The feasible region represented by the constraints of the linear programming problem :
\(x+y \leq 6, y \leq 7, x \geq 4, x, y \geq 0\) is :

If \(A=\left[\begin{array}{l}-2 \\ -1 \\ -4\end{array}\right], B=\left[\begin{array}{lll}-1 & 2 & 3\end{array}\right]\), then the value of \(A^{\prime} B^{\prime}\) is

The area of region bounded by the curve \(y=\cos x\) and \(x\)-axis between \(x=0\) and \(x=\pi\) is

If the lines \(\frac{x-5}{5 \lambda+2}=\frac{2-y}{5}=\frac{1-z}{-1}\) and \(x=\frac{y+1 / 2}{2 \lambda}=\frac{z-1}{3}\) are perpendicular, then the value of \(\lambda\) is equal to

The maximum slope of the curve \(y=-x^3+3 x^2+9 x-27\) is:

Consider the line \(\vec{r}=\hat{i}-2 \hat{j}+4 \hat{k}+\lambda(-\hat{i}+2 \hat{j}-4 \hat{k})\)
Match List-I with List-II

List-I	List-II
(A) A point on the given line	(I) \(\left(\frac{-1}{\sqrt{21}}, \frac{2}{\sqrt{21}}, \frac{-4}{\sqrt{21}}\right)\)
(B) direction ratios of the line	(II) \((4,-2,-2)\)
(C) direction cosines of the line	(III) \((1,-2,4)\)
(D) direction ratios of a line perpendicular to given line	(IV) \((-1,2,-4)\)

Choose the correct answer from the options given below:

Which of the following statement(s) is/are TRUE?
(A) Skew symmetric matrix of even order is always symmetric
(B) Skew symmetric matrix of odd order is non-singular
(C) Skew symmetric matrix of odd order is singular
(D) Skew symmetric matrix is always square matrix
Choose the correct answer from the options given below:

Arrange the following nuclei in the ascending order of their stability.
(A) Oxygen (\( {}^{16}\text{O} \)) with binding energy 127.5 MeV
(B) Uranium (\( {}^{238}\text{U} \)) with binding energy 1808.8 MeV
(C) Helium (\( {}^{4}\text{He} \)) with binding energy 28.3 MeV
(D) Iron (\( {}^{56}\text{Fe} \)) with binding energy 490 MeV
Choose the correct answer from the options given below:

An oil drop of mass m carrying a charge +q is held stationary in air by an electric field E. The electric field is correctly given by

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.
The drug, which is very effective sedative and painkiller and useful for patients who have undergone surgery is -

Select the statements(s) which is/are true for Baculoviruses:
A. They belong to genus Nucleopolytetra viruses.
B. They are species specific in their action.
C. They have narrow spectrum insecticidal application.
D. They don't have any negative impact on non target insects.
Choose the correct answer from the options given below:

Two point charges \( 2 \, \mu\text{C} \) and \( 3 \, \mu\text{C} \) are placed at a distance of 5 cm from each other. The magnitude of the electrostatic force between them is:

Which of the following statements is correct for a charged metallic shell?