Consider two lines \(l_1\) and \(l_2\) with cartesian equations \(\frac{x}{2}=\frac{1-y}{-2}=\frac{z}{1}\) and \(\frac{2 x-5}{16}=\frac{y-2}{-1}=\frac{z-5}{4}\) respectively. Which of the following is/are true?
(A) Direction ratio of \(l_1\) are \(2,2,1\)
(B) Direction cosines of \(l_1\) are \(\frac{2}{3}, \frac{-2}{3}, \frac{1}{3}\)
(C) Direction ratio of \(l_2\) are \(16,-1,4\)
(D) Angle between \(l_1\) and \(l_2\) is \(\cos ^{-1}\left(\frac{38}{3 \sqrt{273}}\right)\)
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A person can sell a maximum of 20 units of shirts and pants on which a profit of ₹40 is made on each shirt and a of ₹30 on each pant. A minimum of 2 shirts are being sold, while pants are sold at least 4 times as many as shirts the maximum profit is:

For \(y \neq 0\), the particular solution of the differential equation \(2 y e^{x / y} d x+\left(y-2 x e^{x / y}\right) d y=0\) at the point \((1,1)\) is

Match List - I with List - II

List - I (Example)	List - II (Component of Time Series)
(A) Lockouts and strikes	(I) Secular trend
(B) Rise and fall of share market	(II) Seasonal trend
(C) Continuous decline in death rate	(III) Irregular trend
(D) The rise in prices before Diwali	(IV) Cyclical trend

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The value of \(\tan ^{-1}(-\sqrt{3})+\cos ^{-1}\left(-\frac{1}{2}\right)\) is:

If \(f(x)=\left\{\begin{array}{cl}\frac{k \cos x}{\pi-2 x}, & x \neq \frac{\pi}{2} \\ 3, & x=\frac{\pi}{2}\end{array}\right.\) is continuous at \(x=\frac{\pi}{2}\), then \(k\) is :

The angle between the lines \(\vec{r}=3 \hat{i}+2 \hat{j}-4 \hat{k}+\lambda(\hat{i}+2 \hat{j}+2 \hat{k})\) and \(\vec{r}=5 \hat{j}-2 \hat{k}+\mu(3 \hat{i}+2 \hat{j}+6 \hat{k})\) is:

The de Broglie wavelength of an electron having kinetic energy 56 eV is :

In which of the following intervals, the function \(f(x)=-x^2-2 x+15\) is decreasing ?

A slab of material of dielectric constant \( k \), having the same area as the plate of a parallel plate capacitor but has a thickness \( \frac{3}{5} \) of the distance between the plates \( d \), is inserted between the plates of the capacitor. When there is air between the plates, the potential difference is \( V_0 \). What is the potential difference between the plates of the capacitor after inserting the dielectric?

Read the following passage carefully and answer the given questions.
Plasmodium, a tiny protozoan is responsible for the disease malaria. 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. Innate immunity consist of four types of barriers. These are – (i) Physical barriers- skin on our body is the main barrier which prevents entry of the micro-organisms. (ii) Physiological barriers- Acid in the stomach, saliva in the mouth, tears from eyes-all prevent microbial growth. (iii) Cellular barriers- Certain types of leukocytes (WBC) of our body like polymorpho-nuclear leukocytes (PMNL-neutrophils) and monocytes and natural killer (type of lymphocytes) in the blood as well as macrophages in tissues can phagocytose and destroy microbes. (iv) Cytokine barriers- virus-infected cells secrete proteins called interferons which protect non-infected cells from further viral infection. Allergy is due to the release of chemicals like histamine and serotonin from the mast cells. 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.
Malignant malaria is caused by _____ is the most serious one and can even be fatal.

Which of the following statements are INCORRECT regarding biodiversity:
A. Rauwolfia vomitoria possess the species diversity in terms of potency and concentration of the active chemical reserpine.
B. Western Ghats have a greater amphibian species diversity than the Eastern Ghats.
C. India has more than 60,000 genetically different strains of rice and 10,000 varieties of mango.
D. India has greater ecosystem diversity than Norway.
Choose the correct answer from the options given below:

What does 'r' in equation dN/dt = rN (K-N / K) represent?