Consider the differential equation \(\frac{d y}{d x}+y \tan x=\sec x\), then which of the following statements are correct?
(A) It is homogeneous
(B) It has \(\sec x\) as its integrating factor
(C) Its general solution is \(y \sec x=\tan x+c\), where \(c\) is an arbitrary constant.
(D) Its degree is not defined
Choose the correct answer from the options given below :

The value of \(c\) for which \(f(x)=x(x-3)^2, 0 \leq x \leq 3\), satisfies Rolle's theorem is:

Consider the LPP: Max \(Z = 5x + 3y\) subject to \(3x + 5y ≤ 15, 5x + 2y ≤ 10 x ≥ 0, y ≥ 0\)
match List - I with List - II

List-I	List-II
(A) Objective function	(I) \(3x + 5y ≥ 15\)
(B) One constraint	(II) \(x, y ≥ 0\)
(C) Non-negative restrictions	(III) \(Z = 5x + 3y\)
(D) Point (1, 2) does not lie in the region	(IV) \(3x + 5y ≤ 15\)

Choose the correct answert from the option given below :

If \(A\) is an invertible matrix, then which of the following statement(s) is/are TRUE?
(A) \(\left|A^{-1}\right|=|A|\)
(B) \(\left(A^{-1}\right)^{-1}=A\)
(C) \(A^{-1}=\frac{\operatorname{adj} A}{|A|}\)
(D) \(\left(A^T\right)^{-1}=\left(A^{-1}\right)^T\)
Choose the correct answer from the options given below :

The effective rate of return equivalent to a nominal rate of 12% per annum compounded quarterly is:
[Given that \((1.03)^4=1.1255\) ]

If \(f(x)=|2 x+5|\), then \(f(x)\) is :

In an LPP, the feasible region represented by the set off constraints \(2 x+3 y \leq 18, x+y \leq 10, x \geq 0, y \geq 0\) is

Out of the given statement, choose the correct statement.
(A) The direction ratios of the vector \(\vec{a}=3 \hat{i}-\hat{j}+4 \hat{k}\) is \(3,-1,4\).
(B) If \(\theta\) is the angle between two vectors \(\vec{a}\) and \(\vec{b}\), then their cross product is given as \(\vec{a} \times \vec{b}=|\vec{a}||\vec{b}| \cos \theta\).
(C) The unit vector in the direction of vector \(\vec{a}=\hat{i}+2 \hat{j}-2 \hat{k}\) is \(\hat{a}=\frac{1}{3}(\hat{i}+2 \hat{j}-2 \hat{k})\).
(D) If \(\vec{a}=3 \hat{i}\) and \(\vec{b}=4 \hat{j}\) then \(\vec{a} \cdot \vec{b}=12\).
(E) If \(\vec{a}\) and \(\vec{b}\) represent the adjacent sides of a triangle then its area is given of \(\frac{1}{2}|\vec{a} \times \vec{b}|\).
Choose the correct answer from the options given below :

Molar mass of a non-volatile solute (in g/mol) in its \(10\%\) by mass aqueous solution showing \(2\%\) decrease in its vapour pressure is :

If \(A=\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{array}\right]\) then \(A^5\) is :

If \(A\) is a square matrix of order 3 and \(|A|=5\), then the value of \(\left|-A A^T\right|\) is :

A radioactive substance is emitting β- particles at a certain rate. When it is heated to a high temperature, the rate of emission

A person invested ₹ \(10000\) in a stock of a company for \(6\) years.
The value of his investment at the end of each year is given below:

2018	2019	2020	2021	2022	2023
₹11000	₹11500	₹13000	₹11800	₹12200	₹14000

The compound annual growth rate (CAGR) of his investment is:
[Given (1.4) \({ }^{\frac{1}{8}}=1.058\) ]