List of practice Questions

What is the ratio of the wavelength of the Lyman series limit to that of the Paschen series limit in the hydrogen spectrum?
Let $ \vec{a} = \hat{i} + 2 \hat{j} + \hat{k} $ and $ \vec{b} = 2 \hat{i} + \hat{j} - \hat{k} $. Let $ \hat{c} $ be a unit vector in the plane of the vectors $ \vec{a} $ and $ \vec{b} $ and perpendicular to $ \vec{a} $. Then such a vector $ \hat{c} $ is:
Two resistors, 4Ω and 6Ω, are connected in parallel, and this combination is connected in series with a 2Ω resistor to a 12V battery. What is the total power dissipated?
A spherical air bubble is formed inside a liquid (like water). The radius of the bubble is 0.5 mm, and the surface tension of the liquid is 0.072 N/m. What is the pressure inside the bubble relative to the outside pressure?
Arun, Bashir and Joseph were partners in a firm sharing profits and losses in the ratio of 5 : 3 : 2. They admitted Daksh as a new partner who acquired his share entirely from Arun. If Arun sacrificed \( \frac{1}{5} \)th from his share to Daksh, Daksh's share in the profits of the firm will be :
If $$ f(x) = \int \frac{1}{x^{1/4} (1 + x^{1/4})} \, dx, \quad f(0) = -6, \text{ then } f(1) \text{ is equal to:} $$ 
The reverse saturation current (I0) of a silicon diode at 27°C is \( 10^{-6} \) A. What will be the approximate value of I0 at 67°C? (Assume \( I_0 \) doubles for every 10°C rise in temperature)

A project involves eight activities with the precedence relationship and duration as shown in the table below. The slack for the activity D is __________ hours (answer in integer). 


 

A company uses 3000 units of a part annually. The units are priced as given in the table below. It costs ₹150 to place an order. Carrying costs are 40 percent of the purchase price per unit on an annual basis. The minimum total annual cost is ₹ _________ (rounded off to 1 decimal place).


 

Cylindrical workpieces of diameter 60 mm and length 400 mm are machined on a lathe at a cutting speed of 25 m/min and a feed of 0.2 mm/rev. The Taylor’s tool life parameters \(C\) and \(n\) for this setup are 75 and 0.25, respectively. The tool changing time is 3 minutes. With a labor and overhead cost of ₹5 per minute, the tool changing cost per piece is ₹_________ (rounded off to 2 decimal places).

Two plates of thickness 10 mm each are to be joined by a transverse fillet weld on one side and the resulting structure is loaded as shown in the figure below. If the ultimate tensile strength of the weld material is 150 MPa and the factor of safety to be used is 3, the minimum length of the weld required to ensure that the weld does NOT fail is ____________ mm (rounded off to 2 decimal places).


 

An offset slider-crank mechanism is shown in the figure below. The length of the stroke of the slider is __________ mm (rounded off to nearest integer).


 

Which organelle is primarily responsible for producing ATP in a cell?
In a DNA molecule, which of the following base-pairings is correct?

An isotropic brittle material is tested in the universal testing machine. The stress-strain diagram for the material shows a bi-linear elastic behavior as shown in the figure given below. The strain energy density is _________ MJ m\(^{-3}\) (rounded off to 2 decimal places).


 

Which of the following processes occurs during the second meiotic division (Meiosis II)?

A simply supported beam of length 1 m is subjected to a uniformly distributed bending moment of 1 N m per meter throughout the length as shown in the figure. The bending moment at the mid-point of the beam is __________ N m (rounded off to the nearest integer).


 

Which of the following factors does NOT affect the rate of an enzyme-catalyzed reaction?
In a monohybrid cross between two heterozygous pea plants (Pp x Pp), what is the expected phenotypic ratio of the offspring?
Which of the following is an example of a primary consumer in an ecosystem?
Which part of the human brain is primarily responsible for regulating basic life functions, such as heart rate and breathing?
Which of the following is the correct equation for photosynthesis?
Which of the following is the primary function of the human respiratory system?
In the reaction: \[ \text{Zn(s)} + \text{CuSO}_4(aq) \rightarrow \text{ZnSO}_4(aq) + \text{Cu(s)} \] Which of the following is the correct oxidation half-reaction?
The energy of the nth orbit of the hydrogen atom is given by: \[ E_n = - \frac{13.6}{n^2} \, \text{eV} \] What is the energy of the second orbit (n = 2) of the hydrogen atom?