Match List-I with List-II

List-I (Integral)	List-II (Value)
(A) \(\int_{-1}^1(|x|+1) d x\)	(I) 0
(B) \(\int_{-2}^2|x+1| d x\)	(II) 2
(C) \(\int_{-1}^1 3|x|^2 d x\)	(III) 5
(D) \(\int_{-1}^1 x|x| d x\)	(IV) 3

Choose the Correct answer from the options given below :

The linear constraints, for which the shaded area in the figure is the feasible region of an LPP, are:

For the linear programming problem (LPP),
Maximize \(Z=4 x+y\)
Subject to:
\(x+y \leq 5\)
\(3 x+y \leq 9\)
\(x, y \geq 0\)
Which of the following are NOT true?
(A) The given LPP has unbounded feasible region.
(B) The corner points of the feasible region are \((0,0),(0,5),(3,2)\) and \((3,0)\).
(C) The optimal value of the objective function is 12.
(D) The given LPP has a unique optimal solution.
Choose the correct answer from the options given below:

Which of the following statement(s) is/are TRUE?
(A) Skew symmetric matrix of even order is always symmetric
(B) Skew symmetric matrix of odd order is non-singular
(C) Skew symmetric matrix of odd order is singular
(D) Skew symmetric matrix is always square matrix
Choose the correct answer from the options given below:

If \(|\vec{a}|=7\) then \(|3 \vec{a}|\) is:

The straight line \(\frac{x+3}{3}=\frac{y+2}{4}=\frac{z+1}{0}\) is

Consider the following data

Year (X)	2014	2016	2018	2020	2022	2024
Profit(in Rs. Thousand) (Y)	7	9	10	12	14	14

Then for the above data the equation of straight line trend by method of least square is given by:

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.
Argyrol is a medicine used for

Benzene ring in phenol is expected to give the characteristic substitution or replacement reactions i.e. halogenation, nitration, sulphonation, alkylation etc. In these reactions, the attacking reagent is electrophile. The phenolic group activates the ortho and para positions in the ring due to conjugation. Disubstitution reactions are quite fast as the electron density in the ring has increased considerably. Phenols do not respond to nucleophilic substitution reactions as it is influenced by phenolic group.
Victor Meyer test gives following observations. Match List I with List II:

List-I	List-II
A. Blood red colouration	I. Tertiary alcohol
B. Blue colouration	II. Phenols
C. Colourless solution	III. Primary alcohol
D. Violet colouration with \(\text{FeCl}_3\)	IV. Secondary alcohol

Choose the correct answer from the options given below:

The resonant frequency of a series LCR circuit with L = 3H, \( C = 27 \mu F \) and R = 20 \( \Omega \) will be:

A spherical conducting shell of inner radius \( r_1 \) and outer radius \( r_2 \) has a charge \( Q \). A charge \( q \) is placed at the centre of the shell. The surface charge density on outer surface of the shell is :

Which of the following compound(s) does not react with Fehling solution?
(A) \(CH _3 CHO\)
(B) \(Ph - CHO\)
(C) Glucose
(D)

choose the correct answer from the options given below:

The integral \(\int \frac{x^4+2}{x^2+1} d x\) is equal to