\(\int_{-5}^{5} (3x^5 + \sqrt{5} x^3) e^x dx\) is equal to:

The value of b , for which the function \(f(x)= \begin{cases} 5x - 4, & 0 < x \leq 1 \\ 4x^2 + 3bx, & 1 < x < 2 \end{cases}\), is continuous at every point of its domain is :

If \(x, y\) and \(z\) are non-zero distinct numbers, then \(\left|\begin{array}{ccc}x+y & y+z & z+x \\ z & x & y \\ 1 & 1 & 1\end{array}\right|\) is equal to

A pair of dice is thrown until the sum of numbers appeared is a perfect square or a non-perfect square sum appeared five times in succession. If random variable \(X\) denotes the number of non perfect square sums appeared. then \(P(X>0)\) is

The following system of equations \(2 x-y+3 z=5,3 x+2 y-z=7,4 x+5 y-\lambda z=\mu\) is consistent. Then

Suppose that A, B and C are matrices of order \(m \times n, n \times 5\) and \(5 \times q\) respectively. The restriction on m, n and q so that AB - BC is defined are

The value of the determinant \(\left|\begin{array}{ccc}a+b & b+c & c+a \\ c & a & b \\ 1 & 1 & 1\end{array}\right|\) is :

\(f(x)=\left\{\begin{array}{ll}\frac{\sqrt{1+p x}-\sqrt{1-p x}}{x}, & -1 \leq x<0 \\\frac{2 x+1}{x-2}, & 0 \leq x \leq 1\end{array}\right.\)
is continuous in the interval \([-1,1]\), then \(p\) is equal to :

The osmotic pressure of a solution at 0°C is 2 atm. What will be its osmotic pressure at 819 K ?

Observe the diagram and answer the following questions:

Identify the correct statements with respect to retrovirus.
A. DNA genome of the virus forms complementary RNA
B. After getting into the body of a person the virus enter into macrophages
C. The viral RNA gets incorporated into host cell DNA
D. The macrophages act like virus factory
Choose the correct answer from the options given below:

Succession occurring after flood is:

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.
A pregnant female is advised not to discard the yellowish fluid called colostrum, secreted during the initial days of lactation, because it is rich in:

A battery of emf 4 V and internal resistance \(1 \, \Omega\) is connected across a wire of resistance \(9.0 \, \Omega\). The number of electrons passing through the cross-section of the wire in 4 s is: