medium/Errors of Measurement
  101. 101In the density measurement of a cube, the mass and edge length are measured as (10.00±0.10)kg\left(10.00\pm 0.10\right)kg and (0.10±0.01)m,\left(0.10\pm 0.01\right)m, respectively. The error in the measurement of density is:JEE Main/MCQ/Medium/Errors of Measurement
  102. 102In a simple pendulum experiment for determination of acceleration due to gravity (g)(g), time taken for 2020 oscillations is measures by using a watch of 11 second least count. The mean value of time taken comes out to be 30s30s. The length of the pendulum is measured by using a meter scale of least count 1mm1mm and the value obtained is 55.0cm55.0cm. The percentage error in the determination of gg is close toJEE Main/MCQ/Medium/Errors of Measurement
  103. 103The diameter and height of a cylinder are measured by a meter scale to be 12.6±0.1cm12.6\pm 0.1 cm and 34.2±0.1cm34.2\pm 0.1 cm , respectively. What will be the value of its volume in appropriate significant figures?JEE Main/MCQ/Medium/Errors of Measurement
  104. 104A copper wire is stretched to make it 0.50.5% longer. The percentage change in its electrical resistance if its volume remains unchanged is:JEE Main/MCQ/Medium/Errors of Measurement
  105. 105The percentage errors in quantities PP, QQ, RR and SS are 0.50.5%, 11%, 33% and 1.51.5% respectively in the measurement of a physical quantity A=P3Q2RSA=\dfrac{{P}^{3}{Q}^{2}}{\sqrt{R} S}. The maximum percentage error in the value of AA will be:JEE Main/MCQ/Medium/Errors of Measurement
  106. 106The relative error in the determination of the surface area of a sphere is α\alpha. The relative error in the determination of its volume isJEE Main/MCQ/Medium/Errors of Measurement
  107. 107The relative error in the determination of the surface area of a sphere is α\alpha. Then the relative error in the determination of its volume isJEE Main/MCQ/Medium/Errors of Measurement
  108. 108The density of a material, in the shape of a cube, is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are 1.51.5% and 11%, respectively, the maximum error in determining the density is:JEE Main/MCQ/Medium/Errors of Measurement
  109. 109A physical quantity PP is described by the relation P=a12b2c3d−4P={a}^{\dfrac{1}{2}}{b}^{2}{c}^{3}{d}^{-4}. If the relative errors in the measurement of aa, bb, cc and dd respectively, are 22%, 11%, 33% and 55%. Then the relative error in PP will be:JEE Main/MCQ/Medium/Errors of Measurement
  110. 110The following observations were taken for determining surface tension TT of water by capillary method:

    diameter of capillary,     D=1.25×10−2mD=1.25\times {10}^{-2}m

    rise of water,     h=1.45×10−2mh=1.45\times {10}^{-2}m

    Using     g=9.80ms−2g=9.80m{s}^{-2} and the simplified relation T=rhg2×103Nm−1T=\dfrac{rhg}{2}\times {10}^{3}N{m}^{-1} the possible error in surface tension is closest to:    JEE Main/MCQ/Medium/Errors of Measurement
  111. 111A thin 1m1m long rod has a radius of 5mm5mm. A force of 50π×103N50{\text{π×10}}^{3}N is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is 0.01mm0.01mm, which of the following statements is false?JEE Main/MCQ/Medium/Errors of Measurement
  112. 112A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be:JEE Main/MCQ/Medium/Errors of Measurement
  113. 113The period of oscillation of a simple pendulum is T=2πlg.T=2\pi \sqrt{\dfrac{l}{g}}. Measured value of ll is 20.0cm20.0cm, known to 1mm1mm accuracy and time for 100100oscillations of the pendulum is found to be 90s90s using a wristwatch of 1s1s resolution. The accuracy in the determination of gg isJEE Main/MCQ/Medium/Errors of Measurement
  114. 114An experiment is performed to obtain the value of acceleration due to gravity g by using a simple pendulum of length L. In this experiment time for 100 oscillations is measured by using a watch of 1 second least count and the value is 90.0 seconds. The length L is measured by using a meter scale of least count 1 mm and the value is 20.0 cm. The error in the determination of g would be :JEE Main/MCQ/Medium/Errors of Measurement
  115. 115The current voltage relation of diode is given by I = (e1000 V/T - 1) mA, where the applied voltage V is in volts and the temperature T is in degree Kelvin. If a student makes an error measuring ±0.01 V\pm \text{0.01 V} while measuring the current of 5 mA at 300 K, what will be the error in the value of current in mA ?JEE Main/MCQ/Medium/Errors of Measurement
  116. 116The amount of heat produced in an electric circuit depends upon the current (I)(I), resistance (R)(R) and time (t)(t). If the error made in the measurements of the above quantities are 2%,1%2 \%, 1 \% and 1%1 \% respectively then the maximum possible error in the total heat produced will beJEE Main/MCQ/Medium/Errors of Measurement
  117. 117Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3%3 \% each, then error in the value of resistance of the wire isJEE Main/MCQ/Medium/Errors of Measurement
  118. 118If a wire is stretched to make it 0.1%0.1 \% longer, its resistance will :JEE Main/MCQ/Medium/Errors of Measurement
  119. 119The respective number of significant figures for the numbers 23.023,0.000323.023,0.0003 and 2.1×10−32.1 \times 10^{-3} areJEE Main/MCQ/Medium/Errors of Measurement
  120. 120The length of a simple pendulum executing simple harmonic motion is increased by 21%21 \%. The percentage increase in the time period of the pendulum of increased length isJEE Main/MCQ/Medium/Errors of Measurement
  121. 121For an experimental expression y=32.3×112527.4y=\frac{32.3 \times 1125}{27.4}, where all the digits are significant. Then to report the value of yy we should writeJEE Main/MCQ/Medium/Significant numbers

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