The value of \(\int_{-1}^1 x^2[x] d x\) is:

Consider the following hypothesis test:
\(H _0: \mu \leq 3432\)
\(H _{ a }: \mu>3432\)
A sample of 96 provided a sample mean \(\bar{x}\) = 3648 and sample standard deviation s = 802 then the degree of freedom of t-distribution is:

Let \(A=\left[\begin{array}{cc}\frac{1}{3} & 2 \\ 0 & 2 x-3\end{array}\right]\) and \(B=\left[\begin{array}{cc}3 & 6 \\ 0 & -1\end{array}\right]\).
If AB = I (where I is an identity matrix of order 2), then the value of x is:

The derivative of \(\frac{\tan ^{-1} x}{1+\tan ^{-1} x}\) with respect to \(\tan ^{-1}\) is :

A machine costing \(\operatorname{Rs} 3,00,000\) will have its scrap value of \(\operatorname{Rs} 50, 000\). The company at present plans to put \(\operatorname{Rs} 36, 650\) per annum at the end of each year in a sinking fund at the rate \(5 \%\) per annum for the replacement of the machine after its useful life. Suppose the new machine will cost \(\operatorname{Rs} 4,00,000\) at that time, then the useful life (approx.) of the machine is :
[Given: \((1.4775)^{\frac{1}{8}} \approx 1.05\) ]

Two persons A and B throw a die alternately till one of them gets a 'three' and wins the game. The probability of A's winning if A starts first is :

If \(\vec{a}=3 \hat{i}-6 \hat{j}+\hat{k}\) and \(\vec{b}=2 \hat{i}-4 \hat{j}+\lambda \hat{k}\) are such that \(\vec{a} \| \vec{b}\), then \(3 \lambda+2=\)

Read the passage carefully and answer the questions.
Amines are considered to be derivatives of ammonia obtained by replacement of hydrogen atoms with alkyl or aryl groups. They are usually prepared from nitro compounds, halides, amides, imides etc. The presence of hydrogen bonding influences its physical properties. In alkylamines, a combination of electron releasing steric and hydrogen bonding factors influences the stability of substituted ammonium cations in protic polar solvents and thus affects the basic nature of amines. Alkyl amines are found to be stronger bases than ammonia which is more basic than water. Primary and secondary amines are engaged in intermolecular association due to hydrogen bonding. This intermolecular association is more in primary amines than in secondary amines. Tertiary amines do not have intermoleulcar association due to the absenceof hydrogen atom available for hydrogen bonding. Thus, the boiling point of amines depends on hydrogen bonding. In aromatic amines, electron releasing and withdrawing groups increase and decrease their basic character. Aryl diazonium salts usually obtained from arylamine undergo replacement of the diazonium group with a variety of nucleophile. Their coupling reaction of aryl diazonium salts with phenol or arylamine results in formation of dyes.
The most basic species in the following is

2-Bromopentane is heated with alcoholic KOH. Which is the correct statement for this reaction?
A. Only pent-2-ene is formed.
B. Only pent-1-ene is formed.
C. Both pent-2-ene and pent-1-ene are formed.
D. pent-2-ene will be major product as it is more stable.
Choose the correct answer from the options given below:

Which of the following has zero average value in a plane electromagnetic wave?
(A) Electric field
(B) Magnetic field
(C) Electric energy
(D) Magnetic energy
Choose the correct answer from the options given below:

Observe the given figure and answer the following questions:

Which of the following are not part of Innate immunity?
(A) Skin and acid in stomach
(B) B-Lymphocytes
(C) IgE and IgG
(D) Tears from eyes

Three charges of magnitude \( -2Q, -3Q \) and \( Q \) are located at \( (a, 0, 0), (3a, 0, 0) \) and \( (5a, 0, 0) \) respectively. What is the magnitude of electric flux due to these charges through a sphere of radius 4a with its centre at the origin?

50,000 different strains of rice are example of: