Vectors & Basic Mathematics PYQs Set 5 (PDF)

Set 5 of 6 · Questions 121-150 of 153

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Mere Teacher · Previous Year Questions JEE Main Physics · Vectors & Basic Mathematics · Set 5 (Q121-150)
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121. $A parallelogram has diagonals expressed as A = 5 i - 4 j + 3 k and B = 3 i + 2 j - k . Area of parallelogram is$ (1) $117 units$ (2) $171 units$ (3) $711 units$ (4) $107 units$ 122. $The distance of the Sun from earth is 1.5 x 1 0^{11} m and its angular diameter is (2000) s when observed from the earth. The diameter of the Sun will be :$ (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) $0.14 x 1 0^{9} m$ 123. $If \| V_{1} + V_{2} \| = \| V_{1} - V_{2} \| and V_{2} is finite, then$ (1) $V_{1} is parallel to V_{2}$ (2) $V_{1} = V_{2}$ (3) $V_{1} and V_{2} are mutually perpendicular$ (4) $\| V_{1} \| = \| V_{2} \|$ 124. $In an octagon ABCDEFGH of equal side, what is the sum of AB + AC + AD + AE + AF + AG + AH If AO = 2 i + 3 j - 4 k$ (1) $16 i + 24 j - 32 k$ (2) $- 16 i - 24 j - 32 k$ (3) $- 16 i - 24 j + 32 k$ (4) $- 16 i + 24 j + 32 k$ 125. $In an experiment, the resistance of a material is plotted as a function of temperature (in some range). As shown in the figure, it is a straight line. One may conclude that :$ (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) $R (T) = R_{0} e^{\frac{T ^{2}}{T _{0}^{2}}}$ 126. $If the cube of side ‘a’ shown in figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be:$ (1) $\frac{1}{2} a (k - i)$ (2) $\frac{1}{2} a (i - k)$ (3) $\frac{1}{2} a (j - i)$ (4) $\frac{1}{2} a (j - k)$ 127. $A pendulum hangs from the ceiling of a jeep moving with a speed v along a circle of radius R. Find the angle with the vertical made by the pendulum.$ (1) $0$ (2) $t a n^{- 1} (v^{2} /Rg)$ (3) $t a n^{- 1} (Rg/ v^{2})$ (4) $None of these$ 128. $A hunter is at (4, -1, 5) units. He observes two preys at P_{1} (-1, 2, 0) units and P_{2} (1, 1, 4), respectively. At zero instant he starts moving in the plane of their positions with uniform speed of 5 units s^{- 1} s in a direction perpendicular to line P_{1} P_{2} till he sees P_{1} and P_{2} collinear at time T. Time T is$ (1) $0.53 s$ (2) $0.73 s$ (3) $0.35 s$ (4) $0.92 s$ 129. $Consider two vectors F_{1} = 2 j + 5 k and F_{2} = 3 j + 4 k . The magnitude of the scalar product of these vectors is$ (1) $20$ (2) $23$ (3) $533$ (4) $26$ 130. $If a vector A is parallel to another vector B then the resultant of the vector A \times B will be equal to$ (1) $A$ (2) $A$ (3) $Zero vector$ (4) $Zero$ 131. $If two vectors 2 i^+ 3 j^- k^and - 4 i^- 6 j^- λ k^are parallel to each other then value of λ be$ (1) $0$ (2) $2$ (3) $3$ (4) $4$ 132. $If vectors A = cos ω t i + sin ω t j and B = cos \frac{ω t}{2} i + sin \frac{ω t}{2} j are functions of time, then the value of t at which they are orthogonal to each other is$ (1) $0$ (2) $\frac{π}{4 ω}$ (3) $\frac{π}{2 ω}$ (4) $\frac{π}{ω}$ 133. $Let ∣ A_{1} ∣ = 3, ∣ A_{2} ∣ = 5 and ∣ A_{1} + A_{2} ∣ = 5 . The value of (2 A_{1} + 3 A_{2}) \cdot (3 A_{1} - 2 A_{2}) is:$ (1) $- 106.5$ (2) $- 99.5$ (3) $- 112.5$ (4) $- 118.5$ 134. $In an clockwise system$ (1) $j \times k = i$ (2) $i . i = 0$ (3) $j \times j = 1$ (4) $k . j = 1$ 135. $The time period of a simple pendulum is given by T = 2 π \frac{l}{g} . The measured value of the length of pendulums 10 cm known to a 1 mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 secondusing a clock of 1 s resolution. The percentage accuracy in the determination of ’ g ’ using this pendulum is ’ x ’ . The value of ’ x ’ to the nearest integer is:-$ (1) $2 %$ (2) $3 %$ (3) $5 %$ (4) $4 %$ 136. $Young's modulus is determined by the equation given by Y = 49000 \frac{m}{1} \frac{dyn}{cm ^{2}} where M is the mass and l is the extension of wire used in the experiment. Now error in Young modules (Y) is estimated by taking data from M - l plot in graph paper. The smallest scale divisions are 5 g and 0.02 cm along load axis and extension axis respectively. If the value of M and l are 500 g and 2 cm respectively then percentage error of Y is:$ (1) $0.5 %$ (2) $2 %$ (3) $0.02 %$ (4) $0.2 %$ 137. $Two towns T_{1} and T_{2} are connected by regular bus service. A scooterist moving from T_{1} to T_{2} speed of 20 k m h^{- 1} notices that a bus goes past it every 21 minute in the direction of his motion and every 7 minute in the opposite direction. If a bus leaves in either direction every T minute, the period T is$ (1) $1.5 minute$ (2) $9.5 minute$ (3) $6 minute$ (4) $10.5 minute$ 138. $Two identical pendulums are tied from the same rigid support. One is tied horizontally. The other is released when they are making the same angle θ with the vertical.$ (1) $tan^{2} θ$ (2) $cot^{2} θ$ (3) $1$ (4) $sec^{2} θ$ 139. $If A = 3 i + 4 j and B = ai + 3 j are perpendicular to each other. The value of a is$ (1) $-4$ (2) $4$ (3) $-3$ (4) $3$ 140. $The vector P = ai + aj + 3 k and Q = ai - 2 j - k are perpendicular to each other. The positive value of a is$ (1) $3$ (2) $4$ (3) $9$ (4) $13$ 141. $If P . Q = PQ, then angle between P and Q is$ (1) $0°$ (2) $30°$ (3) $45°$ (4) $60°$ 142. $If force (F) = 4 i + 5 j and displacement (s) = 3 i + 6 k then the work done is$ (1) $4 \times 3$ (2) $5 \times 6$ (3) $6 \times 3$ (4) $4 \times 6$ 143. $What is the value of linear velocity, if ω = 3 i - 4 j + k and r = 5 i - 6 j + 6 k$ (1) $6 i - 2 j + 3 k$ (2) $6 i - 2 j + 8 k$ (3) $4 i - 13 j + 6 k$ (4) $- 18 i - 13 j + 2 k$ 144. $In an expression a \times 10^{b};$ (1) $b is order of magnitude for a\geq5$ (2) $b is order of magnitude for a\leq5$ (3) $a is order of magnitude for b\leq5$ (4) $b is order of magnitude for 5<a\leq10$ 145. $Two vector A and B have magnitude 3 each A \times B = - 5 k^+ 2 i^. Find angle between A and B$ (1) $cos^{- 1} (\frac{29}{9})$ (2) $tan^{- 1} (\frac{- 5}{2})$ (3) $sin^{- 1} (\frac{2}{5})$ (4) $sin^{- 1} (\frac{29}{9})$ 146. $In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of 0.5 s is measured from time of 100 oscillation with a watch of Is resolution. If measured value of length is 10 cm known to 1mm accuracy. The accuracy in the determination of g is found to be x %. The value of x is$ 147. $The resultant of two vectors A and B is perpendicular to A and its magnitude is half that of B . The angle between vectors A and B is______ o.$ 148. $In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as 5.25 mm and apparent thickness of the glass slab at 5.00 mm. Travelling microscope has 20 divisions in one cm on main scale and 50 divisions on Vernier scale is equal to 49 divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is , where x is ___________$ 149. $The one division of main scale of vernier callipers reads 1 mm and 10 divisions of Vernier scale is equal to the 9 divisions on main scale. When the two jaws of the instrument touch each other the zero of the Vernier lies to the right of zero of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the zero of the Vernier scale lies in between 4.1 cm and 4.2 cm and 6^{t h} Vernier division coincides with a main scale division. The diameter of the bob will be_____1 0^{- 2} cm$ 150. $If the projection of 2 i^+ 4 j^- 2 k^on i^+ 2 j^+ α k^is zero. Then, the value of a will be$