Vectors & Basic Mathematics PYQs Set 4 (PDF)

Set 4 of 5 · Questions 91-120 of 131

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Mere Teacher · Previous Year Questions NEET Physics · Vectors & Basic Mathematics · Set 4 (Q91-120)
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91. $What is the dimensional formula of a b^{- 1} in the equation (P + \frac{a}{V ^{2}}) (V - b) = RT, where letters have their usual meaning.$ (1) $(M^{- 1} L^{5} T^{3})$ (2) $(M^{6} L^{7} T^{4})$ (3) $(ML^{2} T^{- 2})$ (4) $(M^{0} L^{3} T^{- 2})$ 92. $If for two vectors A and B, A \times B = 0, the vectors$ (1) $Are perpendicular to each other$ (2) $Are parallel to each other$ (3) $Act at an angle of 60°$ (4) $Act at an angle of 30°$ 93. $The area of the parallelogram whose sides are represented by the vectors j + 3 k and i + 2 j - k is$ (1) $61 sq.unit$ (2) $59 sq.unit$ (3) $49 sq.unit$ (4) $52 sq.unit$ 94. $A particle moves in the x-y plane under the action of a force F such that the value of its linear momentum (P) at anytime t is P_{x} = 2 cos t, p_{y} = 2 sin t . The angle θ between F and P at a given time t. will be$ (1) $θ = 0°$ (2) $θ = 30°$ (3) $θ = 90°$ (4) $θ = 180°$ 95. $The radius (r), length (l) and resistance (R) of a metal wire was measured in the laboratory as r = (0.35 \pm 0.05) cm R = (100 \pm 10) ohm l = (15 \pm 0.2) cm The percentage error in resistivity of the material of the wire is :$ (1) $25.6 %$ (2) $39.9 %$ (3) $37.3 %$ (4) $35.6 %$ 96. $The value of A \cdot (A \times B) is$ (1) $A^{2} B sinθcosθ$ (2) $A^{2} B$ (3) $0$ (4) $A^{2} Bsin θ$ 97. $The area of the parallelogram represented by the vectors A = 2 i + 3 j and B = i + 4 j is$ (1) $14 units$ (2) $7.5 units$ (3) $10 units$ (4) $5 units$ 98. $The period of oscillation of a simple pendulum is T = 2 π \frac{L}{g} . Measured value of ’ L ’ is 1.0 m from meterscale having a minimum division of 1 mm and time of one complete oscillation is 1.95 s measured fromstopwatch of 0.01 s resolution. The percentage error in the determination of ’ g^{’} will be$ (1) $1.33 %$ (2) $1.30 %$ (3) $1.13 %$ (4) $1.03 %$ 99. $The sum, difference and cross product of two vectors A and B are mutually perpendicular if :$ (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) $\| A \| = \| B \| and their directions are arbitrary$ 100. $A physical quantity P is given as P = \frac{a ^{2} b ^{3}}{c d} . The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4% respectively. The percentage error in the measurement of quantity P will be$ (1) $13%$ (2) $16%$ (3) $12%$ (4) $14%$ 101. $Two resistance are given as R_{1} = (10 \pm 0.5) Ω and R_{2} = (15 \pm 0.5) Ω . The percentage error in the measurement of equivalent resistance when they are connected in parallel is$ (1) $6.33$ (2) $2.33$ (3) $5.33$ (4) $4.33$ 102. $A cylindrical wire of mass (0. 4 \pm 0. 01) g has length (8 \pm 0. 04) cm and radius (6 \pm 0. 03) mm. The maximum error in its density will be$ (1) $3.5%$ (2) $5%$ (3) $1%$ (4) $4%$ 103. $If a particle of mass m is moving with constant velocity v parallel to x-axis in x-y plane as shown in fig. Its angular momentum with respect to origin at any time t will be$ (1) $mvb k$ (2) $- mvb k$ (3) $mvb i$ (4) $mv i$ 104. $Three forces F_{1} = 10 N, F_{2} = 8 N, F_{3} = 6 N are acting on a particle of mass 5 kg. The forces F_{2} and F_{3} are applied perpendicularly so that particle remains at rest. If the force fi is removed, then the acceleration of the particle is$ (1) $7 m s^{- 2}$ (2) $0. 5 m s^{- 2}$ (3) $4. 8 m s^{- 2}$ (4) $2 m s^{- 2}$ 105. $A parallelogram has diagonals expressed as A = 5 i - 4 j + 3 k and B = 3 i + 2 j - k . Area of parallelogram is$ (1) $117 units$ (2) $171 units$ (3) $711 units$ (4) $107 units$ 106. $The distance of the Sun from earth is 1.5 x 1 0^{11} m and its angular diameter is (2000) s when observed from the earth. The diameter of the Sun will be :$ (1) $2.45 x 1 0^{10} m$ (2) $1.45 x 1 0^{10} m$ (3) $1.45 x 1 0^{9} m$ (4) $0.14 x 1 0^{9} m$ 107. $If \| V_{1} + V_{2} \| = \| V_{1} - V_{2} \| and V_{2} is finite, then$ (1) $V_{1} is parallel to V_{2}$ (2) $V_{1} = V_{2}$ (3) $V_{1} and V_{2} are mutually perpendicular$ (4) $\| V_{1} \| = \| V_{2} \|$ 108. $In an octagon ABCDEFGH of equal side, what is the sum of AB + AC + AD + AE + AF + AG + AH If AO = 2 i + 3 j - 4 k$ (1) $16 i + 24 j - 32 k$ (2) $- 16 i - 24 j - 32 k$ (3) $- 16 i - 24 j + 32 k$ (4) $- 16 i + 24 j + 32 k$ 109. $In an experiment, the resistance of a material is plotted as a function of temperature (in some range). As shown in the figure, it is a straight line. One may conclude that :$ (1) $R (T) = \frac{R _{0}}{T ^{2}}$ (2) $R (T) = R_{0} e^{- T_{0}^{2} / T^{2}}$ (3) $R (T) = R_{0}^{- \frac{T ^{2}}{T _{0}^{2}}}$ (4) $R (T) = R_{0} e^{\frac{T ^{2}}{T _{0}^{2}}}$ 110. $If the cube of side ‘a’ shown in figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be:$ (1) $\frac{1}{2} a (k - i)$ (2) $\frac{1}{2} a (i - k)$ (3) $\frac{1}{2} a (j - i)$ (4) $\frac{1}{2} a (j - k)$ 111. $A pendulum hangs from the ceiling of a jeep moving with a speed v along a circle of radius R. Find the angle with the vertical made by the pendulum.$ (1) $0$ (2) $t a n^{- 1} (v^{2} /Rg)$ (3) $t a n^{- 1} (Rg/ v^{2})$ (4) $None of these$ 112. $A hunter is at (4, -1, 5) units. He observes two preys at P_{1} (-1, 2, 0) units and P_{2} (1, 1, 4), respectively. At zero instant he starts moving in the plane of their positions with uniform speed of 5 units s^{- 1} s in a direction perpendicular to line P_{1} P_{2} till he sees P_{1} and P_{2} collinear at time T. Time T is$ (1) $0.53 s$ (2) $0.73 s$ (3) $0.35 s$ (4) $0.92 s$ 113. $Consider two vectors F_{1} = 2 j + 5 k and F_{2} = 3 j + 4 k . The magnitude of the scalar product of these vectors is$ (1) $20$ (2) $23$ (3) $533$ (4) $26$ 114. $If a vector A is parallel to another vector B then the resultant of the vector A \times B will be equal to$ (1) $A$ (2) $A$ (3) $Zero vector$ (4) $Zero$ 115. $If two vectors 2 i^+ 3 j^- k^and - 4 i^- 6 j^- λ k^are parallel to each other then value of λ be$ (1) $0$ (2) $2$ (3) $3$ (4) $4$ 116. $If vectors A = cos ω t i + sin ω t j and B = cos \frac{ω t}{2} i + sin \frac{ω t}{2} j are functions of time, then the value of t at which they are orthogonal to each other is$ (1) $0$ (2) $\frac{π}{4 ω}$ (3) $\frac{π}{2 ω}$ (4) $\frac{π}{ω}$ 117. $Let ∣ A_{1} ∣ = 3, ∣ A_{2} ∣ = 5 and ∣ A_{1} + A_{2} ∣ = 5 . The value of (2 A_{1} + 3 A_{2}) \cdot (3 A_{1} - 2 A_{2}) is:$ (1) $- 106.5$ (2) $- 99.5$ (3) $- 112.5$ (4) $- 118.5$ 118. $In an clockwise system$ (1) $j \times k = i$ (2) $i . i = 0$ (3) $j \times j = 1$ (4) $k . j = 1$ 119. $The time period of a simple pendulum is given by T = 2 π \frac{l}{g} . The measured value of the length of pendulums 10 cm known to a 1 mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 secondusing a clock of 1 s resolution. The percentage accuracy in the determination of ’ g ’ using this pendulum is ’ x ’ . The value of ’ x ’ to the nearest integer is:-$ (1) $2 %$ (2) $3 %$ (3) $5 %$ (4) $4 %$ 120. $Young's modulus is determined by the equation given by Y = 49000 \frac{m}{1} \frac{dyn}{cm ^{2}} where M is the mass and l is the extension of wire used in the experiment. Now error in Young modules (Y) is estimated by taking data from M - l plot in graph paper. The smallest scale divisions are 5 g and 0.02 cm along load axis and extension axis respectively. If the value of M and l are 500 g and 2 cm respectively then percentage error of Y is:$ (1) $0.5 %$ (2) $2 %$ (3) $0.02 %$ (4) $0.2 %$