Which of the following are similarities between the sinking fund and the savings account?
(A) The sinking fund and the savings account are both financial tools.
(B) Both can be used in any emergency.
(C) They both involve setting aside an amount of money for the future.
(D) Both are long-term accounts which can be closed any time.
Choose the correct answer from the options given below

Let \(\vec{a}\) and \(\vec{b}\) be two unit vectors and \(\theta\) is the angle between them. If \(\vec{a}+\vec{b}\) is a unit vector, then \(\theta\) is:

The solution of the differential equation \(y d x+\left(x-y^2\right) d y=0\) is :

Match List - I with List - II

List - I (Time series component)	List - II (Example)
(A) Secular Variation	(I) Pandemic
(B) Seasonal Variation	(II) Recession in business
(C) Cyclic Variation	(III) Monthly sale of woolen clothes
(D) Irregular Variation	(IV) Data regarding National income

Choose the correct answer from the options given below:

Consider the function \(f: R \rightarrow R\) defined by \(f(x)=\frac{x}{x^2+1}\) then

The angle between the two planes \(x+y-z=3\) and \(3 x+2 y+z=5\) is:

The order and degree of the differential equation \(\frac{d^3 y}{d x^3}=\frac{y}{2}+\left(\frac{d y}{d x}\right)^3\), respectively are :

Read the following paragraph carefully and answer the given questions.
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. For determining the cause of allergy, the patient is exposed to or injected with very small doses of possible allergens, and the reactions studied. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Heroin, commonly called smack is chemically diacetylmorphine which is a white, odourless, bitter crystalline compound. This is obtained by acetylation of morphine. 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. 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.
Heroin, commonly called smack is chemically ______ which is a white, odourless, bitter crystalline compound.

Copper can be extracted from:
(A) Cryolite
(B) Malachite
(C) Calamine
(D) Copper glance
(E) Cuprite
Choose the correct answer from the options given below :

Which of the following statements are correct?
(A) A nucleus of mass number A has a radius R given by the expression \( R = R_0 A^{1/3} \)
(B) Volume of nucleus is proportional to mass number A
(C) The density of nucleus increases with the radius of nucleus.
(D) Density of nuclear matter does not depend on its mass number A
Choose the correct answer from the options given below:

Which position of phenol is involved in coupling reaction with benzene diazonium chloride ?

The vapour pressure of pure benzene is } \(0.900\) bar. If a non-volatile electrolytic solid is added, the vapour pressure of the solution becomes \(0.200\) bar. If the number of moles of solute and solvent in the solution are \(1\) and \(2\) respectively, what is the value of van't Hoff factor (i)?

The rate of decomposition is slower if :