If \(X\) is normal distribution random variable with mean \(\mu=10\) and standard deviation \(\sigma=2, Z\) is standard normal variable and \(F(Z)\) is cumulative distribution function, then which of the following are true?
[Given that \(F(1.5)=0.9332, F(3)=0.9986, F(2.25)=0.9878\) and \(F(1)=0.8413\) ]
(A) \(P(X<13)=0.9332\)
(B) \(P(X>16)=0.9986\)
(C) \(P(12<X<14.5)=0.1465\)
(D) \(P(X>8)=0.8413\)
Choose the correct answer from the options given below:

Choose the wrong statement from the following :

The curves \(x=y^2\) and \(x y= K\), cut at right angles if :

If \(A=\left[\begin{array}{cc}-2 & 3 \\ 1 & 2\end{array}\right]\) and \(B=\left[\begin{array}{cc}-1 & 0 \\ 2 & 3\end{array}\right]\), then \((3 A+2 B)^{\prime}\) is:

For the set of all straight lines in a plane, the relation of "perpendicularity" is:
(A) reflexive but neither symmetric nor transitive.
(B) symmetric but neither reflexive nor transitive.
(C) transitive but neither reflexive nor symmetric.
(D) neither reflexive nor symmetric nor transitive.
(E) reflexive, symmetric but not transitive.
Choose the correct answer from the options given below:

The maximum value of \(\frac{\log x^3}{3 x}\) occurs at \(x=\)

About linear programming problem (LPP), which of the following statements are correct ?
(A) In a LPP, the linear inequalities or restrictions on the variables are called linear constraints.
(B) If the feasible region for an LPP is unbounded, then the maximum or minimum value of the objective function \(Z=a x+b y\) never exists.
(C) The feasible region for an LPP is always conver.
(D) The common region determined by all the linear constraints of an LPP is called the feasible region.

Read the paragraph given below and answer the question.
Sutton and Boveri argued that the pairing and separation of a pair of chromosomes would lead to the segregation of a pair of factors they carried. Sutton united the knowledge of chromosomal segregation with Mendelian principles and called it the chromosomal theory of inheritance. Following this synthesis of ideas, experimental verification of the chromosomal theory of inheritance by Thomas Hunt Morgan and his colleagues, led to discovering the basis for the variation that sexual reproduction produced. Morgan worked with the tiny fruit files, which were found very suitable for such studies. They could be grown on simple synthetic medium in the laboratory. They complete their life cycle in a short span of time and a single mating could produce a large number of progeny flies. Also, there was a clear differentiation of the sexes - the male and female flies are easily distinguishable. Also, it has many types of hereditary variations that can be seen with low power microscopes.
Cross performed between yellow bodied, white eyed females and brown bodied red eyed males of Drosophila results in:

Question based on the following passage :
P-Block elements are placed in group 13 to 18 in the periodic table. Group 15 is nitrogen family.
Nitrogen can react with hydrogen, oxygen, halogens etc. It shows multiple oxidation states in its various oxides i.e. \(N_2O, N_2O_3, N_2O_5\) etc. Important allotropic forms of phosphorus are white, red and black phosporus. Various compounds of phosphorus are phosphine, \(PCl_3, PCl_5\) and oxoacids of phosphorus. Oxidation states \(+1\) to \(+5\) are seen in various oxoacids of phosphorus. Group 17 elements are collectively known as halogens. Bond dissociation enthalpy of \(F_2\) is smaller than \(Cl_2\).
The gases present in group 18 are chemically unreactive, they form only few compounds. Neil Bartlett (in 1962) observed the reaction of a noble gas. Since then, many noble gas compounds have been synthesised.
Following statements are given regarding structure of \(N_2O_5\) :
(A) It has an angular structure
(B) It has a planar structure
(C) There are 6 sigma and 2 pi bonds
(D) There are 5 sigma and 2 pi bonds
(E) There are 6 sigma and 3 pi bonds
Choose the correct answer from the options given below :

If \(2 f(x)+f\left(\frac{1}{x}\right)=x^2+1\), then \(\int f(x) d x\) is : (Here \(C\) is an arbitrary constant)

If order of matrices \(A, B\) and \(C\) are \(4 \times 3,5 \times 4\) and \(3 \times 7\) respectively, then order of \(C^{\prime} \times\left(A^{\prime} \times B^{\prime}\right)\) is :

Which one of the following is an example of co-evolution?

Read the passage carefully and answer
When a metal is placed in a solution of its ions, the metal can lose electron and can go in the solution as ion or the metal ion in the solution can take electron from the electrode and get deposited as metal. Thus, the electrode acquires either positive or negative charge with respect to the solution leading to the development of a potential difference between the metal electrode and the solution. This potential difference is called the electrode potential of the metal. The electrode potential of a metal is a measure of relative tendency to undergo oxidation (loss of electron) or reduction (gain of electron). When the concentration of the ions in the solution is unity, the electrode potential is called standard electrode potential. The magni of potential depends upon the nature of electrode, concentration of ions in solution and the temperature. In a galvanic cell, the electrode at which oxidation occurs is known as anodic half-cell and the electrode at which reduction occurs is known as cathodic half cell. The emf of the cell in terms of standard reduction potential is given by \(E_{\text {cell }}^{\circ}=E_{\text {cathode }}^{\circ}-E_{\text {anode. }}^{\circ}\).The standard free energy change of the redox reaction taking place in the cell is related to \(E_{\text {cell }}^{\circ}\) by \(\Delta G^{\circ}=-n F E^{\circ}\). A redox reaction would occur spontaneously if the free energy change is negative. The equilibrium constant of the reaction is related to the standard free energy change by \(\Delta G^{\circ}=-R T \ln K\).
The standard reduction potential of Zinc is represented by the reaction