The area (sq. units) bounded by the curve \(y=\sin x, \pi \leq x \leq 2 \pi\) and the \(x\)-axis is

Let \(X\) denote the number of hours a student studies on a selected day. The probability distribution of \(X\) is given by (where \(k\) is some unknown constant)
\(P\left(X=x_i\right)=\left\{\begin{array}{ll}0.5, & \text { if } x_i=0 \\k x_i, & \text { if } x_i=1 \\k\left(4-x_i\right), & \text { if } x_i=2 \text { or } 3 \\0, & \text { otherwise }\end{array}\right.\)
Then the value of \(k\) is

A square matrix \(B=\left[b_{i j}\right]_{n \times n}\) where
\(b_{i j}=0\) when \(i \neq j\)
\(b_{i j}=k\) when \(i=j\) for some constant \(k\) is called:

A matrix which is symmetric as well as skew symmetric is:

If \(f(x)=\left\{\begin{array}{ll}\frac{\sin \pi x}{5 x}, & x \neq 0 \\ k, & x=0\end{array}\right.\) is continuous at \(x=0\), then \(k\) is :

The demand for a certain product is represented by the function \(p=300+25 x-x^2\) (in rupees), where \(x\) is the number of units demanded and \(p\) is the price per unit, then the marginal revenue when 15 units are sold, is

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

During the p-n junction formation, when an electron diffuses from n \( \rightarrow \) p, it leaves behind an :

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?

If \(A=\left[\begin{array}{ll}1 & -1 \\ 2 & -1\end{array}\right], B=\left[\begin{array}{cc}a & 1 \\ b & -1\end{array}\right]\) and \((A+B)^2=A^2+B^2\) then

The resistivity of a material depends on

The present value of a perpetuity of ₹2,500 payable at the end of each year, if money is worth 10% compounded annually, is:

Select the correct option for the statements given below.
(A) The diffraction pattern is a superposition of waves originating from each point on a single slit.
(B) The interference pattern is the superposition of two waves originating from two narrow slits.
(C) The diffraction pattern in single slit has a central bright maximum brighter than other maxima.
(D) The interference in double slit has a number of equally spaced bright and dark bands.
Choose the correct answer from the options given below :