If A is a square matrix and I is the identity matrix of same order such that \(A^2=I\), then \((A-I)^3+(A+I)^3-3 A\) is equal to:

The semi vertical angle of a right circular cone of maximum volume of a given slant height is

The solution of the differential equation xdy - ydx = 0 represents

The relation R on the set of real numbers defined by \(R=\left\{(a, b): a \leq b^2\right\}\) is
(A) Reflexive
(B) Not symmetric
(C) Neither reflexive nor transitive
(D) Transitive
Choose the correct answer from the options given below:

If \(A=\left[\begin{array}{ccc}2 & 1 & 3 \\ 4 & -3 & 5\end{array}\right]\) and \(B=\left[\begin{array}{cc}-2 & 3 \\ 4 & -5 \\ 1 & 2\end{array}\right]\), then which of the following statements are TRUE?
(A) AB is defined
(B) AB and BA both are defined and \(A B=I\), where I is an identity matrix of order 2
(C) BA is defined
(D) AB and BA both are defined and \(A B=B A\)
Choose the text correct answer from the options given below :

The probability distribution of a random variable X is given by

X	0	1	2
P(X)	\(1-7 a^2\)	\(\frac{1}{2} a+\frac{1}{4}\)	\(a^2\)

If \(a>0\), then \(P(0<X \leq 2)\) is equal to

If A and B are skew-symmetric matrices, then which of the following is not true?

Which one of the following hormones is essential for maintenance of endometrium?

Area of cross section of a wire \(A\) is twice of \(B\) (given the wires are of the same length and of same material) then whose resistance will be more?

Consider the LPP, Min \(Z=3 x-2 y\) subject to the conditions
\(
\begin{array}{l}
4 x+3 y \geq 12 \\
4 x+y \geq 4 \\
x \geq 0, y \geq 0
\end{array}
\)
then which of the following is correct?

If \(\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=\hat{j}-\hat{k}\) and \(\vec{c}=\hat{i}+\hat{j}+\hat{k}\) such that \(\vec{r} \times \vec{b}=\vec{c} \times \vec{b}\) and \(\vec{r} \cdot \vec{a}=0\), then \(\vec{r}\) is :

Read the following paragraph and answer the given questions:
DRUGS AND ALCOHOL ABUSE
The drugs, commonly abused are opioids, cannabinoids, and coca alkaloids. Opioids are the drugs, which bind to specific opioid receptors present in our central nervous system and gastrointestinal tract. Heroin, commonly called smack is chemically diacetylmorphine which is a white, odourless, bitter crystalline compound. Cannabinoids are a group of chemicals, which interact with cannabinoid receptors present principally in the brain. Natural cannabinoids are obtained from the inflorescences of the plant Cannabis sativa. The flower tops, leaves and the resin of cannabis plant are used in various combinations to produce marijuana, hashish, charas and ganja. Generally taken by inhalation and oral ingestion, these are known for their effects on cardiovascular system of the body. It interferes with the transport of the neuro-transmitter dopamine. Cocaine, commonly called coke or crack is usually snorted. It has a potent stimulating action on central nervous system, producing a sense of euphoria and increased energy. Excessive dosage of cocaine causes hallucinations. Other well-known plants with hallucinogenic properties are Atropa belladona and Datura. These days cannabinoids are also being abused by some sportspersons. Drugs like barbiturates, amphetamines, benzodiazepines, and other similar drugs, that are normally used as medicines to help patients cope with mental illnesses like depression and insomnia, are often abused. Morphine is a very effective sedative and painkiller, and is very useful in patients who have undergone surgery. Several plants, fruits and seeds having hallucinogenic properties have been used for hundreds of years in folk-medicine, religious ceremonies and rituals all over the globe.
Which is used as an effective sedative and painkiller and is useful to patients who have undergone surgery?

Consider the following statements:
(A) An emf can be induced by moving a conductor in a magnetic field.
(B) An emf can be induced by changing the magnetic field
(C) An emf can be induced by changing the electric field
(D) An emf can be induced by moving a conductor in an electric field
Choose the correct answer from the options given below: