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An alkene "A" on reaction with $O_3$ and $Zn-H_2O$ gives propanone and ethanal in equimolar ratio. Addition of $HCl$ to alkene "A" gives "B" as the major product. The structure of product "B" is:
A body initially at rest and sliding along a frictionless track from a height $h$ just completes a vertical circle of diameter $AB = D$. The height $h$ is equal to:
A source of unknown frequency gives $4 \text{ beats/s}$ when sounded with a source of known frequency $250 \text{ Hz}$. The second harmonic of the source of unknown frequency gives five beats per second when sounded with a source of frequency $513 \text{ Hz}$. The unknown frequency is
The Young's modulus of steel is twice that of brass. Two wires of the same length and of the same area of cross-section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weight added to the steel and brass wires must be in the ratio of:
The circuit represents a full wave bridge rectifier when switch $S$ is open. The output voltage ($V_0$) pattern across $R_L$ when $S$ is closed:
A mass $m$ is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when:
When a string is divided into three segments of lengths $l_1, l_2$ and $l_3$, the fundamental frequencies of these three segments are $\nu_1, \nu_2$ and $\nu_3$ respectively. The original fundamental frequency ($\nu$) of the string is:
A particle is moving such that its position coordinates $(x, y)$ are $(2\text{ m}, 3\text{ m})$ at time $t = 0$, $(6\text{ m}, 7\text{ m})$ at time $t = 2\text{ s}$ and $(13\text{ m}, 14\text{ m})$ at time $t = 5\text{ s}$. Average velocity vector ($\mathbf{v}_{av}$) from $t = 0$ to $t = 5\text{ s}$ is:
A particle of mass $10 \text{ g}$ moves along a circle of radius $6.4 \text{ cm}$ with a constant tangential acceleration. What is the magnitude of this acceleration, if the kinetic energy of the particle becomes equal to $8 \times 10^{-4} \text{ J}$ by the end of the second revolution after the beginning of the motion?
A particle of mass $m$ is driven by a machine that delivers a constant power of $k$ watts. If the particle starts from rest, the force on the particle at time $t$ is:
A transverse wave is represented by $y=A\sin(\omega t-kx)$. For what value of the wavelength is the wave velocity equal to the maximum particle velocity?
A particle has an initial velocity $(2\hat{i} + 3\hat{j})$ and an acceleration $(0.3\hat{i} + 0.2\hat{j})$. The magnitude of velocity after $10 \text{ s}$ will be:
A projectile is fired from the surface of the earth with a velocity of $5 \text{ m/s}$ and angle $\theta$ with the horizontal. Another projectile fired from another planet with a velocity of $3 \text{ m/s}$ at the same angle follows a trajectory, which is identical to the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet (in $\text{m/s}^2$) is: [Given, $g = 9.8 \text{ m/s}^2$]
A block of mass $10 \text{ kg}$, moving in the $x$-direction with a constant speed of $10 \text{ m/s}$, is subjected to a retarding force $F = 0.1x \text{ J/m}$ during its travel from $x = 20 \text{ m}$ to $30 \text{ m}$. Its final kinetic energy will be:
The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is $20 \text{ cm}$, the length of the open organ pipe is:
The most acidic compound among the following is:
A missile is fired for maximum range with an initial velocity of $20 \text{ m/s}$. If $g=10 \text{ m/s}^2$, the range of the missile is:
A body is moving with velocity $30 \text{ m/s}$ towards east. After $10 \text{ s}$ its velocity becomes $40 \text{ m/s}$ towards north. The average acceleration of the body is:
A transverse wave propagating along the $x$-axis is represented by: $y(x,t) = 8.0\sin(0.5\pi x - 4\pi t - \frac{\pi}{4})$, where $x$ is in meters and $t$ in seconds. The speed of the wave is:
Given below are two statements: **Statement I:** In Lucas test, primary, secondary, and tertiary alcohols are distinguished on the basis of their reactivity with conc. $HCl + ZnCl_2$, known as Lucas Reagent. **Statement II:** Primary alcohols are most reactive and immediately produce turbidity at room temperature on reaction with Lucas Reagent. In light of the above statements, choose the most appropriate answer from the options given below: