The maximum value of a LPP \(z=3 x+4 y\) subject to the constraints: \(x+y \leq 6, x \geq 0, y \geq 0\) is:

The probability that it will rain on any particular day is \(50 \%\). The probability that it rains only on the first 4 days of the week is :

The minimum value of \(Z = 2x + y\) subjected to \(x + y ≥ 10, 2x + 3y ≤ 26, x, y ≥ 0\) is

Given differential equation,
\(\left(1+y^2\right) d x=\left(\tan ^{-1} y-x\right) d y\)
then which of the following is/are true?
(A) Integrating factor \(=\tan ^{-1} x\)
(B) Integrating factor \(=\tan ^{-1} y\)
(C) Integrating factor \(=e^{\tan ^{-1} y}\)
(D) Degree \(=1\)
Choose the correct answer from the options given below :

The maximum value of Z = 3x + y subject to the constraints
x + y \(\le\) 7,
x \(\le\) 5,
y \(\le\) 4,
x \(\ge\) 0, y \(\ge\) 0 is:

The sides of an equilateral triangle are increasing at the rate of 2 cm/s. The rate at which the area increases, when side is 10 cm is:

For the given five values 15, 24, 18, 33, 42, the three-year moving averages are :

Match List I with List II.

LIST I	LIST II
A. Haemophilus influenzae	I. Elephantiasis
B. Rhino viruses	II. Ringworm
C. Wuchereria bancrofti	III. Common cold
D. Trichophyton	IV. Pneumonia

Choose the correct answer from the options given below:

Observe the given figures and answer the question

Miller's experiment resulted in the acceptance that the formation of life was
preceded by:

Read the passage carefully and answer the questions
Alcohols and phenols are formed when a hydrogen atom in a hydrocarbon, aliphatic and aromatic respectively is replaced by -OH group. These are further classified on the basis of number of hydroxy groups and according to the hybridization of the carbon atom \(sp ^2\) or \(sp ^3\) to which the -OH group is attached. They find applications in industry as well as in day-to-day life. One of the most commercially obtained alcohol also known as wood spirit is obtained by destructive distillation of wood. Both alcohols and phenols are acidic in nature. The acidity of alcohols and phenols vary according to the nature of substituent(s) attached to them. Alcohols and phenols react with carboxylic acids, acid chlorides and acid anhydrides to form esters. Introduction of acetyl group in alcohols and phenols is called acetylation. Phenol undergo electrophilic aromatic substitution reaction because the -OH activates the benzene ring. It undergoes nitration, halogenation and sulphonation reactions.
Which compound is also known as 'wood spirit'?

Let \(A=\left[\begin{array}{ccc}1 & 2 & 1 \\ -1 & 3 & 2 \\ 2 & 4 & 1\end{array}\right]\) and \(M_{i j}, A_{i j}\) respectively denote the minor, co-factor of an element \(a_{i j}\) of matrix \(A\), then which of the following are true?
(A) \(M_{22}=-1\)
(B) \(A_{23}=0\)
(C) \(A_{32}=3\)
(D) \(M_{23}=1\)
(E) \(M_{32}=-3\)
Choose the correct answer from the options given below:

Match List-I with List-II

List-I	List-II
(A) Resistive Circuit	(I) No power dissipation
(B) Purely inductive or capacitive circuit	(II) Maximum power dissipated because \( X_L = X_C \)
(C) LCR series circuit	(III) Power dissipated only in resistor
(D) Power dissipated at resonance in LCR circuit	(IV) Maximum power dissipation

Choose the correct answer from the options given below :

The matrix \(X\) in the equation \(A X=B\), such that \(A=\left[\begin{array}{ll}1 & 3 \\ 0 & 2\end{array}\right]\) and \(B=\left[\begin{array}{cc}1 & -1 \\ 0 & 2\end{array}\right]\) is given by