The area bounded by \(x = 1, x = 2, xy = 1\) and x-axis is :

Match List - I with List - II.

LIST I	LIST II
A. \(\left[1+\left(\frac{d y}{d x}\right)^2\right]=\left(\frac{d^2 y}{d x^2}\right)^2\)	I. order \(=2\), degree \(=2\)
B. \(\frac{d^3 y}{d x^3}-3 \frac{d^2 y}{d x^2}+2\left(\frac{d y}{d x}\right)^4=y^4\)	II. order \(=3\), degree \(=2\)
C. \(\left(1+\frac{d y}{d x}\right)^3=\left(\frac{d^3 y}{d x^3}\right)^2\)	III. order \(=2\), degree \(=1\)
D. \(\left[1+\left(\frac{d y}{d x}\right)^2\right]^?=\frac{d^2 y}{d x^2}\)	IV. order \(=3\), degree \(=1\)

Choose the correct answer from the option given below:

If the matrix \(\left(\begin{array}{ccc}2 & 4 & 5 \\ 4 & 2 & 3 \\ K & 3 & 2\end{array}\right)\) is a symmetric matrix, then the value of \(K\) is :

The differential equation that represents the family of lines parallel to x + y = 2 is:

If \(f(x)=\left\{\begin{array}{cl}\frac{k \cos x}{\pi-2 x}, & x \neq \frac{\pi}{2} \\ 3, & x=\frac{\pi}{2}\end{array}\right.\) is continuous at \(x=\frac{\pi}{2}\), then \(k\) is :

If \(x=a \sin ^3 t\) and \(y=a \cos ^3 t\), then \(\frac{d y}{d x}\) is equal to :

Let \(A=\left[\begin{array}{ccc}0 & 2 & -5 \\ -2 & 0 & -7 \\ 5 & 7 & 0\end{array}\right]\) and \(B=\left[\begin{array}{ccc}1 & 5 & 8 \\ 2 & 7 & 4 \\ 3 & 9 & 10\end{array}\right]\) then |AB|=

The aqueous solutions of the following salts were electrolyzed for 30 min with a current of 20 amp. Arrange the
following in the increasing order of the amount of metal deposited at the cathode.
(A) \(\mathrm{WCl}_6\)
(B) \(\mathrm{ZnSO}_4\)
(C) \(\mathrm{HfCl}_4\)
(D) \(\mathrm{AgNO}_3\)
(Atomic mass of: W =184 u, Zn = 65 u, Hf = 178 u and Ag = 108u)
Choose the correct answer from the options given below:

In a linear programming problem, the constraints on decision variables x and y are \(y-2 x \leq 0, y \geq 0,0 \leq x \leq 5\). The feasible region of the above problem :

A cell of emf 1.1 V and internal resistance \(0.5 \Omega\) is connected to a \(0.5 \Omega\) wire. Another cell of same emf is added in series, but current remains unchanged. The second cell's internal resistance is :

Read the following paragraph and answer the given questions.
Cancer detection is based on biopsy and histopathological studies. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs. Do you know why mother's milk is considered very essential for the new-born infant? The yellowish fluid colostrum secreted by mother during the initial days of lactation has abundant antibodies (IgA) to protect the infant. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal. The exaggerated response of the immune system to certain antigens present in the environment is called allergy. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Drugs like barbiturates, amphetamines, benzodiazepines, and other similar drugs, that are normally used as medicines to help patients cope with mental illnesses like depression and insomnia, are often abused. Morphine is a very effective sedative and painkiller, and is very useful in patients who have undergone surgery.
A pregnant female is advised not to discard the yellowish fluid called colostrum, secreted during the initial days of lactation, because it is rich in:

The common region determined by all constraints of a Linear programming problem is called:

Which of the following hormone is not secreted by placenta ?