The value of the determinant \(\left|\begin{array}{ccc}a+1 & b & c \\ a & b+1 & c \\ a & b & c+1\end{array}\right|\) is :

Let A and B be two events. Then which of the following statements are TRUE?
(A) \(P(B \mid A)=\frac{P(A \cap B)}{P(A)}\), provided \(P(A) \neq 0\)
(B) \(P\left(B^{\prime}\right)=1+P(B)\)
(C) \(P(A \cup B)=P(A)+P(B)+P(A \cap B)\)
(D) \(P(A \cap B)=P(A) \cdot P(B)\) if A and B are independent events
Choose the correct answer from the options given below:

\(\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{d x}{1+\sqrt{\tan x}}\) is equal to:

A random sample of size 16 has 53 as mean. The sum of the squares of the deviations taken from mean is 150 . If the population mean is 56 then the value of \(t\)-test statistic is :

If \(A\) and \(B\) are invertible matrices of same order, then which one of the following is NOT true?

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

A machine costing Rs.50,000 has a useful life of 4 years .The estimated scrap value is Rs 10,000. The rate of depreciation per annum is :

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.
Which noble gas is generally used in illuminating warning signals?

Adenosine deaminase deficiency is caused by ________ of the gene.

A moving hydrogen atom absorbs a photon of wavelength 221 nm and stops. If the mass of the hydrogen atom is \(1.67 \times 10^{-27} \text{ kg}\), the linear momentum of the photon will be: (Given: \(h = 6.63 \times 10^{-34} \text{ J}⋅­­s\))

The resistance of a given carbon resistor is \(3.6 \times 10^6 \Omega \pm 5 \%\). What are the sequence of colour strips on the resistor?

Which one of the following is also called 'Terror of Bengal'?

Two light beams of intensities in the ratio 25:9 are allowed to interfere. The ratio of the intensities of maxima and minima will be