List of practice Questions

What is the pH of a solution if the concentration of $ \text{H}^+ $ ions is $ 1 \times 10^{-5} $ mol/L?

Two bikes were sold for a total of Rs.1,50,000. One bike was sold at $33\frac{1}{3}$% loss and the other at 20% profit. The cost price of the first bike is equal to the selling price of the other bike. Find the overall loss.

Describe the structure and working of a sparged stirred-tank bioreactor.

A force of 49 N acts tangentially at the highest point of a sphere (solid of mass 20 kg) kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is:

Choose the option that correctly matches the items in Group 1 with those in Group 2.

Assertion (A): Cu-T, Cu-7 and LNG-20 are the most widely used copper-releasing IUDs.
Reason (R): Cu-ions in IUDs effectively suppress sperm motility and the fertilising capacity of sperms.

Solve the equation $4x^2 - 9x + 3 = 0$, using quadratic formula.

Consider a process with transfer function: \[ G_p = \frac{2e^{-s}}{(5s + 1)^2} \] A first-order plus dead time (FOPDT) model is to be fitted to the unit step process reaction curve (PRC) by applying the maximum slope method. Let $ \tau_m $ and $ \theta_m $ denote the time constant and dead time, respectively, of the fitted FOPDT model. The value of $ \frac{\tau_m}{\theta_m} $ is __________ (rounded off to 2 decimal places).
Given: For $ G = \frac{1}{(\tau s + 1)^2} $, the unit step output response is: \[ y(t) = 1 - \left(1 + \frac{t}{\tau}\right)e^{-t/\tau} \] The first and second derivatives of $ y(t) $ are: \[ \frac{dy(t)}{dt} = \frac{t}{\tau^2} e^{-t/\tau} \] \[ \frac{d^2y(t)}{dt^2} = \frac{1}{\tau^2} \left(1 - \frac{t}{\tau}\right) e^{-t/\tau} \]

Assertion (A): n-Butyl chloride has higher boiling point than n-Butyl bromide.
Reason (R): C—Cl bond is more polar than C—Br bond.

Two cells of emf 10 V each, two resistors of 20 $ \Omega $ and 10 $ \Omega $, and a bulb B of 10 $ \Omega $ resistance are connected together as shown in the figure. Find the current that flows through the bulb.

If $ y = y(x) $ is the solution of the differential equation, \[ \sqrt{4 - x^2} \frac{dy}{dx} = \left( \left( \sin^{-1} \left( \frac{x}{2} \right) \right)^2 - y \right) \sin^{-1} \left( \frac{x}{2} \right), \] where $ -2 \leq x \leq 2 $, and $ y(2) = \frac{\pi^2 - 8}{4} $, then $ y^2(0) $ is equal to:

If 'QUICK' is written as 'RYRSJ', how is 'DELHI' written in that code?

Which would be the proper order of the following in ascending order?
Trillion
Thousand
Billion
Hundred
Million

An electrical wire of 2 mm diameter and 5 m length is insulated with a plastic layer of thickness 2 mm and thermal conductivity $ k = 0.1 $ W/(m·K). It is exposed to ambient air at 30°C. For a current of 5 A, the potential drop across the wire is 2 V. The air-side heat transfer coefficient is 20 W/(m²·K). Neglecting the thermal resistance of the wire, the steady-state temperature at the wire-insulation interface __________°C (rounded off to 1 decimal place).

GIVEN:
Kinematic viscosity: $ \nu = 1.0 \times 10^{-6} \, {m}^2/{s} $
Prandtl number: $ {Pr} = 7.01 $
Velocity boundary layer thickness: \[ \delta_H = \frac{4.91 x}{\sqrt{x \nu}} \]

Match the following airlines with the countries where they are headquartered.

Airlines	Countries
1. AirAsia	A. Singapore
2. AZAL	B. South Korea
3. Jeju Air	C. Azerbaijan
4. Indigo	D. India
5. Tigerair	E. Malaysia

Use integration to find the area of the region enclosed by the curve $y = -x^2$ and the straight lines $x = -3$, $x = 2$ and $y = 0$. Sketch a rough figure to illustrate the bounded region.

How many molecules of carbon dioxide are formed when 0.6 g carbon is burnt in air?

Let the triangle PQR be the image of the triangle with vertices $ (1, 3), (3, 1) $ and $ (2, 4) $ in the line $ x + 2y = 2 $. If the centroid of $ \Delta PQR $ is the point $ (\alpha, \beta) $, then $ 15(\alpha - \beta) $ is equal to :

A and B can complete a task in the ratio 3:2. If together they complete the task in 20 days, how long will A alone take?

A metal sheet is inserted between the plates of a parallel plate capacitor of capacitance C. If the sheet partly occupies the space between the plates, the capacitance:

Consider a part of an electrical network as shown below. Some node voltages, and the current flowing through the $ 3\,\Omega $ resistor are as indicated.
The voltage (in Volts) at node $ X $ is _________.

Suppose A and B are the coefficients of the 30th and 12th terms respectively in the binomial expansion of $ (1 + x)^{2n - 1} $. If $ 2A = 5B $, then $ n $ is equal to:

In a regular semi-circular arch of 2 m clear span, the thickness of the arch is 30 cm and the breadth of the wall is 40 cm. The total quantity of brickwork in the arch is _______ m$^3$. (rounded off to two decimal places)

All Cherry are Pink. Some Pink are made into cake. All cake is eaten. Banana is Pink. Examine the following statements:
I. Banana is a Cherry
II. Banana is not a Cherry
III. Banana may be made into cake
IV. Banana will definitely be made into a cake
V. If Banana is Cherry, then it will be eaten
Choose the most appropriate answer:

For the curve $ \sqrt{x} + \sqrt{y} = 1 $, find the value of $ \frac{dy}{dx} $ at the point $ \left(\frac{1}{9}, \frac{1}{9}\right) $.