List of practice Questions

Paraga company decided to raise 40% of funds through debentures. Which financial decision is it?
Gang Plank is used in the case of Emergency.
Rules are specific statements that inform what is to be done.
Let $A = \{2, 3, 5, 7, 9\}$. Let $R$ be the relation on $A$ defined by $xRy$ if and only if $2x \le 3y$. Let $l$ be the number of elements in $R$, and $m$ be the minimum number of elements required to be added in $R$ to make it a symmetric relation. Then $l + m$ is equal to :

A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 

(i) Express \(y\) as a function of \(x\) from the given equation of ellipse. 
(ii) Integrate the function obtained in (i) with respect to \(x\). 
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration. 
OR 
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\). 
 

Consider the following reaction sequence.

If \( g(x) = 3x^2 + 2x - 3 \), \( f(0) = -3 \) and \( 4g(f(x)) = 3x^2 - 32x + 72 \), then \( f(g(2)) \) is equal to:
Mention two safety procedures for safe and clean handling of the accommodation area.
If \( \alpha \) and \( \beta \) (\( \alpha<\beta \)) are the roots of the equation \( (-2 + \sqrt{3})(\sqrt{x} - 3) + (x - 6\sqrt{x}) + (9 - 2\sqrt{3}) = 0 \), \( x \ge 0 \), then \( \sqrt{\frac{\beta}{\alpha}} + \sqrt{\alpha\beta} \) is equal to:
The pulley shown in figure is made using a thin rim and two rods of length equal to diameter of the rim. The rim and each rod have a mass of $M$. Two blocks of mass of $M$ and $m$ are attached to two ends of a light string passing over the pulley, which is hinged to rotate freely in vertical plane about its center. The magnitudes of the acceleration experienced by the blocks is _________ (assume no slipping of string on pulley).
In SQL, which clause is used to filter the results of an aggregate function?
Let the area of the region bounded by the curve \( y = \max \{ \sin x, \cos x \} \), lines \( x = 0 \), \( x = 3\pi/2 \), and the x-axis be A. Then, \( A + A^2 \) is equal to :
If the null hypothesis \(H_0\) is rejected when it is actually true, what type of error has been committed?
What are the reagents used to rectify ``over-bluing'' in white cotton fabrics?
Which apparel production system relies on teamwork and shared responsibility for output quality?
Sucrose is classified as a non-reducing sugar because it lacks what specific chemical feature?
Which research prerequisite involves defining the roadmap for data collection and analysis?
What is the process of removing grease or dirt from wool through washing called?
Which clause in the Consumer Protection Act (2019) defines the rights of a consumer?
A diet where food is administered directly into the veins is known as what?
Which term in the history of Indian costumes was used in the Vedic age to describe a lower garment?
What is the primary difference between the sugars found in DNA and RNA?
Which developmental psychologist emphasized the ``Zone of Proximal Development''?
When was the POSHAN Abhiyaan (National Nutrition Mission) launched by the Indian government?
Which type of dye forms a covalent bond with the fiber?