Which of the following is correct about the compound annual growth rate (CAGR)?

The value of \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}(\sin |x|-\cos |x|) d x\) is :

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

Components of Time Series are :
(A) Secular Trend Component
(B) Seasonal Component
(C) Moving Average Component
(D) Cyclical Component
Choose the correct answer from the options given below :

If matrix \(A=\left[\begin{array}{ll}3 & x \\ y & 0\end{array}\right]\) and \(A^{\prime}=A\), then :

A solenoid with \(2 \times 10^4\) turns per meter, diameter 0.1 m , has a coil of 100 turns and 0.01 m radius placed inside. If solenoid current decreases from 4 A to 0 in 0.05 s , total charge through coil is :

If \(\mathbb{Z}\) and \(\mathbb{R}\) set of integers and set of real numbers respectively, then match List I with List II.

List - I	List - II
(A) \(5 x-3<3 x+1, x \in \mathbb{Z}\)	(I) \(x \in(-\infty,-3)\)
(B) \(3 x+17 \leq 2(1-x), x \in \mathbb{R}\)	(II) \(x \in(-\infty,-1)\)
(C) \(13 x+17<2(1-x), x \in \mathbb{R}\)	(III) \(\{\ldots,-4,-3, \ldots, 0,1\}\)
(D) \(\frac{2 x+3}{5}-2>\frac{3(x-2)}{5}, x \in \mathbb{Z}\)	(IV) \(\{\ldots,-4,-3,-2\}\)

Choose the correct answer from the options given below:

\(\lim _{x \rightarrow \infty}\left(\frac{x+7}{x+1}\right)^x\) is equal to:

Answer the question on basis of passage given below :
A ketone \([A]\) which undergoes haloform reaction gives compound \([B]\) on reduction. Compound \([B]\) on heating with sulphuric acid gives compound \([C]\) which forms monozonide \([D]\). The compound [D] on hydrolysis in the presence of zinc dust gives compound [E].
Compound [E] on oxidation gives \(C _2 H _4 O _2\) [F]
The boiling point of \([ A ]\) observed is exceptionally high because of :

Read the passage carefully and answer the questions based on the passage:
The number of reacting species (atoms, ions or molecules) taking part in an elementary reaction, which must collide simultaneously in order to bring about a chemical reaction is called molecularity of a reaction. In the rate equation Rate \(=k[\mathrm{~A}]^x[\mathrm{~B}]^y\)
\(x\) and \(y\) indicate how sensitive the rate is to the change in concentration of A and B, respectively. Sum of these exponents, i.e., \(x +y\) gives the overall order of a reaction where \(x\) and \(y\) represent the order with respect to the reactants A and B respectively. Hence, the sum of powers of the concentration of the reactants in the rate law expression is called the order of that chemical reaction. For a first order reaction, the concentration of the reactant varies as \([\mathrm{R}]=[\mathrm{R}]_0 e^{-k t}\)
Which of the following statements is not true for order of a reaction?

If \(\vec{a}, \vec{b}\), and \(\vec{c}\) are unit vectors such that \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}\), then value of \(\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}\) is :

Read the given passage and answer the question given below.
The sex linked recessive disease, which shows its transmission from unaffected carrier female to some of the male progeny has been widely studied. In this disease, a single protein that is a part of the cascade of proteins involved in the clotting of blood is affected. Due to this in an affected individual a simple cut will result in non-stop bleeding. The heterozygous female (carrier) for the disease may transmit it to sons. The possibility of a female becoming a sufferer of disease is extremely rare because mother of such a female has to be at least carrier and the father should be sufferer. The family pedigree of Queen Victoria shows a number of suffering descendents as she was a carrier of the disease.
Identify the type of genetic disorder explained in this paragraph:

A square shaped wire loop of side L is carrying a current I. What is the magnetic field at the point of intersection of diagonals of the square wire loop ?