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A missile is fired for a maximum range with an initial velocity of $20 \text{ m/s}$. If $g=10 \text{ m/s}^2$, then the range of the missile will be:

Consider the following reactions: 1. $R-COOH \xrightarrow{\text{(i) } X} \xrightarrow{\text{(ii) } H_2O/HCl} R-CH_2OH$ 2. $R-CH=CH_2 \xrightarrow{\text{(i) } X} \xrightarrow{\text{(ii) } H_2O/NaOH/H_2O_2} R-CH_2-CH_2-OH$ Identify 'X' in the above reactions:

The correct order of decreasing acid strength of trichloroacetic acid (A), trifluoroacetic acid (B), acetic acid (C), and formic acid (D) is:

Given below are two statements: Statement I: Primary aliphatic amines react with $HNO_2$ to give unstable diazonium salts. Statement II: Primary aromatic amines react with $HNO_2$ to form diazonium salts which are stable even above $300\text{ K}$. In the light of the above statements, choose the most appropriate answer from the options given below:

Two trains, each $50 \text{ m}$ long, are travelling in the opposite direction with velocities $10 \text{ m/s}$ and $15 \text{ m/s}$. The time of crossing is:

The height $y$ and the distance $x$ along the vertical plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $y = (8t - 5t^2)$ meter and $x = 6t$ meter, where $t$ is in second. The velocity with which the projectile is projected is:

A particle (A) is dropped from a height and another particle (B) is thrown in the horizontal direction with a speed of 5 m/sec from the same height. The correct statement is:

If a body A of mass $M$ is thrown with a velocity $v$ at an angle of $30^{\circ}$ to the horizontal and another body B of the same mass is thrown with the same speed at an angle of $60^{\circ}$ to the horizontal. The ratio of horizontal range of A to B will be:

An electric fan has blades of length $30\text{ cm}$ as measured from the axis of rotation. If the fan is rotating at $1200\text{ r.p.m}$, the acceleration of a point on the tip of the blade is about:

For a prism, when the light undergoes minimum deviation, the relationship between the angle of incidence ($i$) and the angle of emergence ($i'$) is:

Two bullets are fired horizontally and simultaneously towards each other from the rooftops of two buildings (building being $100 \text{ m}$ apart and being of the same height of $200 \text{ m}$) with the same velocity of $25 \text{ m/s}$. When and where will the two bullets collide? ($g=10 \text{ m/s}^2$)

The range of a particle when launched at an angle of $15^\circ$ with the horizontal is $1.5\text{ km}$. What is the range of the projectile when launched at an angle of $45^\circ$ to the horizontal?

A particle starts its motion from rest under the action of a constant force. If the distance covered in the first 10 s is S₁ and that covered in the first 20 s is S₂, then:

Mark the reaction among the following that does not give benzoic acid as the major product:

In a reaction of aniline a coloured product C was obtained. The structure of C would be:

The compound that does not give an iodoform test is:

The fundamental frequency of a closed organ pipe of a length $20 \text{ cm}$ is equal to the second overtone of an organ pipe open at both ends. The length of the organ pipe open at both ends will be:

The displacement of a particle as a function of time is shown in the figure. The figure shows that

The acceleration of a moving body can be found from:

During the electrolysis of molten sodium chloride, the time required to produce $0.10 \text{ mol}$ of chlorine gas using a current of $3 \text{ amperes}$ is