If the feasible region R for a linear programming problem is bounded, then the objective function \(Z=A x+B y\) has

The shortest distance between the following lines :
\(\vec{r}=(\hat{i}+\hat{j}-\hat{k})+s(2 \hat{i}+\hat{j}+\hat{k})\)
\(\vec{r}=(\hat{i}+\hat{j}+2 \hat{k})+t(4 \hat{i}+2 \hat{j}+2 \hat{k})\), where \(s\) and \(t\) are scalars, is :

Which one of the following options is incorrect?
For a square matrix \(A\) in the matrix equation \(A X=B\).

Let \(\left|\begin{array}{ll}3 & y \\ x & 1\end{array}\right|=\left|\begin{array}{ll}3 & 2 \\ 4 & 1\end{array}\right|\) and \(x, y\) are natural numbers, then the number of solutions for the system is :

Magnetic moment of a thin bar magnet is ' M '. If it is bent into a semicircular form, its new magnetic moment will be

If \(A\) is a square matrix of order 2 , then \(|\operatorname{adj} A|\) is equal to:

The total cost \(C(x)\) in Rupees associated with the production of \(x\) units of an item is given by
\(C(x)=0.007 x^3+26 x^2+15 x+400\) 
The marginal cost when 10 items are produced is:

Find the value of \(\text{E}^{\circ}\) in the missing link in the following diagram.
\(Fe ^{3+} \xrightarrow{E_1^{\circ}=0.77 V} Fe ^{2+} \xrightarrow{E_2^{\circ}=-0.44 V} Fe\)
\(Fe ^{3+} \xrightarrow{E_3^{\circ}=?} Fe\)

Read the paragraph given below and answer the question.
Insulin used for diabetes was earlier extracted from slaughtered cattle and pigs. Insulin from an animal source, though caused some patients to develop allergy or other type of reactions. Insulin consists of two short polypeptide chains: chain A and chain B, that are linked bridges. In mammals, including human, insulin is synthesised as a pro-hormone.
Bonds which link 'A' and 'B' peptide chains of human insulin are

Match List-l with List-ll:

List-l (Representation)	List-II (Common name)
(A) \(10^{-6} M\) solution	(I) Decimolar solution
(B) 0.1 M solution	(II) Micromolar solution
(C) 0.001 M solution	(III) Millimolar solution
(D) 0.01 M solution	(IV) Centimolar solution

Choose the correct answer from the options given below:

Read the paragraph and answer the question.
Broadly, genetic disorders may be grouped into two categories - Mendelian disorders and Chromosomal disorders. Mendelian disorders are mainly determined by alteration or mutation in the single gene. These disorders are transmitted to the offspring on the same lines as we have studied in the principle of inheritance. The trait may also be linked to the sex chromosome as in case of haemophilia. It is evident that this X-linked recessive trait shows transmission from carrier female of male progeny.
Which of the following disease is a result of aneuploidy?
(A) Turner's Syndrome
(B) Klinefelter's Syndrome
(C) Down's Syndrome
(D) Phenylketonuria
Choose the correct answer from the options given below:

Given \(p \neq 1\), then \(\int \frac{d x}{x\left(\log _e x\right)^p}\) is equal to:

In the given figure, a diode D is connected to an external resistance R = 100 \( \Omega \) and an emf of 2.5 V. During forward bias, if the barrier potential developed across the diode is 0.6 V, the current in the circuit will be