The standard deviation of the number of tails in three tosses of a coin is :

The degree of the differential equation
\(\left[1+\left(\frac{d y}{d x}\right)\right]^3=\left(\frac{d^2 y}{d x^2}\right)^2\) is :

Let \(A\) and \(B\) be \(3 \times 3\) matrices such that \(A \neq B\). If \(A^3=B^3\) and \(A^2 B=B^2 A\), then the determinant of \(A^2+B^2\) is :

The points on the curve \(2 x=y^2\) which are nearest to the point \((5,0)\) lie in
A. I Quadrant
B. II Quadrant
C. III Quadrant
D. IV Quadrant
Choose the correct answer from the options given below:

If \(\theta\) is an acute angle and the vector \(\vec{a}=(\sin \theta) \hat{i}+(\cos \theta) \hat{j}\) is perpendicular to the vector \(\vec{b}=\hat{i}-\sqrt{3} \hat{j}\) then \(\theta\) is equal to:

Arrange the principal values of the following functions in ascending order
(A) \(\operatorname{cosec}^{-1}(2)\)
(B) \(\tan ^{-1}(-\sqrt{3})\)
(C) \(\tan ^{-1}(1)\)
(D) \(\tan ^{-1}\left(\cos \frac{3 \pi}{2}\right)\)
Choose the correct answer from the options given below:

Match List-l with List-ll
Let \(A\) be any invertible square matrix. Then

List-l	List-ll
(A) \(A-A^T\)	(I) \(|A| A^{-1}\)
(B) \(A A^T\)	(II) Skew-symmetric
(C) \(\operatorname{det}\left(A^{-1}\right)\)	(III) Symmetric
(D) \(\operatorname{adj} A\)	(IV) \([\operatorname{det}(A)]^{-1}\)

Choose the correct answer from the options given below :

Mucosa-associated lymphoid tissue (MALT) is located within the lining of -

Two parallel plate capacitors of capacitances \(2 \mu F\) and \(3 \mu F\) are joined in series and connected to a battery of \(V\) volts. The values of potential across the two capacitors V1 and V2 and energy stored in them U1 and U2 are related as :

The rate of biomass production is expressed in terms of __________ to compare the productivity of different ecosystems.

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?

Which was the first discovered antibiotic ?

Elements of group-15, 16 and 17 form compounds with hydrogen with general formula MH3, \(H 2 M\) and HX (called hydrogen halides). Stability of these hydrides, along with M-H bond strength and basic nature decreases down the group. Boiling point of these hydrides mainly depends on the strength of their inter molecular forces.
Decreasing order of boiling point of group 15 hydrides is:
A. \(NH _3\)
B. \(PH _3\)
C. \(AsH _3\)
D. \(SbH _3\)
E. \(BiH _3\)
Choose the correct answer from the options given below: