If \(m\) and \(n\) are respectively the order and degree of the differential equation
\(\left(\frac{d^2 y}{d x^2}\right)^2+\left(\frac{d y}{d x}\right)^3+y=4 x\),
then the value of \((m+n)\) is :

Ram invested Rs. 20,000 in a mutual fund in the year 2012.
The value of the mutual fund increased to Rs. 32,000 in the year 2017.
The compound annual growth rate (CAGR) of his investment is (Given : \((1.6)^{\frac{1}{5}}=1.098\))

The differential coefficient of \(\log _e\left[\log _e\left(\log _e x^5\right)\right]\) with respect to \(x\) is:

\(\int_0^8\left(x^{\frac{2}{3}}+1\right) d x\) is equal to

Let A = \(\left[\begin{array}{ccc}152 & 105 & 3 \\ 149 & 25 & 35 \\ 2 & 1 & 0\end{array}\right]\) . If \(A_{i j}\) denotes the co-factor of an element \(a_{i j}\) of the matrix A, then the value of \(a_{11} A_{21}+a_{12} A_{22}+a_{13} A_{23}\) is equal to

Let \(A =\left[a_{i j}\right]\) be a \(2 \times 2\) matrix such that \(a_{i j}=\frac{|-3 i+j|}{2}\) then \(a_{21}\) is :

A random variable y has the following probability distribution

y	1	2	3	4	5
P(y)	2k	3k	k	4k	5k

Match List-l with List-ll

List - I	List - II
(A) P(y > 2)	(I) \(\frac{2}{5}\)
(B) k	(II) \(\frac{2}{3}\)
(C) \(P(y \leq 3)\)	(II) \(\frac{8}{15}\)
(D) \(P(2 \leq y \leq 4)\)	(II) \(\frac{1}{15}\)

Choose the correct answer from the options given below

What is the coordination number of Ni in \([Ni(NH_{3})_{4}]\) complex?

The area enclosed by the curve \(x=8 \cos t, y=4 \sin t\) between the lines \(x=0\) and \(x=4 \sqrt{3}\) is:

The units of rate of reaction and rate constant are identical for a

Which of the following statement(s) is/are correct with reference to electrophilic aromatic substitution of \(\text{C}_6\text{H}_5\text{Cl}\)?
(A) Cl acts as an activating and o/p directing group
(B) Cl acts as a deactivating and o/p directing group
(C) acts as an activating and m directing group
(D) Cl acts as a deactivating and m directing group
(E) Presence of \(\text{NO}_2\) at p-position facilitates the reactions
Choose the correct answer from the options given below :

Which of the following is correct about the nature of ligand?

Read the passage carefully and answer the Questions
Carboxylic acids are the earliest organic compounds isolated from nature. These are also known as organic acids but are weaker acids as compared to mineral acids. However, they are more acidic than alcohols and phenols because of greater resonance stabilization of the parent acid and its conjugate base. The acidic strength is determined by the \(K _a\), which is called the acidity constant. The greater the value of \(K _a\), the greater the tendency of the acid to ionize and hence the stronger the acid. The acidic strength of the saturated aliphatic carboxylic acid depends upon the inductive effect and its position with respect to - COOH groups. Electron -donating substituents tend to decrease whereas electron-withdrawing substituents tend to increase the acidic strength. The acidic strength of the aromatic carboxylic acid, on the other hand depends upon both the inductive effect and the resonance effect of the substituents.
Which of the following groups when attached directly does not increase the acidity of the carboxylic acid?