Vectors & Basic Mathematics PYQs Set 3 (PDF)

Set 3 of 6 · Questions 61-90 of 153

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Mere Teacher · Previous Year Questions JEE Main Physics · Vectors & Basic Mathematics · Set 3 (Q61-90)
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61. $Find out the unit vector perpendicular to both vectors i - j + k and i + j + k .$ (1) $i + j$ (2) $\frac{- i + k}{2}$ (3) $j + k$ (4) $i + j 2$ 62. $A body, acted upon by a force of 50 N is displaced through a distance 10 meter in a direction making an angle of 60° with the force. The work done by the force be$ (1) $200 J$ (2) $100 J$ (3) $300$ (4) $250 J$ 63. $If a and b are two-unit vectors such that a + 2 b and 5 a - 4 b are perpendicular to each other, then the angle between a and b is$ (1) $45^{\circ}$ (2) $60^{\circ}$ (3) $cos^{- 1} (\frac{1}{3})$ (4) $cos^{- 1} (\frac{2}{7})$ 64. $If ϵ_{0} is the permittivity of free space and E is the electric field, then ϵ_{0} E^{2} has the dimensions :$ (1) $M^{- 1} L^{- 3} T^{4} A^{2}$ (2) $M L^{2} T^{- 2}$ (3) $M^{0} L^{- 2} T A$ (4) $M L^{- 1} T^{- 2}$ 65. $The area of a square is 5.29 c m^{2} . The area of 7 such squares taking into account the significant figures is:$ (1) $37 c m^{2}$ (2) $37.030 c m^{2}$ (3) $37.03 c m^{2}$ (4) $37.0 c m^{2}$ 66. $The equation of state of a real gas is given by (P + \frac{a}{V ^{2}}) (V - b) = RT, where P, V and T are pressure. volume and temperature respectively and R is the universal gas constant. The dimensions of \frac{a}{b ^{2}} is similar to that of :$ (1) $PV$ (2) $P$ (3) $RT$ (4) $R$ 67. $If a vector (2 i + 3 j + 8 k) is perpendicular to the vector - 4 i + 4 j + α k, then the value of α is-$ (1) $-1$ (2) $\frac{1}{2}$ (3) $\frac{- 1}{2}$ (4) $1$ 68. $Which of the following relations is true for two unit vectors A and B making an angle θ to each other?$ (1) $(A + B) = (A - B) tan \frac{θ}{2}$ (2) $(A - B) = (A + B) tan \frac{θ}{2}$ (3) $(A + B) = (A - B) cos \frac{θ}{2}$ (4) $(A - B) = (A + B) cos \frac{θ}{2}$ 69. $A wire of 1Ω has a length of 1 m . It is stretched till its length increases by 25 % . The percentage change in aresistance to the nearest integer is:$ (1) $25 %$ (2) $12.5 %$ (3) $76 %$ (4) $56 %$ 70. $When A . B = - \| A \| \| B \|, then$ (1) $A and B are perpendicular to each other$ (2) $A and B act in the same direction$ (3) $A and B act in the opposite direction$ (4) $A and B can act in any direction$ 71. $If three non-zero vectors A, B, and C satisfy the relation A \cdot B = 0 and A \cdot C = 0, then A can be parallel to$ (1) $B$ (2) $C$ (3) $B \cdot C$ (4) $B \times C$ 72. $Two vector A and B have equal magnitudes. Then the vector A + B is perpendicular to$ (1) $A \times B$ (2) $A - B$ (3) $3A - 3B$ (4) $All of these$ 73. $Angle between the vectors (i + j) and (j - k) is$ (1) $90°$ (2) $0°$ (3) $180°$ (4) $60°$ 74. $The linear velocity of a rotating body is given by v = ω \times r, where ω is the angular velocity and r is the radius vector. The angular velocity of a body is ω = i - 2 j + 2 k and the radius vector r = 4 j - 3 k, then \| v \| is$ (1) $29 units$ (2) $31 units$ (3) $37 units$ (4) $41 units$ 75. $Two forces P and Q, of magnitude 2F and 3F, respectively, are at an angle θ with each other. If the forces Q is doubled, then their resultant also gets doubled. Then, the angle is$ (1) $120°$ (2) $60°$ (3) $90°$ (4) $30°$ 76. $The dimensional formula of latent heat is :$ (1) $(ML^{2} T^{- 2})$ (2) $(M^{0} L^{2} T^{- 2})$ (3) $(MLT^{- 2})$ (4) $(M^{\circ} LT^{- 2})$ 77. $The position vectors of points A, B, C and D are A = 3 i + 4 j + 5 k, B = 4 i + 5 j + 6 k, C = 7 i + 9 j + 3 k and D = 4 i + 6 j then the displacement vectors AB and CD are$ (1) $Perpendicular$ (2) $Parallel$ (3) $Antiparallel$ (4) $Inclined at an angle of 60°$ 78. $Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as 4.62 s, 4.632 s, 4.6 s and 4.64 s . The arithmetic mean of these readings in correct significant figure is:$ (1) $5 s$ (2) $4.623 s$ (3) $4.6 s$ (4) $4.62 s$ 79. $Applying the principle of homogeneity of dimensions, determine which one is correct, where T is time period, G is gravitational constant, M is mass, r is radius of orbit.$ (1) $T^{2} = \frac{4 π ^{2} r ^{2}}{GM}$ (2) $T^{2} = \frac{4 π ^{2} r}{G M ^{2}}$ (3) $T^{2} = \frac{4 π ^{2} r ^{3}}{GM}$ (4) $T^{2} = 4 π^{2} r^{3}$ 80. $The resistance R = \frac{V}{I} where V = (200 \pm 5) V and I = (20 \pm 0.2) A, the percentage error in the measurement of R is :$ (1) $3.5 %$ (2) $7 %$ (3) $3 %$ (4) $5.5 %$ 81. $Given that A + B + C = 0, out of three vectors two are equal in magnitude and the magnitude of third vector is 2 times that of either of the two having equal magnitude. Then the angles between vectors are given by -$ (1) $30^{\circ}, 60^{\circ}, 90^{\circ}$ (2) $45^{\circ}, 45^{\circ}, 90^{\circ}$ (3) $45^{0}, 60^{0}, 90^{0}$ (4) $90^{0}, 135^{0}, 135^{0}$ 82. $Consider a vector F = 4 i - 3 j . Another vector that is perpendicular to F is$ (1) $4 i + 3 j$ (2) $6 i$ (3) $7 k$ (4) $3 i - 4 j$ 83. $If two vectors 2 i + 3 j - k and - 4 i - 6 j - λk are parallel to each other, the value of λ is$ (1) $2$ (2) $-2$ (3) $3$ (4) $-3$ 84. $The angle between vectors (A \times B) and (B \times A) is$ (1) $Zero$ (2) $π$ (3) $π/4$ (4) $π/2$ 85. $If A \to \times B \to= B \to \times A \to then the angle between A and B is$ (1) $π /2$ (2) $π /3$ (3) $0 or π$ (4) $π /4$ 86. $A force F = (5 i + 3 j) N is applied over a particle which displaces it from its original position to the point s = (2 i - 1 j) m. The work done on the particle is$ (1) $+ 11 J$ (2) $+ 7 J$ (3) $+ 13 J$ (4) $- 7 J$ 87. $The angle between the vectors A and B is θ . The value of the triple product A . (B \times A) is$ (1) $A^{2} B$ (2) $Zero$ (3) $A^{2} B sin θ$ (4) $A^{2} B cos θ$ 88. $Two particles are moving with velocity v_{1} = i - 2 t j m / s and v_{2} = 4 i + j m / s respectively Time at which they are moving perpendicular to each other is.$ 89. $For three vectors A = (- x i - 6 j - 2 k), B = (- i + 4 j + 3 k) and C = (- 8 i - j + 3 k), if A \cdot (B \times C) = 0, then value of x is______$ 90. $The length of a metallic wire is increased by 20% and its area of cross-section is reduced by 4%. The percentage change in resistance of the metallic wire is$