\(\int \frac{\left(x^4-x\right)^{1 / 4}}{x^5} d x\) is equal to

If \(A=\left[\begin{array}{ccc}x+z & 2 & -3 \\ x & 0 & 4 \\ 3 & x-y & 0\end{array}\right]\) is a skew-symmetric matrix, then which of the following are true?
(A) \(y>z>x\)
(B) \(x>y\)
(C) \(x+y+z>0\)
(D) \(z>z\)
Choose the correct answer from the options given below :

Which of the following are NOT correct about "Sinking Fund"?
(A) It does not have any specific purpose.
(B) It can be used in any emergency.
(C) Any amount, any time can be deposited in it.
(D) It is set up for a particular upcoming expense.
Choose the correct answer from the options given below:

If a line makes angles \(\frac{2 \pi}{3}\) and \(\frac{\pi}{3}\) with positive direction of \(x\)-axis and \(y\)-axis respectively,
then the acute angle made by the line with positive \(z\)-axis is:

For a \(3 \times 3\) matrix \(A=\left[a_{i j}\right]\), whose element \(a_{i j}\) is given by \(a_{i j}=\sqrt{i^2+3 j}\), then what is element \(a_{31}\) ?

The maximum value of \(\left(\frac{1}{x}\right)^x\) for \(x>0\) is

If \(y=3 e^{2 x}+2 e^{3 x}\), then \(\frac{d^2 y}{d x^2}+6 y\) is equal to:

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

For a square matrix \(A\) of order 3, if \(|A|=2\), then \(|\operatorname{adj}(2 A)|=\)

The intercept made by the plane \(2 x-3 y+5 z+4=0\) on \(z\)-axis is :

Identify the primary lymphoid organs, where immature lymphocytes differentiate into antigen sensitive lymphocytes.
(A) Bone marrow
(B) Spleen
(C) Thymus
(D) Appendix
Choose the correct answer from the options given below:

In a game, a man wins ₹ \( 8\) for getting a number greater than 3 and loses ₹ 3 otherwise, when a fair die is thrown.
The man decided to throw a die 4 times but to quit as and when he gets a number greater than 3.
If \(X\) denotes the amount which the man wins or loses, then which of the following are correct?
(A) All the possible values of \(X\) are \(8,5,2\) and -1 .
(B) The probability distribution of \(X\) is :

X	8	5	2	-1	-12
P(X)	1/2	1/4	1/8	1/16	1/16

(C) The mean value of \(X\) is \(\frac{75}{16}\).
(D) The variance of \(X\) is \(\frac{6615}{256}\).
Choose the correct answer from the options given below :

The magnitude of a magnetic force on a current carrying conductor is given by :