Vectors & Basic Mathematics PYQs Set 2 (PDF)

Set 2 of 6 · Questions 31-60 of 153

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Mere Teacher · Previous Year Questions JEE Main Physics · Vectors & Basic Mathematics · Set 2 (Q31-60)
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31. $Match List-I with List-II. List-I A. Coefficient of viscosity B. Surface Tension C. Angular momentum D. Rotational kinetic energy List-II I. (ML^{2} T^{- 2}) II. (ML^{2} T^{- 1}) III. (ML^{- 1} T^{- 1}) IV. (ML^{0} T^{- 2})$ (1) $A-II, B-I, C-IV, D-III$ (2) $A-I, B-II, C-III, D-IV$ (3) $A-III, B-IV, C-II, D-I$ (4) $A-IV, B-III, C-II, D-I$ 32. $An aeroplane is moving in a circular path with a speed 250 km/hr. What is the change in velocity in half revolution ?$ (1) $500 km/hr$ (2) $250 km/hr$ (3) $125 km/hr$ (4) $Zero$ 33. $The value of (A + B) \times (A - B) is$ (1) $0$ (2) $A^{2} - B^{2}$ (3) $B \times A$ (4) $2 (B \times A)$ 34. $The diagonals of a parallelogram are 2 i and 2 j . What is the area of the parallelogram$ (1) $0.5 units$ (2) $1 unit$ (3) $2 units$ (4) $4 units$ 35. $The pitch of the screw guage is 1 mm and there are 100 divisions on the circular scale. When nothing is put inbetween the jaws, the zero of the circular scale lines 8 divisions below the reference line. When a wire isplaced between the jaws, the first linear scale division is clearly visible while 72^{nd} division on circular scale coincides with the reference line. The radius of the wire is:$ (1) $1.64 mm$ (2) $1.80 mm$ (3) $0.82 mm$ (4) $0.90 mm$ 36. $If A and B are perpendicular vectors and vector A = 5 i + 7 j - 3 k and B = 2 i + 2 j - ak . The value of a is$ (1) $- 2$ (2) $8$ (3) $- 7$ (4) $- 8$ 37. $Electrons in a TV tube move horizontally South to North. Vertical component of earth’s magnetic field points down. The electron is deflected towards$ (1) $West$ (2) $No deflection$ (3) $East$ (4) $North to South$ 38. $Given: a + b = c and a + 2 b = R . If R is perpendicular to a, find \frac{\| b \|}{\| c \|} .$ (1) $3$ (2) $2$ (3) $1$ (4) $0$ 39. $A particle moves with a velocity 6 i - 4 j + 3 k m / s under the influence of a constant force F = 20 i + 15 j - 5 k N . The instantaneous power applied to the particle is$ (1) $35 J/s$ (2) $45 J/s$ (3) $25 J/s$ (4) $195 J/s$ 40. $If for two vector A and B, sum (A + B) is perpendicular to the difference (A - B) . The ratio of their magnitude is$ (1) $1$ (2) $2$ (3) $3$ (4) $None of these$ 41. $If Z = \frac{A ^{2} B ^{3}}{C ^{4}}, then the relative error in Z will be :$ (1) $\frac{∆ A}{A} + \frac{∆ B}{B} + \frac{∆ C}{C}$ (2) $\frac{2∆ A}{A} + \frac{3∆ B}{B} - \frac{4∆ C}{C}$ (3) $\frac{2∆ A}{A} + \frac{3∆ B}{B} + \frac{4∆ C}{C}$ (4) $\frac{∆ A}{A} + \frac{∆ B}{B} - \frac{∆ C}{C}$ 42. $If two vectors P = i + 2 mj + mk and Q = 4 i - 2 j + mk are perpendicular to each other. Then, the value of m will be:$ (1) $1$ (2) $-l$ (3) $- 3$ (4) $2$ 43. $Angle between the two vectors 2 i + 5 j and i + j + k is cos^{- 1} (α) . The value of α is$ (1) $\frac{6}{86}$ (2) $\frac{7}{87}$ (3) $\frac{8}{88}$ (4) $\frac{9}{89}$ 44. $The angle between two vectors given by 6 i + 6 j - 3 k and 7 i + 4 j + 4 k is$ (1) $cos^{- 1} (\frac{1}{3})$ (2) $cos^{- 1} (\frac{5}{3})$ (3) $sin^{- 1} (\frac{2}{3})$ (4) $sin^{- 1} (\frac{5}{3})$ 45. $Let A = i Acos θ + j Asin θ, be any vector. Another vector B which is normal to A is :-$ (1) $Bcos θ i + Bsin θ j$ (2) $Bsin θ i + Bcos θ j$ (3) $Bsin θ i - Bcos θ j$ (4) $Acos θ i - Acos θ j$ 46. $If a vector 2 i + 3 j + 8 k is perpendicular to the vector 4 j - 4 i + α k . Then the value of α is$ (1) $-1$ (2) $\frac{1}{2}$ (3) $- \frac{1}{2}$ (4) $1$ 47. $What is the unit vector perpendicular to the following vectors 2 i + 2 j - k and 6 i - 3 j + 2 k$ (1) $\frac{i + 10 j - 18 k}{5 17}$ (2) $\frac{i - 10 j + 18 k}{5 17}$ (3) $\frac{i - 10 j - 18 k}{5 17}$ (4) $\frac{i + 10 j + 18 k}{5 17}$ 48. $A body, constrained to move in the Y-direction is subjected to a force given by F = (- 2 i + 15 j + 6 k) N . What is the work done by this force in moving the body a distance 10 m along the Y-axis$ (1) $20 J$ (2) $150 J$ (3) $160 J$ (4) $190 J$ 49. $A vector F_{1} is along the positive X-axis. If its vector product with another vector F_{2} is zero then F_{2} could be$ (1) $4 j$ (2) $- (i + j)$ (3) $(j + k)$ (4) $(- 4 i)$ 50. $The dimensional formula of angular impulse is :$ (1) $M L^{- 2} T^{- 1}$ (2) $M L^{2} T^{- 2}$ (3) $M L T^{- 1}$ (4) $M L^{2} T^{- 1}$ 51. $The resultant of the two vectors having magnitude 2 and 3 is 1. What is their cross product$ (1) $6$ (2) $3$ (3) $1$ (4) $0$ 52. $A force F = 5 i + 6 j + 4 k acting on a body, produces a displacement S = 6 i - 5 k . Work done by the force is$ (1) $10 units$ (2) $18 units$ (3) $11 units$ (4) $5 units$ 53. $A sliver wire has mass (0.6\pm0.006)g, radius (0,5 \pm 0.005) mm and length (4 \pm 0.04) cm. The maximum percentage error in the measurement of its density will be :$ (1) $4%$ (2) $3%$ (3) $6%$ (4) $7%$ 54. $Two adjacent sides of a parallelogram are represented by the two vectors i + 2 j + 3 k and 3 i - 2 j + k . What is the area of parallelogram$ (1) $8$ (2) $83$ (3) $38$ (4) $192$ 55. $If P = 3 i + 3 j + 2 k and Q = 4 i + 3 j + 2.5 k then, The unit vector in the direction of P \times Q is \frac{1}{x} (3 i + j - 23 k) . The value of x is$ 56. $If P \times Q = Q \times P, the angle between P and Q is θ (0^{\circ} < θ < 360^{\circ}) . The value of ' θ' will be$ 57. $The resultant of two vectors A and B is perpendicular to A and its magnitude is half that of B . The angle between vectors A and B is) _______^{\circ} .$ 58. $The resistance R = \frac{V}{I}, where V = (50 \pm 2) V and I = (20 \pm 0.2) A . The percentage error in R is ’ x ’ % . The value of ’ x^{’} to the nearest integer is____$ 59. $A vector has magnitude same as that of A = 3 i + 4 j and is parallel to B = 4 i + 3 j . The x and y components of this vector in first quadrant are x and 3 respectively where x = .$ 60. $If a and b makes an angle cos^{- 1} (\frac{5}{9}) with each other, then \| a + b \| = 2 \| a - b \| for \| a \| = n \| b \| The integer value of n is_____$