The corner points of the bounded feasible region for an LPP are (0, 20), (3, 12), (6,8), (0, 15).
The objective function is \(Z=a x+\beta y\), where \(a, \beta>0\).
If the maximum of Z occurs at the corner points (3, 12) and (6,8), then the relationship between \(a\) and \(\beta\) is:

The value of the integral \(I=\int_0^1 \frac{1}{\sqrt{x^2+2 x+3}} d x\) is :

The EMI (in) under the flat rate on a loan of 6,00,000 rupees with 20% annual interest for 5 years is :

\(\int \frac{x \sin ^{-1} x}{\sqrt{1-x^2}} d x=\)

For a \(3 \times 3\) matrix \(A\), if \(A(\operatorname{adj} A)=\left[\begin{array}{ccc}99 & 0 & 0 \\ 0 & 99 & 0 \\ 0 & 0 & 99\end{array}\right]\) then \(\operatorname{det}(A)\) is equal to:

The equation of the curve whose slope is given by \(\frac{d y}{d x}=\frac{4 x}{y}, x>0, y>0\) and which passes through the point \((2,2)\) is:

The interval in which the function \(f(x)=10-6 x-2 x^2\) is decreasing is :

Identify the correct combination of statements for sacred groves.
(A) These are in-situ conservation strategies.
(B) These are ex-situ conservation strategies.
(C) These are found in the Khasi and Jaintia hills in Meghalaya.
(D) These hold religious values.
Choose the correct answer from the options given below:

Which is not the salient feature of human genome project-

Read the following paragraph and answer the given questions.
Cancer detection is based on biopsy and histopathological studies. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs. Do you know why mother's milk is considered very essential for the new-born infant? The yellowish fluid colostrum secreted by mother during the initial days of lactation has abundant antibodies (IgA) to protect the infant. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal. The exaggerated response of the immune system to certain antigens present in the environment is called allergy. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. 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.
Which one of the following is not used for detection of cancer?

The value of \(\left|\begin{array}{ccc}1 & x & y \\ 1 & x+y & y \\ 1 & x & x+y\end{array}\right|\) is

The energy of a photon of wavelength (\( \lambda \)) is given by the expression: (Symbols have their usual meaning: h = Planck's constant, c = speed of light)

The probability distribution function of a normal variate with mean \(\mu\) and variance \(\sigma^2\) is given by :
\(f(x)=\frac{1}{\sigma \sqrt{2 \pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2},-\infty< x< \infty,-\infty < \mu < \infty, \sigma>0\)
If \(y=f(x)\) be the normal probability curve, then which of the following is correct?
(A) The normal curve is symmetrical about the line \(x=\mu\).
(B) Mean, median and mode of the distribution coincide.
(C) \(Y\)-axis is an asymptote to the normal curve.
(D) If \(x\) increases numerically, \(f(x)\) decreases rapidly.
Choose the correct answer from the options given below :