If \(A=\left[\begin{array}{ll}1 & 0 \\ 3 & 1\end{array}\right]\) and \(A^4=\left[\begin{array}{ll}1 & 0 \\ k & 1\end{array}\right]\), then the value of \(k\) is :

The particular solution of the differential equation \(x d y=\left(2 x^2+1\right) d x, x \neq 0\), given that \(y=1\) when \(x=1\) is:

The general solution of the differential equation \(\frac{d y}{d x}+y \tan x=\sec x\) is :
(Where \(C\) is constant of integration)

In a 500 metres race, the ratio of speeds of two participants Meena and Kamal is 4: 5 respectively. If Meena has a start of 200 metres, find the distance by which Meena wins.

The value of the integral \(\int \frac{\log x^3}{x} d x\) is :

If A is a matrix of order \(m \times n\) and B is a matrix such that \(A B^T\) and \(B^T A\) are both well-defined matrices, then order of matrix B is

The solution of the differential equation \(x \frac{d y}{d x}+2 y=x^2\) is: ( \(C\) is constant of integration)

Relation \(R\) on the set \(A=\{1,2,\)...,\(15\}\) defined as \(R=\{(x, y): y-4 x=0\}\) is

Sudhir had Rs 45,000. He lent a part of it at 4% p.a. and the remaining at 10% p.a. simple interest. He earned a total profit at 8% p.a. on the money lent, what sum did he lend at 10% p.a ?

What is the correct sequence of increasing reactivity of the following compounds towards nucleophilic addition reaction?
(A) Ethanal
(B) Propanone
(C) Propanal
(D) Butanone
Choose the correct answer from the options given below :

Read the following passage carefully and answer the given questions
The earthworm is referred to as the farmer's friend. This is because they help in the breakdown of complex organic matter as well as in loosening of soil. Similarly, decomposers break down complex organic matter into inorganic substances like carbon dioxide, water and nutrients and the process is called decomposition. Dead plant remains such as leaves, bark, flowers and dead remains of animals, including fecal matter, constitute detritus, which is the raw material for decomposition. Some of the steps in the process of decomposition are fragmentation, catabolism, leaching, humification etc.
The process of breaking down of detritus into smaller particles is called:

The correct arrangement of electromagnetic spectrum in decreasing order of wavelength is :

Match List-I with List-II

List-I (Types of solutions)	List-II (Examples)
(A) Gas in Gas solution	(I) Oxygen dissolved in water
(B) Gas in Liquid solution	(II) Copper dissolved in gold
(C) Liquid in Solid solution	(III) Mixture of oxygen and nitrogen gases
(D) Solid in Solid solution	(IV) Amalgam of mercury with sodium

Choose the correct answer from the options given below: