List of practice Questions

If the half-life of the sample is 5 years and the initial weight of the sample is 64 gm, then the weight remaining after 15 years is:
A 0.1 molal aqueous solution of glucose boils at \( 100.16^\circ \text{C} \). The boiling point of a 0.5 molal aqueous solution of glucose will be:
If \( f(x) = 2x^3 - 15x^2 - 144x - 7 \), then \( f(x) \) is strictly decreasing in:
One of the principal solutions of \( \sqrt{3} \sec x = -2 \) is equal to:

IUPAC name of the given ether is:

Which of the following represents the Gattermann-Koch reaction?
A wire of length \( 1 \, \text{m} \) moving with velocity \( 8 \, \text{m/s} \) at right angles to a magnetic field of \( 2 \, \text{T} \). The magnitude of induced emf between the ends of the wire will be:
The value of \( \int \frac{x \sin^{-1} x}{\sqrt{1 - x^2}} dx \) is equal to:
The solution of the differential equation \( y^2 dx + (x^2 - xy + y^2) dy = 0 \) is
Two players A and B are alternately throwing a coin and a die together. A player who first throws a head and a 6 wins the game. If A starts the game, then the probability that B wins the game is:
The solution of the differential equation \( \sqrt{1 - y^2} \, dx + x \, dy - \sin^{-1} y \, dy = 0 \) is:
Which of the following compounds is likely to be more soluble in water?
If \( AX = B \), where \[ A = \begin{bmatrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{bmatrix}, \quad X = \begin{bmatrix} x \\ y \\ z \end{bmatrix}, \quad B = \begin{bmatrix} 4 \\ 0 \\ 2 \end{bmatrix}, \] then \( 2x + y - z \) is:
In a BCC (Body-Centered Cubic) structure, the radius of the atoms is:
\( \sin^{-1}[\sin(-600^\circ)] + \cot^{-1}(-\sqrt{3}) = \)
Which of the following correctly represents the AND logic gate?
What is the polymer of elastomer?
Identify the name reaction for Swarts reaction and Witting reaction.
Relative permittivity and permeability of a material are \( \varepsilon_r \) and \( \mu_r \), respectively. Which of the following values of these quantities are allowed for a diamagnetic material?
The longest wavelength associated with the Paschen series is: $$ \text{(Given } R_H = 1.097 \times 10^7 \, \text{SI unit)}. $$ 
Point charge of \( 10 \, \mu C \) is placed at the origin. At what location on the X-axis should a point charge of \( 40 \, \mu C \) be placed so that the net electric field is zero at \( x = 2 \, \text{cm} \) on the X-axis?
A magnetic needle is kept in a non-uniform magnetic field. It experiences:
A liquid is allowed to flow into a tube of truncated cone shape. Identify the correct statement:
Which of the following arrangements does not represent the correct order of the property stated against it?
Tincture of iodine is the common name for: