A manufacturer can sell x items at a price of mp 3x + 5 each. The cost price of x items is ₹\(x^2\ + 5x.
If z is the number of items she should sell to get no profit and no loss, then:

The direction cosines of a line equally inclined with the co-ordinate axes are :

If the points \(A, B, C\) with position vectors \(20 \hat{i}+\lambda \hat{j}, 5 \hat{i}-\hat{j}\) and \(10 \hat{i}-13 \hat{j}\) respectively are collinear, then the value of \(\lambda\) is:

In a linear programming problem, the linear constraints are as follows :
\(x-3 y \geq 0, y \geq 0,0 \leq x \leq 6 \)
where \(z=x+2 y\)
Which of the following statement/s is/are correct ?
(A) The feasible region is not the first quadrant
(B) The feasible region is unbounded in the first quadrant
(C) The feasible region is bounded in the first quadrant
(D) The feasible region is a triangular region
(E) The maximum value of \(z\) is 10
Choose the correct answer from the options given below :

\(\vec{n}\) is a vector of magnitude \(2 \sqrt{3}\) such that it makes equal angles with coordinate axes. The vector equation of the plane passing through (1, -1, 2) and perpendicular to \(\vec{n}\) is:

The area of the region bounded by \(y^2=9 x, x=2, x=4\) and the \(x\)-axis in the first quadrant, is

If the system of equation
\(x-y+z=4\)
\(x-2 y-2 z=9\)
\(2 x+y+\lambda z=1\)
has a unique solution, then

Read the passage carefully and answer the questions given along
Our immune system plays the major role in preventing diseases when we are exposed to disease-causing agents. Immunity is of two types: (i) Innate immunity and (ii) Acquired immunity. The human immune system consists of lymphoid organs, tissues, cells and soluble molecules like antibodies. The immune system also plays an important role in allergic reactions, auto-immune diseases and organ transplantation. The primary lymphoid organs are bone marrow and thymus. The secondary lymphoid organs are spleen, lymph nodes, tonsils, Peyer's patches of small intestine and appendix. There is lymphoid tissue also located within the lining of the major tracts (respiratory, digestive and urogenital tracts) called mucosa associated lymphoid tissue (MALT). It is important to note that HIV/AIDS is not spread by mere touch or physical contact; it spreads only through body fluids. AIDS has no cure, prevention is the best option. Adolescence is accompanied by several biological and behavioural changes and surveys and statistics show that use of drugs and alcohol has been on the rise especially among the youth. Factors associated with drug and alcohol abuse among adolescents are a child's natural curiosity, stress, the perception among youth that it is 'cool' or progressive to smoke, media exposure and an unstable or unsupportive family structures and peer pressure. It is best to identify the situations that may push an adolescent towards use of drugs or alcohol, and to take remedial measures well in time.
Mucosa associated lymphoid tissue is absent in the

Which of the following is not a venereal disease?

Match List - I with List - II

List - I (Laws/properties)	List - II (Statements)
(A) Colligative properties	(I) for a solution of volatile liquids, the partial vapour pressure of each component of the solution is directly proportional to its mole fraction present in the solution.
(B) Henry's law	(II) the total pressure over the solution phase in the container will be the sum of the partial pressures of all the components of the solution.
(C) Raoult's law	(III) depends on the number of solute particles, irrespective of their nature.
(D) Dalton's law of partial pressures	(IV) at a constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas present above the surface of a liquid or solution.

Choose the correct answer from the options given below:

Choooose the wrong statement:

At one place on earth, the resultant magnetic field is 0.25 G and the angle of dip is 45°. The horizontal component of earth's magnetic field will be

A pipe A can fill a tank in 4 hours. There are two outlet pipes, B and C, from the tank which can empty it in 8 and 10 hours respectively. If all the three pipes are opened simultaneously, how long will it take to fill the tank?