Vectors & Basic Mathematics PYQs Set 1 (PDF)

Set 1 of 6 · Questions 1-30 of 153

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Mere Teacher · Previous Year Questions JEE Main Physics · Vectors & Basic Mathematics · Set 1 (Q1-30)
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1. $A force is represented by F = a x^{2} + b t^{1/2} Where x = distance and t = time. The dimensions of b^{2} / a are :$ (1) $M L^{3} T^{- 3}$ (2) $M L T^{- 2}$ (3) $M L^{- 1} T^{- 1}$ (4) $M L^{2} T^{- 3}$ 2. $A = 3 i^+ 4 j^Find a vector perpendicular to A in the plane of A$ (1) $k^$ (2) $- 3 i^- 4 j^$ (3) $4 j^- 3 i^$ (4) $4 i^- 3 j^$ 3. $Given below are two statements : Statement (I) : Planck's constant and angular momentum have same dimensions. Statement (II) : Linear momentum and moment of force have same dimensions. In the light of the above statements, choose the correct answer from the options given below :$ (1) $Statement I is true but Statement II is false$ (2) $Both Statement I and Statement II are false$ (3) $Both Statement I and Statement II are true$ (4) $Statement I is false but Statement II is true$ 4. $If A = 3 i + j + 2 k and B = 2 i - 2 j + 4 k then value of \| A \times B \| will be-$ (1) $82$ (2) $83$ (3) $85$ (4) $58$ 5. $The position of a particle is given by r = (i + 2 j - k) and momentum p = (3 i + 4 j - 2 k) . The angular momentum is perpendicular to the$ (1) $x -axis$ (2) $y -axis$ (3) $z -axis$ (4) $yz-plane$ 6. $Consider two physical quantities A and B related to each other as E = \frac{B - x ^{2}}{At} where E, x and t have dimensions of energy, length and time respectively. The dimension of AB is$ (1) $L^{- 2} M^{1} T^{0}$ (2) $L^{2} M^{- 1} T^{1}$ (3) $L^{- 2} M^{- 1} T^{1}$ (4) $L^{0} M^{- 1} T^{1}$ 7. $What is the angle between (P + Q) and (P \times Q)$ (1) $0$ (2) $\frac{π}{2}$ (3) $\frac{π}{4}$ (4) $π$ 8. $Two vectors A and B have equal magnitudes. The magnitude of (A + B) is ‘n’ times the magnitude of (A - B) The angle between A and B is$ (1) $cos^{- 1} (\frac{n ^{2} - 1}{n ^{2} + 1})$ (2) $cos^{- 1} (\frac{n - 1}{n + 1})$ (3) $sin^{- 1} (\frac{n ^{2} - 1}{n ^{2} + 1})$ (4) $sin^{- 1} (\frac{n - 1}{n + 1})$ 9. $The torque of the force F = (2 i - 3 j + 4 k) N acting at the point r = (3 i + 2 j + 3 k) m about the origin be$ (1) $6 i - 6 j + 12 k$ (2) $17 i - 6 j - 13 k$ (3) $- 6 i + 6 j - 12 k$ (4) $- 17 i + 6 j + 13 k$ 10. $Match List I with List II LIST I A. Torque B. Magnetic field C. Magnetic moment D. Permeability of free space LIST II I. (M^{1} L^{1} T^{- 2} A^{- 2}) II. (L^{2} A^{1}) III. (M^{1} T^{- 2} A^{- 1}) IV. (M^{1} L^{2} T^{- 2}) Choose the correct answer from the options given below:$ (1) $A-III, B-I, C-II, D-IV$ (2) $A-IV, B-II, C-III, D-I$ (3) $A-IV, B-III, C-II, D-I$ (4) $A-I, B-III, C-II, D-IV$ 11. $If a_{1} and a_{2} are two non collinear unit vectors and if (a_{1} + a_{2}) = 3, then the value of (a_{1} - a_{2}) . (2 a_{1} + a_{2}) is -$ (1) $2$ (2) $\frac{3}{2}$ (3) $\frac{1}{2}$ (4) $1$ 12. $Force acting on a particle is (2 i + 3 j) N . Work done by this force is zero, when a particle is moved on the line 3 y + kx = 5 . Here value of k is -$ (1) $2$ (2) $4$ (3) $6$ (4) $8$ 13. $If G be the gravitational constant and u be the energy density then which of the following quantity have the dimensions as that of the uG :$ (1) $pressure gradient per unit mass$ (2) $Gravitational potential$ (3) $Energy per unit mass$ (4) $Force per unit mass$ 14. $The number of density of molecules of a gas depends on their distance r from the origin as, n (r) = n_{0} e^{- αr 4} . Then the total number of molecules is proportional to:$ (1) $n_{0} α^{- 3/4}$ (2) $n_{0} α^{\frac{1}{2}}$ (3) $n_{0} α^{\frac{1}{4}}$ (4) $n_{0} α^{- 3}$ 15. $The value of (A + B) \times (A - B) is$ (1) $0$ (2) $A^{2} - B^{2}$ (3) $B \times A$ (4) $2 (B \times A)$ 16. $Two vectors A and B have equal magnitudes. If magnitude of A + B is equal to two times the magnitude of A - B, then the angle between A and B will be :$ (1) $sin^{- 1} (\frac{3}{5})$ (2) $sin^{- 1} (\frac{1}{3})$ (3) $cos^{- 1} (\frac{3}{5})$ (4) $cos^{- 1} (\frac{1}{3})$ 17. $A force F = 3 i + c j + 2 k acting on a particle causes a displacement S = - 4 i + 2 j - 3 k in its own direction. If the work done is 6J, then the value of c will be$ (1) $12$ (2) $6$ (3) $1$ (4) $0$ 18. $If two vectors A and B having equal magnitude R are inclined at angle θ, then$ (1) $\| A + B \| = 2 Rcos (\frac{θ}{2})$ (2) $\| A - B \| = 2 Rcos (\frac{θ}{2})$ (3) $\| A - B \| = 2 Rsin (\frac{θ}{2})$ (4) $\| A + B \| = 2 Rsin (\frac{θ}{2})$ 19. $The angle between the vectors (i + j) and (j + k) is$ (1) $30°$ (2) $45°$ (3) $60°$ (4) $90°$ 20. $A physical quantity Q is found to depend on quantities a, b, c by the relation Q = \frac{a ^{4} b ^{3}}{c ^{2}} . The percentage error in a, b and c are 3 %, 4 % and 5 % respectively. Then, the percentage error in Q is :$ (1) $66 %$ (2) $43 %$ (3) $34 %$ (4) $14 %$ 21. $The angle between vector Q and the resultant of (2 Q + 2 P) and (2 Q - 2 P) is :$ (1) $tan^{- 1} (2Q-2P)2Q+2P$ (2) $0^{\circ}$ (3) $tan^{- 1} (P / Q)$ (4) $tan^{- 1} (2 Q / P)$ 22. $Dot product of two mutual perpendicular vector is$ (1) $0$ (2) $1$ (4) $None of these$ 23. $A force vector applied on a mass is represented as F = 6 i - 8 j + 10 k and accelerates with 1 m / s^{2} . What will be the mass of the body in kg.$ (1) $102$ (2) $20$ (3) $210$ (4) $10$ 24. $The equation of stationary wave is : y = 2 a sin (\frac{2 πnt}{λ}) cos (\frac{2 πx}{λ}) . Which of the following is NOT correct :$ (1) $The dimensions of n / λ is [T]$ (2) $The dimensions of n is (LT^{- 1})$ (3) $The dimensions of x is [L]$ (4) $The dimensions of nt is [L]$ 25. $A particle moves from position 3 i + 2 j - 6 k to 14 i + 13 j + 9 k due to a uniform force of (4 i + j + 3 k) N . If the displacement in meters then work done will be$ (1) $100 J$ (2) $200 J$ (3) $300 J$ (4) $250 J$ 26. $In an experiment to measure focal length (f) of convex lens, the least counts of the measuring scales for the position of object (u) and for the position of image (v) are Δ u and Δ v, respectively. The error in the measurement of the focal length of the convex lens will be:$ (1) $2 f (\frac{Δ u}{u} + \frac{Δ v}{v})$ (2) $\frac{Δ u}{u} + \frac{Δ v}{v}$ (3) $f^{2} (\frac{Δ u}{u ^{2}} + \frac{Δ v}{v ^{2}})$ (4) $f (\frac{Δ u}{u} + \frac{Δ v}{v})$ 27. $If the percentage errors in measuring the length and the diameter of a wire are 0.1 % each. The percentage error in measuring its resistance will be:$ (1) $0.2 %$ (2) $0.3 %$ (3) $0.1 %$ (4) $0.144 %$ 28. $Match List - I with List - II. List - I (Number) (A) 1001 (B) 010.1 (C) 100.100 (D) 0.0010010 List - II (Significant figure) (I) 3 (II) 4 (III) 5 (IV) 6 Choose the correct answer from the options given below:$ (1) $(A)-(III), (B)-(IV), (C)-(II), (D)-(I)$ (2) $(A)-(IV), (B)-(III), (C)-(I), (D)-(II)$ (3) $(A)-(II), (B)-(I), (C)-(IV), (D)-(III)$ (4) $(A)-(I), (B)-(II), (C)-(III), (D)-(IV)$ 29. $The angle between two vectors - 2 i + 3 j + k and i + 2 j - 4 k is$ (1) $0°$ (2) $90°$ (3) $180°$ (4) $None of the above$ 30. $Two particles are located at equal distance from origin. The position vectors of those are represented by A = 2 i + 3 nj + 2 k and B = 2 i - 2 j + 4 p k, respectively. If both the vectors are at right angle to each other, the value of n^{- 1} is ________.$