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A particle moves in a straight line with a constant acceleration. It changes its velocity from 10 ms⁻¹ to 20 ms⁻¹ while passing through a distance of 135 m in t seconds. The value of t is:
Dimensional formula of magnetic flux is:
A bus is moving with a speed of 10 ms⁻¹ on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what minimum speed should the scooterist chase the bus?
A stone falls freely under gravity. It covers distances h₁, h₂ and h₃ in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h₁, h₂ and h₃ is:
Two bodies, A (of mass 1 kg) and B (of mass 3 kg) are dropped from heights of 16 m and 25 m, respectively. The ratio of the time taken by them to reach the ground is:
A particle is moving such that its position coordinates (x, y) are (2 m, 3 m) at time t = 0, (6 m, 7 m) at time t = 2 s, and (13 m, 14 m) at time t = 5 s. The average velocity vector v_avg from t = 0 to t = 5 s is:
A car moves from X to Y with a uniform speed vᵤ and returns to X with a uniform speed v_d. The average speed for this round trip is:
Velocity-time (v-t) graph for a moving object is shown in the figure. Total displacement of the object during the time interval when there is non-zero acceleration or retardation is:
A particle moving along the x-axis has acceleration f, at time t, given by f = f₀(1 - t/T), where f₀ and T are constants. The particle at t = 0 has zero velocity. In the time interval between t = 0 and the instant when f = 0, the particle’s velocity (vₓ) is:
The initial velocity of a particle is $u$ (at $t = 0$) and the acceleration $f$ is given by $at$. Which of the following relations is valid?
Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t₁. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t₂. The time taken by her to walk upon the moving escalator will be:
A person standing on the floor of an elevator drops a coin. The coin reaches the floor in time $t_1$ if the elevator is moving uniformly and time $t_2$ if the elevator is stationary. Then:
The graph between the displacement $x$ and time $t$ for a particle moving in a straight line is shown in the figure. During the intervals OA, AB, BC, and CD, the acceleration of the particle is:
A wave in a string has an amplitude of $2 \text{ cm}$. The wave travels in the positive direction of the x-axis with a speed of $128 \text{ m/s}$ and it is noted that $5$ complete waves fit in the $4 \text{ m}$ length of the string. The equation describing the wave is:
A tuning fork with a frequency of $800 \text{ Hz}$ produces resonance in a resonance column tube with the upper end open and the lower end closed by the water surface. Successive resonances are observed at lengths of $9.75 \text{ cm}$, $31.25 \text{ cm}$, and $52.75 \text{ cm}$. The speed of the sound in the air is:
Given below are two statements: Assertion (A): A glass tube partially filled with water represents an open organ pipe. Reason (R): The open end corresponds to an antinode and the end in contact with water, to a node. In the light of the above statements, choose the correct answer from the options given below:
The $4^{\text{th}}$ overtone of a closed organ pipe is the same as that of the $3^{\text{rd}}$ overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is:
The length of the string of a musical instrument is $90\text{ cm}$ and has a fundamental frequency of $120\text{ Hz}$. Where should it be pressed to produce a fundamental frequency of $180\text{ Hz}$?
The peak voltage of the ac source is equal to
A biconvex lens has radii of curvature, $20\text{ cm}$ each. If the refractive index of the material of the lens is $1.5$, the power of the lens is