Consider the reaction,
This reaction will be the fastest in:
1. Ethanol
2. Methanol
3. N, N'-dimethylformamide (DMF)
4. Water
Which among the given molecules can exhibit tautomerism?
1. III only
2. Both I and III
3. Both I and II
4. Both II and III
What is the correct order of the carboxylic acids' strength?
| I. |  |
II. |  |
III. |  |
| 1. | I > II > III | 2. | II > III > I |
| 3. | III > II > I | 4. | II > I > III |
The compound that will react most readily with gaseous bromine has the formula:
| 1. | \(\mathrm{C_3H_6}\) | 2. | \(\mathrm{C_2H_2}\) |
| 3. | \(\mathrm{C_4H_{10}}\) | 4. | \(\mathrm{C_2H_4}\) |
Planck's constant (\(h\)), speed of light in the vacuum (\(c\)), and Newton's gravitational constant (\(G\)) are the three fundamental constants. Which of the following combinations of these has the dimension of length?
| 1. | \(\dfrac{\sqrt{hG}}{c^{3/2}}\) | 2. | \(\dfrac{\sqrt{hG}}{c^{5/2}}\) |
| 3. | \(\dfrac{\sqrt{hG}}{G}\) | 4. | \(\dfrac{\sqrt{Gc}}{h^{3/2}}\) |
Two cars \(P\) and \(Q\) start from a point at the same time in a straight line and their positions are represented by; \(x_p(t)= at+bt^2\) and \(x_Q(t) = ft-t^2. \) At what time do the cars have the same velocity?
| 1. | \(\dfrac{a-f}{1+b}\) | 2. | \(\dfrac{a+f}{2(b-1)}\) |
| 3. | \(\dfrac{a+f}{2(b+1)}\) | 4. | \(\dfrac{f-a}{2(1+b)}\) |
In the given figure, \(a=15\) m/s2 represents the total acceleration of a particle moving in the clockwise direction in a circle of radius \(R=2.5\) m at a given instant of time. The speed of the particle is:
1. \(4.5\) m/s
2. \(5.0\) m/s
3. \(5.7\) m/s
4. \(6.2\) m/s
A rigid ball of mass \(M\) strikes a rigid wall at \(60^{\circ}\) and gets reflected without loss of speed, as shown in the figure. The value of the impulse imparted by the wall on the ball will be:
| 1. | \(Mv\) | 2. | \(2Mv\) |
| 3. | \(\dfrac{Mv}{2}\) | 4. | \(\dfrac{Mv}{3}\) |
A bullet of mass \(10\) g moving horizontal with a velocity of \(400\) m/s strikes a wood block of mass \(2\) kg which is suspended by light inextensible string of length \(5\) m. As a result, the centre of gravity of the block is found to rise a vertical distance of \(10\) cm. The speed of the bullet after it emerges horizontally from the block will be:
| 1. | \(100\) m/s | 2. | \(80\) m/s |
| 3. | \(120\) m/s | 4. | \(160\) m/s |
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