In a game of 100 points, A can give B 20 points and C 28 points. How many points can B give C?

If \(\left[\begin{array}{ccc}a-b & 0 & 0 \\ 0 & b-c & 0 \\ 0 & 0 & c-2\end{array}\right]\) is a scalar matrix such that a + b + c = 0, then, which of the following are TRUE?
(A) a = 0
(B) b = 0
(C) a = 1
(D) c = 1
Choose the correct answer from the options given below:

The value of the integral \(I=\int_0^1 \frac{1}{\sqrt{x^2+2 x+3}} d x\) is :

A random variable has the following probability distribution:\(\begin{array}{llllll}X= x_{-} i & 2 & 3 & 4 & 5 \\P\left(X=x \_i\right) & 4 k & k & 5 k & 2 k\end{array}\)The value of \(P(X<3)\) is

Consider \(f: R ^{+} \rightarrow[4, \infty)\) given by \(f(x)=x^2+4\)
(where \(R ^{+}\)is set of non negative real numbers) then \(f^{-1}(x)\) is :

In a 900 meters race, Ram gives Shyam a start of 150 meters and defeats him by 50 seconds. If the speed of Ram is 4.5 m/sec, then the speed of Shyam is

If the matrix \(\left[\begin{array}{ccc}0 & 7 & -12 \\ -7 & 0 & -5 \\ 2 a & 5 & 3 b\end{array}\right]\) is skew-symmetric, then the value of \((4 a+3 b)\) is :

The solution set of the linear inequation \(|4 x-3| \leq \frac{3}{4}\) is :

Answer the question on the basis of passage given below :
Aldehydes and ketones represent two essential classes of organic compounds which are extensively used in the synthesis of a wide variety of other organic molecules.
Due to the inherent polarity of the central carbonyl group, these substances readily undergo nucleophilic addition reactions.Broadly speaking, these addition reactions can be categorized into two types:
one in which simple addition of the nucleophilic reagent occurs across the \(> C = O\) bond, and the second type where the initial addition is subsequently followed by the elimination of a water molecule.
A variety of ammonia derivatives, including hydroxylamine, hydrazine, phenylhydraaine, 2, 4-dinitroplhenylhdrazine, and semicarbazide, all belong to this second category of reactions.
These specific derivatives are fundamentally used for the identification and definitive characterization of aldehydes and ketones. Significantly, both types of nucleophilic addition reactions are strongly influenced by both steric and electronic factors.
As a general rule, aliphatic aldehydes exhibit higher reactivity compared to aromatic aldehydes.
The aliphatic aldehydes demonstrate the ability to reduce both Fehling's solution and Tollen's reagent, whereas aromatic aldehydes are limited to reducing only Tollen's reagent.
In a similar manner to aldehydes, aromatic ketones are observed to be less reactive than aliphatic ketones towards all nucleophilic addition reactions.
In a separate context, phenols and carboxylic acids both exhibit acidic properties in nature.
Both classes of compounds readily dissolve in NaOH solution and cause blue litmus to turn red.
However, carboxylic acids stand out as much stronger acids than phenols and thus can decompose sodium bicarbonate \(\left( NaHCO _3\right)\) with the distinct evolution of \(CO _2\) gas, a reaction which phenols do not undergo.
It is important to note that both electron- donating and electron- withdrawing substituents significantly influence the acid strength of both aliphatic as well as aromatic carboxylic acids.
Furthermore, unlike all other common aliphatic acids, formic acid uniquely possesses reducing properties and simultaneously does not display the typical reactions characteristic of the alkyl group.
Carboxylic acid do not give the characteristic reaction of carbonyl group because:

A storage battery of EMF 10 V and internal resistance 1 \( \Omega \) is being charged by a 120 V dc supply using a series resistor of 21 \( \Omega \). What is the terminal voltage of the battery during charging ?

The feasible region of an LPP Max Z = 3x + 2y subject to \(x \geq 0, y \geq 0, x -2 y \leq 3\) is:

Answer the question on the basis of passage given below :
Adsorption is the phenomenon of attracting and retaining the molecules of a substance on the surface of a solid resulting into a higher concentration on the surface than in the bulk. The substance adsorbed is known as adsorbate and the substance on which adsorption takes place is called adsorbent. In physisorption adsorbate is held to the adsorbent by weak van der Waals forces and in chemisorption by strong chemical bond.
Out of Milk, butter, ice cream, fruit juice and lemonade. Identify the one which is not a colloid.

Match List - I with List - II. If \(A=\left|\begin{array}{ccc}3 & -2 & 3 \\ 2 & 1 & -1 \\ 4 & -3 & 2\end{array}\right|\)

List - I	List - II
(A) \(M_{23}\)	(I) -17
(B) \(A_{32}+a_{13}\)	(II) -1
(C) \(A\) (Determinant value)	(III) 0
(D) \(a_{13} A_{12}+a_{23} A_{22}+a_{33} A_{32}\)	(IV) 12

Choose the correct answer from the options given below :