The value of integral \(\int \frac{\cos 2 x-\cos 2 \alpha}{\cos x-\cos \alpha} d x\), where \(\alpha\) is a constant is :

If the objective function for an L.P.P. is \(z=3 x-4 y\) and the corner points for the bounded feasible region are \((0,0),(5,0),(6,5),(6,8),(4,10)\) and \((0,8)\), then the minimum value of \(z\) occurs at :

The area of the region \(\left\{(x, y): y \geq x^2\right.\) and \(\left.y \leq|x|\right\}\) is

The value of \(\sin \left(2 \sin ^{-1} \frac{4}{5}\right)\) is given by :

The area of the region enclosed between the two circles \(x^2+y^2=1\) and \((x-1)^2+y^2=1\) is

Three mangoes and three apples are kept in a box. If two fruits are selected at random from the box, the probability that the selection will contain one mango and one apple is :

If \((x+1) e^y=1\), then :

Consider two independent events A and B such that P(A) = 0.3, P(B) = 0.6.
match List - I with List - II

List - I	List - II
(A) P(A and B)	(I) 0.28
(B) P(A and not B)	(II) 0.18
(C) P(A or B)	(III) 0.12
(D) P(neither A nor B)	(IV) 0.72

Choose the correct answert from the option given below :

Which of the following is the most species-rich taxonomic group among animals?

The karyotype of an individual was found to be 44 + XXY. The individual is suffering from which of the following disorder?

Medical termination of pregnancy (MTPs) are considered safe during the -

Read the passage carefully and answer the questions
Amines are considered as derivatives of ammonia obtained by replacement of hydrogen atoms with alkyl or aryl groups. In nature they occur among proteins, vitamins, alkaloids and hormones. These can be primary, secondary or tertiary depending on the number of hydrogen groups replaced. They can be prepared from nitro compounds, alkyl halides, nitriles, amides etc. Due to unshared pair of electrons they behave as Lewis bases. Influence of the number of hydrogen atoms at nitrogen atom is displayed in physical properties such as solubility, boiling point and chemical reactions including basicity. Basic character of amines is expressed in terms of their K, and pK; values. Three classes of amines can be distinguished with p-toluene sulphonyl chloride which reacts with primary and secondary mines. Amino group when ttached to benzene ring behaves as an activating and ortho para directing group.
Give the IUPAC name of the compound

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.
Carbohydrates are also known as Saccharides because