List of practice Questions

The system of equations \( 3x + 5y = 4 \); \( 6x + ky = 8 \) has infinitely many solutions if \( k \) is equal to
The value of \( k \) for which the system of equations \( x + ky + 3z = 0 \); \( 3x + ky + 2z = 0 \); \( 2x + 3y + 4z = 0 \) has a non-trivial solution is
Among the following complex ions, the one which is EPR active is:
The asymmetric nature of the visible absorption band of \( [\text{Ti(H}_2\text{O})_6]^{3+ \) is due to}
Which of the following will have the lower CO stretching frequency?
The alkali metals dissolve in liquid ammonia, it is found that
The pair of compounds having the same hybridization for the central atom is:
One mole of a monatomic ideal gas is expanded by a process described by \( PV^3 = C \), where \( C \) is a constant. The heat capacity of the gas during the process is given by (R is the gas constant)
An unpolarized beam of intensity \( I_0 \) is incident on a pair of Nicol’s prism making an angle of 60 degrees with each other. The intensity of the light emerging from the pair is
The dimensions of the area \( A \) of a black hole can be written in terms of the universal constant \( G \), its mass \( M \), and the speed of light \( c \) as \( A = G^\alpha M^\beta c^\gamma \). Here
One mole of a monatomic ideal gas is expanded by a process described by \( PV^3 = C \), where \( C \) is a constant. The heat capacity of the gas during the process is given by (R is the gas constant)
A certain p-n junction, having a depletion region of width 20mm was found to have a breakdown voltage of 100V. If the width of the depletion region is reduced to 1 mm during its production, then it can be used as a Zener diode for voltage regulation of
For the differential equation given below, which one of the following options is correct? \[ \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0, \quad 0 \leq x \leq 1, 0 \leq y \leq 1 \]
The divergence of the curl of a vector field is:
If two unbiased coins are tossed, then what is the probability of having at least one head?

Let a spherical block of ice at -7 °C be exposed to atmospheric air at 30 °C with the gravitational direction as shown in the figure below. What will be the overall direction of air flow in this situation?


 

In a laboratory experiment using a scaled down model to measure scour at a bridge pier, the Froude number is important. The ratio of the prototype length to the model length is 100. If the velocity of the model is 1 m/s, the velocity (in m/s) of the prototype is:
In a psychrometric chart, one axis represents dry-bulb temperature. The axis that is perpendicular to the dry-bulb temperature axis represents:
Among the following surface hardening processes, steel is heated to the lowest temperature in:
The welding process commonly used for fabricating tailor-welded blanks of dissimilar thickness for automotive applications is:
The yield stress of a metal in uniaxial tension is 200 MPa. According to von Mises yield criterion, the yield stress (in MPa) of the metal in pure shear is closest to:
In computer aided design (CAD), solid models can be constructed using:
Ceramics and glass are machined by:
When assembled, the hole \(30^{+0.030}_{0.000}\) mm and shaft \(30^{+0.020}_{-0.020}\) mm will result in:

A rigid circular disc of radius \(r\) (in m) is rolling without slipping on a flat surface as shown in the figure below. The angular velocity of the disc is \(\omega\) (in rad/ssuperscript{-1}). The velocities (in m/ssuperscript{-1}) at points 0 and A, respectively, are: