Consider the LPP: Maximize \(Z=x+y\) subject to the constraints \(x+2 y \leq 70,2 x+y \leq 95, x, y \geq 0\). The optimal feasible solution is:

Two infinitely long parallel conductors carrying currents I 1 and I 2 are at distance d apart. The force \(F\) on length \(L\) of one conductor due to the other is :

If the corner points of Linear Programming Problem having objective function \(\operatorname{Max} z=2 x+y\) are \(O(0,0), A(30,0), B(20,30), C(0,50)\), then the optimal value will be at the point :

Time reversal test is satisfied by:

The vector in the direction of the vector \(2 \hat{i}-\hat{j}-2 \hat{k}\) that has magnitude 9 units is :

Consider a L.P.P, Maximize \(Z=3 x+5 y\) subject to constraints \(2 x+6 y \leq 6, x-y \geq 0, x \geq 0, y \geq 0\). Then which of the following are true?
(A) The feasible region of L.P.P is bounded region
(B) The corner points of the feasible region are \((0,0),(2,2),(0,1)\)
(C) Maximum value of Z is 9
(D) Point \((1,3)\) lies in the feasible region
Choose the correct answer from the options given below :

Let \(f: R \rightarrow R\) be defined as \(f(x)=3 x+4\). Choose the correct answer.

A negatively charged object A is repelled by another charged object B. However, an object C is attracted to object B.
Which of the following is the most probable for the charge of object C?

Answer the question on the basis of passage given below:
Proteins are the polymers of about twenty different a-amino acids which are linked by peptide bonds. Proteins perform various structural and dynamic functions in the organisms. Proteins which contain only a-amino acids are called simple proteins. The secondary or tertiary structure of proteins get disturbed on change of pH or temperature and they are not able to perform their functions. This is called denaturation of proteins. Enzymes are biocatalysts which speed up the reactions in biosystems. Vitamins are accessory food factors required in the diet. They are classified as fat soluble (A, D, E and K) and water soluble (B group and C). Deficiency of vitamins leads to many diseases. Nucleic acids are the polymers of nucleotides which in turn consist of a base, a pentose sugar and phosphate moiety.Nucleic acids are responsible for the transfer of characters from parents to offsprings. There are two types of nucleic acids DNA and RNA. DNA contains a five carbon sugar molecule called 2-deoxyribose whereas RNA contains ribose.
During denaturation of proteins:

A container contains 48 litres of buffalo milk. From this container 8 litres of buffalo milk was taken out and replaced with cow milk. This process was repeated further 3 more times. How much buffalo milk is there in the container now ?

"The correct statement regarding the basicity of arylamines is :
A. Arylamines are generally more basic than alkylamines because of aryl group.
B. Aryl amines are generally more basic than alkylamines because the nitrogen atom in arylamines is 𝑠⁢𝑝 hybridised.
C. Aryl amines are generally less basic than alkylamines because the lone pair of electrons of nitrogen are delocalised by interaction with the pi electrons of the aromatic ring.
D. Aryl amines are generally more basic than alkylamines because the lone pair of electron of nitrogen are not delocalised by interaction with the pi electrons of aromatic ring.
E. Aryl amines are generally weaker bases than alkylamines due to electron withdrawing nature shown by aryl group.
Choose the correct answer from the options given below:"

Curd is at \(80^{\circ} F\),five minutes later it came down at \(60^{\circ} F\).
After another 5 minutes, its temperature became \(50^{\circ} F\).
Given that the rate of change of temperature is proportional to (T - S).
where S is temperature of surroundings and T is temperature of the curd at any time t.
Then the temperature of the surroundings is :

A die is tossed once. If the random variable X is defined as \(\mathbf{X}=\left\{\begin{array}{ll}1, & \text { if the die result in an odd number } \\ -1, & \text { if the die result in an even number }\end{array}\right.\) then the variance of X is