Out of students in a school, it is known that \(65 \%\) reside in hostel and \(35 \%\) are day scholars. Previous year results report that \(40 \%\) of the students who reside in hostel attain A grade and \(20 \%\) of day scholars attain A grade in their annual examination.
At the end of the year, one student is chosen at random from the class.
Probability of the selected student attaining grade \(A\) is:

Which one of the following set of constraints does the given shaded region represent?

Interval in which the function \(f\) given by \(f(x)=\tan x-4 x, x \in\left(0, \frac{\pi}{2}\right)\) is strictly decreasing is

If \(y=x^4-10\) and if x changes from 2 to 1.99, then the changed value of y is approximately :

The value of \(\int_0^{\pi / 2} \frac{\tan ^7 x}{\cot ^7 x+\tan ^7 x} d x\) is

If \(A=\left[\begin{array}{l}-2 \\ -1 \\ -4\end{array}\right], B=\left[\begin{array}{lll}-1 & 2 & 3\end{array}\right]\), then the value of \(A^{\prime} B^{\prime}\) is

If \(A\) is a square matrix of order 3 such that \(|A|=2\), then the value of \(|\operatorname{adj}(\operatorname{adj} A)|\) is :

If the elementary column transformation \(C_1 \rightarrow 2 C_1\) is carried out on the following matrix equation.
\(\left[\begin{array}{ll}1 & 3 \\ 2 & 4\end{array}\right]\left[\begin{array}{cc}-1 & 2 \\ 5 & 0\end{array}\right]=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]\) Then the transformed equation will be:

The direction ratios of the line perpendicular to the lines \(\frac{x-7}{-6}=\frac{y+17}{4}=\frac{z-6}{2}\) and \(\frac{x+5}{6}=\frac{y+3}{3}=\frac{z-4}{-6}\) are proportional to:

Which of the following shows both, Frenkel and Schottky defect ?

For the first order reaction :
(A) The degree of dissociation is equal to \((1 – e^{-kt})\)
(B) A plot of reciprocal concentration of the reactant v/s time gives a straight line
(C) The time taken for the completion of 75\% reaction is thrice the half life of the reaction
(D) 1st order reaction never completes
Choose the correct answer from the options given below :

The time taken by light to travel normally through a glass plate of thickness 1 mm would be : (Take refractive index of glass = 1.5)

Read the passage and answer the following
Microbes are organisms that cannot be seen with the naked eye. They include bacteria, archaea, protists, viruses, prions, and fungi. They account for most of the diversity of life on earth. Far more microbes inhabit a single person's body than there are people on the entire planet. Microbes also dominate in terms of their ability to live and thrive in extreme environments, including clouds, deep-sea volcanoes, springs, ice caps, and animal intestines. Most animals, including humans, exhibit numerous associations with microbes. Our "human microbiome" includes our skin, hair, mouth, and gut.
Which of the following is a non-pathogenic microbe?