Vectors & Basic Mathematics PYQs Set 4 (PDF)

Set 4 of 6 · Questions 91-120 of 153

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Mere Teacher · Previous Year Questions JEE Main Physics · Vectors & Basic Mathematics · Set 4 (Q91-120)
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91. $If A \cdot B = 0, then which of the following is definitely INCORRECT?$ (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) $\|A\|=\|B\|\neq0, and angle between A and B is 0^{\circ}$ 92. $Three vectors a, b and c satisfy the relation a . b = 0 and a . c = 0. The vector a is parallel to$ (1) $b$ (2) $c$ (3) $b . c$ (4) $b \times c$ 93. $A vector A points vertically upward and B points towards north. The vector product A \times B is$ (1) $Zero$ (2) $Along west$ (3) $Along east$ (4) $Vertically downward$ 94. $The position vector of a particle changes with time according to the relation r (t) = 15 t^{2} i + (4 - 20 t^{2}) j . What is the magnitude of the acceleration at t = 1 ?$ (1) $40$ (2) $25$ (3) $100$ (4) $50$ 95. $Given below are two statements : Statement (I) : Dimensions of specific heat is (L^{2} T^{- 2} K^{- 1}) . Statement (II) : Dimensions of gas constant is (ML^{2} T^{- 1} K^{- 1}) . In the light of the above statements, choose the most appropriate answer from the options given below.$ (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) $Statement (I) is incorrect but statement (II) is correct$ 96. $Angle between two vectors (i + j) and (i - j) is-$ (1) $30^{\circ}$ (2) $60^{\circ}$ (3) $45^{\circ}$ (4) $90^{\circ}$ 97. $If \| A \times B \| = 3 A . B, then the value of \| A + B \| is$ (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) $(A^{2} + B^{2} + AB)^{1/2}$ 98. $If A \times B = C, then which of the following statements is wrong$ (1) $C ⊥ A$ (2) $C ⊥ B$ (3) $C ⊥ (A + B)$ (4) $C ⊥ (A \times B)$ 99. $Two vectors A and B are at right angles to each other, when$ (1) $A + B = 0$ (2) $A - B = 0$ (3) $A \times B = 0$ (4) $A . B = 0$ 100. $To find the spring constant (k) of a spring experimentally, a student commits 2 % positive error in the measurement of time and 1 % negative error in measurement of mass. The percentage error in determining value of k is:$ (1) $5 %$ (2) $1 %$ (3) $3 %$ (4) $4 %$ 101. $What is the dimensional formula of a b^{- 1} in the equation (P + \frac{a}{V ^{2}}) (V - b) = RT, where letters have their usual meaning.$ (1) $(M^{- 1} L^{5} T^{3})$ (2) $(M^{6} L^{7} T^{4})$ (3) $(ML^{2} T^{- 2})$ (4) $(M^{0} L^{3} T^{- 2})$ 102. $If for two vectors A and B, A \times B = 0, the vectors$ (1) $Are perpendicular to each other$ (2) $Are parallel to each other$ (3) $Act at an angle of 60°$ (4) $Act at an angle of 30°$ 103. $The area of the parallelogram whose sides are represented by the vectors j + 3 k and i + 2 j - k is$ (1) $61 sq.unit$ (2) $59 sq.unit$ (3) $49 sq.unit$ (4) $52 sq.unit$ 104. $A particle moves in the x-y plane under the action of a force F such that the value of its linear momentum (P) at anytime t is P_{x} = 2 cos t, p_{y} = 2 sin t . The angle θ between F and P at a given time t. will be$ (1) $θ = 0°$ (2) $θ = 30°$ (3) $θ = 90°$ (4) $θ = 180°$ 105. $The radius (r), length (l) and resistance (R) of a metal wire was measured in the laboratory as r = (0.35 \pm 0.05) cm R = (100 \pm 10) ohm l = (15 \pm 0.2) cm The percentage error in resistivity of the material of the wire is :$ (1) $25.6 %$ (2) $39.9 %$ (3) $37.3 %$ (4) $35.6 %$ 106. $The value of A \cdot (A \times B) is$ (1) $A^{2} B sinθcosθ$ (2) $A^{2} B$ (3) $0$ (4) $A^{2} Bsin θ$ 107. $The area of the parallelogram represented by the vectors A = 2 i + 3 j and B = i + 4 j is$ (1) $14 units$ (2) $7.5 units$ (3) $10 units$ (4) $5 units$ 108. $The period of oscillation of a simple pendulum is T = 2 π \frac{L}{g} . Measured value of ’ L ’ is 1.0 m from meterscale having a minimum division of 1 mm and time of one complete oscillation is 1.95 s measured fromstopwatch of 0.01 s resolution. The percentage error in the determination of ’ g^{’} will be$ (1) $1.33 %$ (2) $1.30 %$ (3) $1.13 %$ (4) $1.03 %$ 109. $The sum, difference and cross product of two vectors A and B are mutually perpendicular if :$ (1) $A and B are perpendicular to each other and \| A \| = \| B \|$ (2) $A and B are perpendicular to each other$ (3) $A and B are perpendicular but their magnitudes are arbitrary$ (4) $\| A \| = \| B \| and their directions are arbitrary$ 110. $A physical quantity P is given as P = \frac{a ^{2} b ^{3}}{c d} . The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4% respectively. The percentage error in the measurement of quantity P will be$ (1) $13%$ (2) $16%$ (3) $12%$ (4) $14%$ 111. $Two resistance are given as R_{1} = (10 \pm 0.5) Ω and R_{2} = (15 \pm 0.5) Ω . The percentage error in the measurement of equivalent resistance when they are connected in parallel is$ (1) $6.33$ (2) $2.33$ (3) $5.33$ (4) $4.33$ 112. $A cylindrical wire of mass (0. 4 \pm 0. 01) g has length (8 \pm 0. 04) cm and radius (6 \pm 0. 03) mm. The maximum error in its density will be$ (1) $3.5%$ (2) $5%$ (3) $1%$ (4) $4%$ 113. $If a particle of mass m is moving with constant velocity v parallel to x-axis in x-y plane as shown in fig. Its angular momentum with respect to origin at any time t will be$ (1) $mvb k$ (2) $- mvb k$ (3) $mvb i$ (4) $mv i$ 114. $Three forces F_{1} = 10 N, F_{2} = 8 N, F_{3} = 6 N are acting on a particle of mass 5 kg. The forces F_{2} and F_{3} are applied perpendicularly so that particle remains at rest. If the force fi is removed, then the acceleration of the particle is$ (1) $7 m s^{- 2}$ (2) $0. 5 m s^{- 2}$ (3) $4. 8 m s^{- 2}$ (4) $2 m s^{- 2}$ 115. $The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by 4 % will be____%$ 116. $Vectors ai + bj + k and 2 i - 3 j + 4 k are perpendicular to each other when 3a + 2b = 7, the x ratio of a to b is \frac{x}{2} The value of x is_______.$ 117. $The radius of a sphere is measured to be (7.50 \pm 0.85) cm . Suppose the percentage error in its volume is x .The value of x, to the nearest x, is____$ 118. $Motion of a particle is defined by the position vector r = A (cos t + tsin t) i + A (sin t - tcos t) j, where t is time in sec. Value of ' t' for which position vector and acceleration are perpendicular to each other is -$ 119. $For z = a^{2} x^{3} y^{\frac{1}{2}}, where 'a' is a constant If percentage error in measurement of 'x' and 'y' are 4% and 12%, respectively, then the percentage error for 'z' will be %.$ 120. $Three vectors OP, OQ and OR each of magnitude A are acting as shown in figure. The resultant of the three vectors is A x . The value of x is____$