Vectors & Basic Mathematics PYQs Set 3 (PDF)

Set 3 of 5 · Questions 61-90 of 131

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Mere Teacher · Previous Year Questions NEET Physics · Vectors & Basic Mathematics · Set 3 (Q61-90)
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61. $Which of the following relations is true for two unit vectors A and B making an angle θ to each other?$ (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) $(A - B) = (A + B) cos \frac{θ}{2}$ 62. $A wire of 1Ω has a length of 1 m . It is stretched till its length increases by 25 % . The percentage change in aresistance to the nearest integer is:$ (1) $25 %$ (2) $12.5 %$ (3) $76 %$ (4) $56 %$ 63. $When A . B = - \| A \| \| B \|, then$ (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) $A and B can act in any direction$ 64. $If three non-zero vectors A, B, and C satisfy the relation A \cdot B = 0 and A \cdot C = 0, then A can be parallel to$ (1) $B$ (2) $C$ (3) $B \cdot C$ (4) $B \times C$ 65. $Two vector A and B have equal magnitudes. Then the vector A + B is perpendicular to$ (1) $A \times B$ (2) $A - B$ (3) $3A - 3B$ (4) $All of these$ 66. $Angle between the vectors (i + j) and (j - k) is$ (1) $90°$ (2) $0°$ (3) $180°$ (4) $60°$ 67. $The linear velocity of a rotating body is given by v = ω \times r, where ω is the angular velocity and r is the radius vector. The angular velocity of a body is ω = i - 2 j + 2 k and the radius vector r = 4 j - 3 k, then \| v \| is$ (1) $29 units$ (2) $31 units$ (3) $37 units$ (4) $41 units$ 68. $Two forces P and Q, of magnitude 2F and 3F, respectively, are at an angle θ with each other. If the forces Q is doubled, then their resultant also gets doubled. Then, the angle is$ (1) $120°$ (2) $60°$ (3) $90°$ (4) $30°$ 69. $The dimensional formula of latent heat is :$ (1) $(ML^{2} T^{- 2})$ (2) $(M^{0} L^{2} T^{- 2})$ (3) $(MLT^{- 2})$ (4) $(M^{\circ} LT^{- 2})$ 70. $The position vectors of points A, B, C and D are A = 3 i + 4 j + 5 k, B = 4 i + 5 j + 6 k, C = 7 i + 9 j + 3 k and D = 4 i + 6 j then the displacement vectors AB and CD are$ (1) $Perpendicular$ (2) $Parallel$ (3) $Antiparallel$ (4) $Inclined at an angle of 60°$ 71. $Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as 4.62 s, 4.632 s, 4.6 s and 4.64 s . The arithmetic mean of these readings in correct significant figure is:$ (1) $5 s$ (2) $4.623 s$ (3) $4.6 s$ (4) $4.62 s$ 72. $Applying the principle of homogeneity of dimensions, determine which one is correct, where T is time period, G is gravitational constant, M is mass, r is radius of orbit.$ (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) $T^{2} = 4 π^{2} r^{3}$ 73. $The resistance R = \frac{V}{I} where V = (200 \pm 5) V and I = (20 \pm 0.2) A, the percentage error in the measurement of R is :$ (1) $3.5 %$ (2) $7 %$ (3) $3 %$ (4) $5.5 %$ 74. $Given that A + B + C = 0, out of three vectors two are equal in magnitude and the magnitude of third vector is 2 times that of either of the two having equal magnitude. Then the angles between vectors are given by -$ (1) $30^{\circ}, 60^{\circ}, 90^{\circ}$ (2) $45^{\circ}, 45^{\circ}, 90^{\circ}$ (3) $45^{0}, 60^{0}, 90^{0}$ (4) $90^{0}, 135^{0}, 135^{0}$ 75. $Consider a vector F = 4 i - 3 j . Another vector that is perpendicular to F is$ (1) $4 i + 3 j$ (2) $6 i$ (3) $7 k$ (4) $3 i - 4 j$ 76. $If two vectors 2 i + 3 j - k and - 4 i - 6 j - λk are parallel to each other, the value of λ is$ (1) $2$ (2) $-2$ (3) $3$ (4) $-3$ 77. $The angle between vectors (A \times B) and (B \times A) is$ (1) $Zero$ (2) $π$ (3) $π/4$ (4) $π/2$ 78. $If A \to \times B \to= B \to \times A \to then the angle between A and B is$ (1) $π /2$ (2) $π /3$ (3) $0 or π$ (4) $π /4$ 79. $A force F = (5 i + 3 j) N is applied over a particle which displaces it from its original position to the point s = (2 i - 1 j) m. The work done on the particle is$ (1) $+ 11 J$ (2) $+ 7 J$ (3) $+ 13 J$ (4) $- 7 J$ 80. $The angle between the vectors A and B is θ . The value of the triple product A . (B \times A) is$ (1) $A^{2} B$ (2) $Zero$ (3) $A^{2} B sin θ$ (4) $A^{2} B cos θ$ 81. $If A \cdot B = 0, then which of the following is definitely INCORRECT?$ (1) $\| A \| = 0 and \| B \| \neq = 0$ (2) $\| A \| \neq = 0 and \| B \| = 0$ (3) $\|A\|\neq0,\|B\|\neq0, and angle between. A and B is 90^{\circ}$ (4) $\|A\|=\|B\|\neq0, and angle between A and B is 0^{\circ}$ 82. $Three vectors a, b and c satisfy the relation a . b = 0 and a . c = 0. The vector a is parallel to$ (1) $b$ (2) $c$ (3) $b . c$ (4) $b \times c$ 83. $A vector A points vertically upward and B points towards north. The vector product A \times B is$ (1) $Zero$ (2) $Along west$ (3) $Along east$ (4) $Vertically downward$ 84. $The position vector of a particle changes with time according to the relation r (t) = 15 t^{2} i + (4 - 20 t^{2}) j . What is the magnitude of the acceleration at t = 1 ?$ (1) $40$ (2) $25$ (3) $100$ (4) $50$ 85. $Given below are two statements : Statement (I) : Dimensions of specific heat is (L^{2} T^{- 2} K^{- 1}) . Statement (II) : Dimensions of gas constant is (ML^{2} T^{- 1} K^{- 1}) . In the light of the above statements, choose the most appropriate answer from the options given below.$ (1) $Both statement (I) and statement (II) are correct$ (2) $Statement (I) is correct but statement (II) is incorrect$ (3) $Both statement (I) and statement (II) are incorrect Statement (I) is incorrect but statement (II) is correct$ (4) $Statement (I) is incorrect but statement (II) is correct$ 86. $Angle between two vectors (i + j) and (i - j) is-$ (1) $30^{\circ}$ (2) $60^{\circ}$ (3) $45^{\circ}$ (4) $90^{\circ}$ 87. $If \| A \times B \| = 3 A . B, then the value of \| A + B \| is$ (1) $(A^{2} + B^{2} + \frac{AB}{3})^{\frac{1}{2}}$ (2) $A + B$ (3) $(A^{2} + B^{2} + 3 AB)^{\frac{1}{2}}$ (4) $(A^{2} + B^{2} + AB)^{1/2}$ 88. $If A \times B = C, then which of the following statements is wrong$ (1) $C ⊥ A$ (2) $C ⊥ B$ (3) $C ⊥ (A + B)$ (4) $C ⊥ (A \times B)$ 89. $Two vectors A and B are at right angles to each other, when$ (1) $A + B = 0$ (2) $A - B = 0$ (3) $A \times B = 0$ (4) $A . B = 0$ 90. $To find the spring constant (k) of a spring experimentally, a student commits 2 % positive error in the measurement of time and 1 % negative error in measurement of mass. The percentage error in determining value of k is:$ (1) $5 %$ (2) $1 %$ (3) $3 %$ (4) $4 %$