\(\int \frac{1}{(x+1)(x+2)} d x=\)

The area of the region bounded by parabola \(x^2=4 y\), straight line \(x=2\) and \(x\)-axis, is

\(\int \frac{1}{x^2\left(x^4+1\right)^{3 / 4}} d x\) is equal to :

Match List - I with List - II

List - I (Differential Equations)	List - II (Order and degree)
(A) \(ydx + xlog(y/x)dy - 2xdy = 0\)	(I) Order: 2, degree:1
(B) \(\left(\frac{d^3 y}{d x^3}\right)^2+3 \frac{d^2 y}{d x^2}+2\left(\frac{d y}{d x}\right)^4=y^2\)	(II) Order :1, degree:1
(C) \(\frac{d y}{d x}+\log \left(\frac{d y}{d x}\right)+x=y\)	(III) Order: 3, degree:2
(D) \(\left(\frac{d s}{d t}\right)^4+2 s \frac{d^2 s}{d t^2}=0\)	(IV) Order: 1, degree: Not defined

Choose the correct answer from the options given below:

The mean of the numbers obtained on throwing a die having 1 on three faces, 2 on two faces and 5 on one face is:

If the matrix \(A=\left[\begin{array}{ccc}0 & x+y & 1 \\ 3 & z & 2 \\ x-y & -2 & 0\end{array}\right]\) is skew-symmetric, then:

If \(\vec{a}, \vec{b}, \vec{c}\) are three mutually perpendicular unit vectors, then \(|\vec{a}+\vec{b}+\vec{c}|\) is equal to:

Read the given paragraph and answer the question:
Humans have 23 pairs of chromosomes. 22 pairs are exactly same in both males and females; these are the autosomes. A pair of X-chromosome are present in the female, whereas the presence of an X and Y chromosome are determinant of the male characteristic.
A number of disorders in human beings have been found to be associated with the inheritance of changed or altered genes or chromosomes. Broadly, genetic disorder may be grouped into two categories-Mendelian disorders and Chromosomal disorders.
A haemophilic man marries a normal woman. What is the possibility that their child have haemophilia?

Answer the question on the basis of passage given below :
For the transition elements
Sc \(\quad\) Ti \(\quad\) V \(\quad\) Cr \(\quad\) Mn\(\quad\) Fe \(\quad\) Co \(\quad\) Ni \(\quad\) Cu \(\quad\) Zn
Atomic numbers :
21 \(\quad\) 22 \(\quad\) 23 \(\quad\) 24 \(\quad\) 25 \(\quad\) 26 \(\quad\) 27 \(\quad\) 28 \(\quad\) 29 \(\quad\) 30 \(\quad\)
Which transition element has large enthalpy of atomization \(\Delta H_a^{\circ} \text{ (kJ mol}^{-1}\))?

Polygenic traits are controlled by:

The solution of the differential equation \(\frac{d y}{d x}=\frac{3 e^{2 x}+3 e^{4 x}}{e^x+e^{-x}}\) is:

Read the passage carefully and answer the questions
Alcohols and phenols are formed when a hydrogen atom in a hydrocarbon, aliphatic and aromatic respectively is replaced by - OH group. These are further classified on the basis of number of hydroxy groups and according to the hybridization of the carbon atom \(sp ^2\) or \(sp ^3\) to which the -OH group is attached. They find applications in industry as well as in day-to-day life. One of the most commercially obtained alcohol also known as wood spirit is obtained by destructive distillation of wood. Both alcohols and phenols are acidic in nature. The acidity of alcohols and phenols vary according to the nature of substituent(s) attached to them. Alcohols and phenols react with carboxylic acids, acid chlorides and acid anhydrides to form esters. Introduction of acetyl group in alcohols and phenols is called acetylation. Phenol undergo electrophilic aromatic substitution reaction because the -OH activates the benzene ring. It undergoes nitration, halogenation and sulphonation reactions.
Identiify the strongest acidic compound

Select the seeds with perisperm from the following options.