If \(A=\left[\begin{array}{ll}4 & 5 \\ 2 & 1\end{array}\right]\) and \(I\) is an identity matrix of order \(2\) , then \(A-3 I\) equals :

Consider the following hypothesis test:
\(\begin{aligned} & H_0: \mu=20 \\ & H_a: \mu \neq 20\end{aligned}\)
A sample of 40 provided a sample mean of 19. The standard deviation is 3. Then the value of the t-test statistic is:

Based on the data available for the production ( \(y_i\) in thousand tons) of a cloth factory for 7 years (\(x_i\)) using the method of least squares, the straight line trend is given by \(y=a+b x\) with \(\sum y_i=608, \sum x_i=0, \sum x_i y_i=116, \sum x_i^2=28\). Then, the increase in production per year is :

If X is a normal variate with mean 16 and standard deviation 4, then the value of the standard normal variate Z corresponding to X = 17 is :

The number of all possible matrices of order 2 × 2 with each entry 0 or 1 is:

Let the matrix \(A=\left[a_{i j}\right]_{3 \times 3}\) be defined by
\(a_{i j}=\left\{\begin{array}{ll}2 i+3 j, & i<j \\5, & i=j \\3 i-2 j, & i>j\end{array}\right.\)
The number of elements in the matrix \(A\) which are greater than 7 , 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 :

If the sequence of one strand of DNA is written as: 5'-ATCGTGCTATGAGCATGC-3'.
The sequence of its complementary strands will be?

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?

The critical points of \(f(x)=x^3+x^2+x+1\) are

If \(A\) and \(B\) are two invertible matrices, then which of the following statements are correct?
(A) \(\left|A^{-1}\right|=|A|^{-1}\)
(B) \(\operatorname{adj} A=|A| A^{-1}\)
(C) \((A B)^{-1}=A^{-1} B^{-1}\)
(D) \((A+B)^{-1}=A^{-1}+B^{-1}\)
Choose the correct answer from the options given below:

The entry of pollen tube in the embryo sac is guided by :

Which of the following could not be a rate determining step?