An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?

Which one of the following statement is not correct?

If \(\int \frac{d x}{(x+1)(x+2)}=\int \frac{A}{x+1} d x+\int \frac{B}{x+2} d x\), then \(A+B=\)

If the objective function \(z=p x+q y\) has its maximum value at the points \((2,1)\) and \((0,6)\), then the relationship between \(p\) and \(q\) is :

The area of the region enclosed between the two circles \(x^2+y^2=1\) and \((x-1)^2+y^2=1\) is

Probability distribution of random variable \(X\) is:

x	\(0\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)
\(P(X)\)	\[3k\]	\(3k\)	\(2k\)	\(2k^2\)	\(3k^2\)	\(4k^2\)

The value of \(k\) is:

Match List - I with List - II

List - I (Time series component)	List - II (Example)
(A) Secular Variation	(I) Pandemic
(B) Seasonal Variation	(II) Recession in business
(C) Cyclic Variation	(III) Monthly sale of woolen clothes
(D) Irregular Variation	(IV) Data regarding National income

Choose the correct answer from the options given below:

Answer the question on the basis of passage given below :
Adsorption is the phenomenon of attracting and retaining the molecules of a substance on the surface of a solid resulting into a higher concentration on the surface than in the bulk. The substance adsorbed is known as adsorbate and the substance on which adsorption takes place is called adsorbent. In physisorption adsorbate is held to the adsorbent by weak van der Waals forces and in chemisorption by strong chemical bond.
Out of Milk, butter, ice cream, fruit juice and lemonade. Identify the one which is not a colloid.

A person has purchased a home for Rs. 10,00,000 with a down payment of Rs. 2,00,000. He amortizes the balance at 9% per annum compounded monthly for 25 years.
Then the equal monthly instalment (EMI) is :
[Given that \(\frac{(1.0075)^{300}-1}{(0.0075)(1.0075)^{300}}=119.1616\) ]

The mutual inductance of a pair of solenoid depends :
(A) on their separation
(B) on their relative orientation
(C) on the current flowing
(D) on the number of turns in the solenoids
Choose the correct answer from the options given below:

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.
Heroine (Smack) which is extracted from the latex of poppy plant is chemically called:

Which of the following statements are not true for equipotential surfaces ?
A. Equipotential surface through a point is normal to electric field at that point.
B. There is a constant potential difference between any two points on the equipotential surface.
C. No work is required to move a test charge on the equipotential surface.
D. The vale of electric potential is constant at all points on the equipotential surface.
E. Equipotential surfaces can not be drawn for an electric dipole.
Choose the correct answer from the options given below :

The straight line \(\frac{x+3}{3}=\frac{y+2}{4}=\frac{z+1}{0}\) is