List of practice Questions

Maximum height reached by a rocket fired with a speed equal to 50\% of the escape speed from the surface of the earth is (R – Radius of the earth)
If ambient temperature is 300 K, the rate of cooling at 600 K is H. In the same surroundings, the rate of cooling at 900 K is
A block of mass 1.5 kg kept on a rough horizontal surface is given a horizontal velocity of 10 ms\(^{-1}\). If the block comes to rest after travelling a distance of 12.5 m, the coefficient of kinetic friction between the surface and the block is (Acceleration due to gravity = 10 ms\(^{-2}\))
The perpendicular distance from the point \( (-1,1,0) \) to the line joining the points \( (0,2,4) \) and \( (3,0,1) \) is:
The locus of the midpoints of the chords of the hyperbola \( x^2 - y^2 = a^2 \) which touch the parabola \( y^2 = 4ax \) is:
If the product of the eccentricities of the ellipse \( \frac{x^2}{16} + \frac{y^2}{b^2} = 1 \) and the hyperbola \( \frac{x^2}{9} - \frac{y^2}{16} = 1 \) is 1, then the value of \( b^2 \) is:
A bag contains 2 white, 3 green, and 5 red balls. If three balls are drawn one after the other without replacement, then the probability that the last ball drawn was red is:
If the radio horizon of a transmitting antenna is 21.6 km, the height of the antenna is:
An electromagnetic wave travels in a medium of relative permeability \(1.3\) and relative permittivity \(2.3\). Then the speed of an electromagnetic wave in that medium is
A bar magnet of moment \(0.4 \times 10^{-3} \, {Am}^2\) is kept in a magnetic field of \(2\pi \times 10^{-3} \, {T}\). The magnet makes an angle of \(45^\circ\) with the direction of magnetic field. The torque acting on the magnet is:
Which one of the following sets is not correctly matched?
Arrange the following pesticides in the chronological order of their release into the market: A: Organophosphates
B: Organochlorides
C: Sodium chlorate
Identify the incorrect statements from the following: I. \( \Delta S_{\text{system}} = (\Delta S_{\text{total}} + \Delta S_{\text{sur}}) \) II. \( A(l) \rightarrow A(s) \); for this process entropy change decreases III. Entropy units are \( J \ K^{-1} \ mol^{-1} \)
Drift speed \( v \) varies with the intensity of the electric field \( E \) as per the relation
Two point charges +6 \(\mu\)C and +10 \(\mu\)C kept at a certain distance repel each other with a force of 30 N. If each charge is given an additional charge of -8 \(\mu\)C, the two charges
The moments of inertia of a solid cylinder and a hollow cylinder of the same mass and same radius about the axes of the cylinders are \( I_1 \) and \( I_2 \). The relation between \( I_1 \) and \( I_2 \) is
Find the general solution of the differential equation \( (x - y -1) dy = (x + y + 1) dx \).
Find the area enclosed by the curve \( y = x^3 - 19x + 30 \) and the X-axis.
Evaluate \( \int_{ \log 4}^{ \log 5} \frac{e^{2x} + e^x}{e^{2x} - 5e^x +6} dx \):
Evaluate the integral: \[ I = \int (\tan^7 x + \tan x) dx. \]
Evaluate the integral: \[ I = \int \frac{\csc x}{3\cos x + 4\sin x} dx. \]
By considering \( 1' = 0.0175 \), the approximate value of \( \cot 45^\circ 2' \) is:
Evaluate the limit: \[ \lim_{x \to \infty} \left( \frac{3x^2 - 2x + 3}{3x^2 + x - 2} \right)^{3x - 2} \]
Let \( P(a, 4, 7) \) and \( Q(3, \beta, 8) \) be two points. If the YZ-plane divides the join of the points P and Q in the ratio 2:3 and the ZX-plane divides the join of P and Q in the ratio 4:5, then the length of line segment PQ is:
If the coordinate axes are rotated by \( 45^\circ \) about the origin in the counterclockwise direction, then the transformed equation of \( y^2 = 4ax \) is: