If \(\left|\begin{array}{ccc}-1 & 1 & 0 \\ a & b & 1 \\ 1 & 2 & 1\end{array}\right|\) is a singular matrix, then the relation between a and b is:

The value of \(\left|\begin{array}{cc}a+i b & c+i d \\ -c+i d & a-i b\end{array}\right|\) is:

Which of the following statement are correct?
(A) \(A=\left[a_{i j}\right]_{n \times n}\) is a diagonal matrix if \(a_{i j}=0\) when \(i=j\)
(B) A square matrix \(A=\left[a_{i j}\right]\) is called a symmetric matrix if \(a_{i j}=a_{j i}\) for all \(i, j\)
(C) A square matrix \(A=\left[a_{i j}\right]\) is called a skew-symmetric matrix if \(a_{i j}=-a_{j i}\) for all \(i, j\)
(D) For every square matrix A, there exist an identity matrix of the same order such that \(I A=A I=I\)
Choose the correct answer from the options given below:

The general solution of the differential equation \(x d y+e^{-y} d x=x e^{x-y} d x\) is (given C is constant of integration)

The area of the region bounded by the lines x = 2y + 3, x = 0, y = 1 and y = - 1 is:

The general solution of differential equation \(\frac{dy}{dx} - xy = e^{\frac{x^2}{2}}\) 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 :

Answer the question on the basis of passage given below :
Living systems are made up of various complex bio-molecules like carbohydrates, proteins, nucleic acids, lipids etc. Proteins and carbohydrates are essential constituents of our food. Carbohydrates are primarily produced by plants and form a very large group of naturally occurring organic compounds. Some common examples are cane sugar, glucose, starch etc.
Match List I with List II

LIST I	LIST II
A. Carbohydrates	I. Amide linkage
B. Proteins	II. Ester linkage
C. Nucleic acids	III. Ether linkage
D. Lipids	IV. phosphodiester linkage

Choose the correct answer from the options given below:

Oral contraceptive pills used by females, function through:

"Answer the question on basis of passage given below:
\(G = \frac{\kappa A}{l}\) =k(both \(A\) and \(l\) are unity in their appropriate units in m or cm)
Molar conductivity of a solution at a given concentration is the conductance of the volume \(V\) of solution containing one mole of electrolyte kept between two electrodes with area of cross section \(A\) and distance of unit length (\(l\)). Therefore,
\(\Lambda_m = \frac{\kappa A}{l}\)
Since \(l = 1\) and \(A = V\) (volume containing 1 mole of electrolyte),
\(\Lambda_m = \kappa V\)
Molar conductance for 0.2 M AgCl solution showing resistance of 40 \(\Omega\) in a cell having distance between electrodes as 2 cm and surface area of 4 cm\(^2\) will be:"

Consider the relation R in the set Z of integers which is given by \(R=\{(a, b): 2\) divides \(a-b\}\).
Choose the correct option for the relation \(R\) :

Which one of the following hormones is produced only during pregnancy?

Monochromatic lights of wavelengths \(6 2 0 ~ n m\) and \(6 2 6 ~ n m\), respectively are used to study diffraction at a single slit of aperture \(0 . 7 ~ m m\). The distance between the slit and the screen is 1.8 m . The separation between the positions of the first maxima of the diffraction pattern obtained in the two cases is