If \(A=\left[\begin{array}{cc}2 & 1 \\ 1 & 4 \\ -1 & 6 \\ 0 & 7\end{array}\right]\) and \(B=\left[\begin{array}{cccc}1 & 2 & 3 & 0 \\ 2 & -1 & 6 & 7\end{array}\right]\), then

A bag contains 12 white and 18 red balls. Two balls are drawn in succession without replacement. The probability that the first is red and the second is white is:

If \(P(A)=\frac{3}{10}, P(B)=\frac{2}{5}\) and \(P(A \cup B)=\frac{3}{5}\), then the value of \(P(B \mid A)+P(A \mid B)\) is :

The value of \(\left[\begin{array}{lll}1 & b c & b c(b+c) \\ 1 & c a & c a(c+a) \\ 1 & a b & a b(a+b)\end{array}\right]\) is

Inlet pipe A can fill a tank in 30 minutes and outlet pipes B and C can empty the tank in 2 hours each. If all three pipes operate together, the tank will be filled in

Consider a binary operation \(*\) on \(N\) defined as \(a * b=a^3+b^3\), choose the correct answer :

Which one of the following statement is incorrect about sinking fund?

In the given figure, a diode D is connected to an external resistance R = 100 \( \Omega \) and an emf of 2.5 V. During forward bias, if the barrier potential developed across the diode is 0.6 V, the current in the circuit will be

The following data is available for two independent samples:

	SAMPLE-1	SAMPLE-2
sample size	8	10
sample mean	191	199
sample standard deviation	10	12

Match List - I with List - II.

List-I	List-II
(A) Cuckoo lays egg in crow’s nest	(IV) Brood parasitism
(B) Orchid grows in mango tree	(I) Commensalism
(C) Ticks live on skin of dogs	(II) Parasitism
(D) Species of Wasp and fig species	(III) Mutualism

Choose the correct answer from the options given below :

In a linear programming problem (LPP), the maximum value of the objective function \(Z=2 x+5 y\) subjected to the constraints :
\(\begin{array}{l}2 x+3 y \leq 6 \\2 x+y \leq 4 \\x, y \geq 0\end{array}\)
is

If R and S are two equivalence relations on a set A, then

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.
__________ are used as medicines to help patients cope with mental illnesses like depression and insomnia.