Which of the following statements are correct?
(A) If \(A\) is a square matrix, then \(\left|A^2\right|=|A|^2\).
(B) If \(A\) and \(B\) are square matrices of the same order, then \(\operatorname{det}(A B)=\operatorname{det}(A)+\operatorname{det}(B)\).
(C) If \(A\) is a square matrix of order 3 and \(|A|=2\), then the value of \(|-3 A|\) is 54 .
(D) If the matrix \(\left[\begin{array}{cc}5-x & x-1 \\ 3 & 5\end{array}\right]\) is singular, then the value of \(x\) is \(\frac{7}{2}\).
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Let \(f(x)=[x]\) and \(g(x)=|x|\). Then gof \(\left(\frac{-5}{3}\right)\) - fog \(\left(\frac{-5}{3}\right)\) where [x] is greatest integer valued function and |x| is modulus function.

If \(I_n=\int_0^{\pi / 4} \tan ^n x d x\) then \(I_{2024}+I_{2026}\) is equal to :

In an electromagnetic wave, the ratio of energy densities of electric and magnetic fields is :

If A is a square matrix of order 3, B = kA and |B| = x|A| then,

In a 200 m race, Rohan completes the race in 8 seconds and Vivan completes the race in 10 seconds. By how much distance Rohan beats Vivan?

The value of the integral \(I=\int e^x\left(\tan ^{-1} x+\frac{1}{1+x^2}\right) d x\) is :

Match List - I with List - II.

List - I	List - II
(A) \(Ni ^{2+}\)	(I) Pink
(B) \(Cu ^{2+}\)	(II) Purple
(C) \(Mn ^{2+}\)	(III) Green
(D) \(Ti ^{3+}\)	(IV) Blue

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In the given figure, the potentiometer wire, AB has a resistance of 5 \( \Omega \) and length 10 m. The balancing length AJ for 0.4 V is nearly:

Three charges of magnitude \( -2Q, -3Q \) and \( Q \) are located at \( (a, 0, 0), (3a, 0, 0) \) and \( (5a, 0, 0) \) respectively. What is the magnitude of electric flux due to these charges through a sphere of radius 4a with its centre at the origin?

Answer the question on basis of passage given below :
The noble gases have closed shell electronic configuration and are monatomic gases under normal conditions. The low boiling points of lighter noble gases are due to the weak dispersion forces between the atoms and the absence of other inter atomic interaction. The direct reaction of xenon with fluorine leads to a series of compounds with oxidation numbers \(+2, +4\) and \(+6\).
\(\text{XeF}_4\) reacts violently with water to give \(\text{XeO}_3\). The compound of Xenon exhibit stereoisomerism and their geometries can be deduced considering the total number of electrons in the valence shell.
\(X e F _4 \quad\) and \(X e F _6 \quad\) are expected to be :

Match List-I with List-II

List-I (Contraceptive methods)	List-II (Respective actions)
(A) Diaphragms	(I) Inhibit ovulation and implantation
(B) Contraceptive pills	(II) Increase phagocytosis of sperm within uterus
(C) Intra Uterine Devices	(III) Absence of menstrual cycle and ovulation following parturition
(D) Lactational amenorrhea	(IV) They cover the cervix blocking the entry of sperms

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Match List-I with List-II

List-I (Structure of Protein)	List-II (Function)
(A) Primary Structure	(I) Gives rise to Fibrous and Globular Proteins
(B) Secondary structure	(II) Sequence of amino acid
(C) Tertiary Structure	(III) shape of polypeptide chain
(D) Quaternary Structure	(IV) Spatial arrangement of sub-units

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