If \(z\)-coordinate of a point P on the line joining the points A (2, 2, 1) and B (5, 1, -2) is -1, than \(x\)-coordinate of point P is

The value of \(\left|\begin{array}{ccc}x & x+y & x+y+z \\ 2 x & 3 x+2 y & 4 x+3 y+2 z \\ 3 x & 6 x+3 y & 10 x+6 y+3 z\end{array}\right|\) is

The maximum profit that a company can make if the profit function is
\(P(x)=41+24 x-18 x^2\) is :

Two runners, Ajay and Vijay complete a \(600\) m race in \(38\) seconds and \(48\) seconds respectively. By how many meters will Ajay defeat Vijay?

For real numbers x and y, the relation R is defined as R = {(x, y) : x + y - \(\pi\) is an irrational number}, then the relation R is:

For the LPP: minimize z = 6x + 3y subject to the constraints
\(4 x+y \geq 80\)
\(x+5 y \geq 115\)
\(3 x+2 y \leq 150\)
\(x \geq 0, y \geq 0\) then the minimum value of z is

The relation R on the set of real numbers defined by \(R=\left\{(a, b): a \leq b^2\right\}\) is
(A) Reflexive
(B) Not symmetric
(C) Neither reflexive nor transitive
(D) Transitive
Choose the correct answer from the options given below:

Match List - I with List - II

List - I	List - II
(A) Simple microscope	(I) A concave mirror is used as an objective
(B) Compound microscope	(II) Two convex lenses both of small focal length
(C) Refracting Telescope	(III) Two convex lenses, one of small focal length other of large focal length
(D) Reflecting Telescope	(IV) Single convex lens of small focal length

Choose the correct answer from the options given below:

Choooose the wrong statement:

Osmotic pressure of 0.02 M urea solution at \(27^{\circ} C\), is (given \(R=0.0821 atm L mol ^{-1} K^{-1}\) )

Read the passage carefully and answer the questions based on the passage:
Pest Resistance Plants
Various nematodes parasitize a wide variety of plants and animals, including human beings. A nematode, Meloidogyne incognitia, infects the roots of tobacco plants and causes a great reduction in yield. A noval strategy was adopted to prevent this infestation which was based on the process of RNA interference (RNAi). RNAi takes place in all eukaryotic organisms as a method of cellular defense. This method involves silencing of a specific mRNA due to a complementary dsRNA molecule that binds to and prevents translation of the mRNA (silencing). Plants, bacteria, fungi and animals whose genes have been altered by manipulation are called Genetically Modified Organisms (GMO). GM plants have been useful in many ways. Genetic modification has: (i) made crops more tolerant to abiotic stresses (cold, drought, salt, heat). (ii) reduced reliance on chemical pesticides (pest-resistant crops). (iii) helped to reduce post harvest losses. (iv) increased efficiency of mineral usage by plants (this prevents early exhaustion of fertility of soil). (v) enhanced nutritional value of food, e.g., golden rice, i.e., Vitamin 'A' enriched rice. Genetic modification of organisms can have unpredicatable results when such organisms are introduced into the ecosystem. Therefore, the Indian Government has set up organisations such as GEAC (Genetic Engineering Approval Committee), which will make decisions regarding the validity of GM research and the safety of introducing GM-organisms for public services. Some strains of Bacillus thuringiensis produce proteins that kill certain insects such as lepidopterans (tobacco budworm, armyworm), coleopterans (beetles) and dipterans (flies, mosquitoes).
RNA interference involves:

A fair coin is tossed a fixed number of times. If the probability of getting 11 heads is equal to the probability of getting 13 heads, then the probability of getting 2 heads is:

The vector equation of line passing through (2, -1, 3) and perpendicular to the lines \(\frac{x-2}{3}=\frac{y-1}{1}=\frac{z+2}{2} \quad\) and \(\quad \frac{x+3}{-4}=\frac{y-5}{-3}=\frac{z+1}{2}\)
(Here \(\lambda\) is a parameter)