Match List-I with List-II

List-I	List-II
(A) The value of \(\int_0^4|x| d x\) is	(I) 3
(B) The value of \(\int_{-2}^2|x| d x\) is	(II) -1
(C) The value of \(\int_0^3[x] d x\) is	(III) 8
(D) The value of \(\int_{-1}^1[x] d x\) is	(IV) 4

Choose the correct answer from the options given below :

If the system of equations \(2 x+3 y=10\) and \(x+k y=4\) has a unique solution, then

A parallelogram is constructed on the vectors \(\vec{a}=3 \vec{\alpha}-\vec{\beta}, \vec{b}=\vec{\alpha}+3 \vec{\beta}\). If \(|\vec{\alpha}|=|\vec{\beta}|=2\) and the angle between \(\vec{\alpha}\) and \[\vec{\beta}\] is \(\frac{\pi}{3}\), then length of the diagonal of the parallelogram is:

The area enclosed between \(y^2=4 x\) and \(x^2=4 y\) is:

The following data shows the percentage of rural and urban Indian households who have a high speed internet connection.

Year(x)	Rural Household \((y \%)\)	Urban Household\((y \%)\)
2020	2	6
2021	3	7
2022	3	9
2023	4	15
2024	5	20

Based on the above data, which of the following statements are correct?
(A) A straight line trend by the method of least squares for rural Indians \(y_t=3.4+0.7(x-2022)\)
(B) A straight line trend by the method of least squares for urban Indians is \(y_t=11.4+4.3(x-2022)\)
(C) The forecast for the year 2025 for urban group using the trend equation is \(22.2 \%\)
(D) The forecast for the year 2025 for rural group using the trend equation is \(5.5 \%\)
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The volume of a cube is increasing at a rate of 9 cubic centimeter per second. Then rate of change of surface area when the length of an edge is 10 centimeter is:

The angle between 2 vectors \(\vec{a}\) and \(\vec{b}\) with magnitude 1 and 2 respectively when \(\vec{a} \cdot \vec{b}=1\) is:

The value of b for which the function \(f(x) = \sin x - bx + C\), where b and C are constants is decreasing for \(x \in R\) is given by

The number of equivalence relation on the set {1, 2, 3} containing (1, 2) and (2, 1) is

Find the odd one out with reference to terrestrial ecosystem:

Which of the following inequalities are NOT correct?
(A) If \(a>1, b>1\), then \(\log _b a+\log _a b \leq 2\)
(B) For any real number \(x,\left(9^x+9^{1-x}\right) \geq 9\)
(C) If \(a, b, c\) are non-zero real numbers of the same sign, then \(\left(\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\right) \leq 3\)
(D) If \(a, b, c\) are three distinct real numbers, then \((a+b)(b+c)(c+a) \geq 8 a b c\)
Choose the correct answer from the options given below:

Which of the following statements are correct about the Compound Annual Growth Rate (CAGR)?
(A) It can be used to compare historical returns on different investment portfolios.
(B) It helps smooth returns when growth rates are expected to be volatile and inconsistent.
(C) It is unable to track the performance of various business measures of one or multiple companies alongside one another.
(D) It can be used to calculate the average growth of a single investment.
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The 'lungs of the planet' name is given to :