The probability distribution of a discrete random variable x is given below:

\(x\)	\(2\)	\(3\)	\(4\)	\(5\)
\(p(x)\)	\(\frac{5}{k}\)	\(\frac{7}{k}\)	\(\frac{9}{k}\)	\(\frac{10}{k}\)

The value of \(k\) is

The point estimate of the population standard deviation as per the below mentioned data from a simple random sample 6, 10, 15, 12, 9, 8 will be :-

If \(f: R \rightarrow A\) given by \(f(x)=x^2-6 x+12\) is a surjective function, then the set \(A\) is :

If the direction ratios of two lines are \(a, b, c\) and \((b-c),(c-a),(a-b)\) respectively, then the angle between these lines is :

Let \(f(x)=|x|\) and \(g(x)=[x]\), then the value of \(f \circ g\left(-\frac{9}{2}\right)-g \circ f\left(-\frac{9}{2}\right)\) is :

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

If \(\cos^2 y + \sin(xy) = \lambda\), then \(\frac{dy}{dx} =\)

Arrange the following stages of oogenesis in correct sequence of their formation.
(A) Secondary oocyte
(B) Oogonials
(C) Ovum
(D) Primary oocyte
Choose the correct answer from the options given below:

The electric field and magnetic field of a plane electromagnetic wave propagating in vacuum are expressed as
\(E_x=E_0 \sin (k z-\omega t)\)
\(B_y=B_0 \sin (k z-\omega t)\)
Which of the following statements are correct?
(A). The wave is propagating along the z- direction.
(B). The electric field Ex and magnetic field By are perpendicular to each other and perpendicular to the z direction.
(C) The electric and magnetic fields Ex and By are perpendicular to each other, and parallel to the direction of propagation.
(D) k is related to the wave length À of the wave by the usual equation \(k = A / 2 Tt\)
Choose the correct answer from the options given below:

Read the given paragraph carefully and answer the following questions:
Since the DNA is enclosed within the membranes, we have to break the cell open to release DNA along with other macromolecules such as RNA, proteins, polysaccharides and also lipids. This can be achieved by treating the bacterial cells/plant or animal tissue with enzymes such as lysozyme (bacteria), cellulase (plant cells), chitinase (fungus). There are some basic steps in genetically modifying an organism (i) identification of DNA with desirable genes; (ii) introduction of the identified DNA into the host; (iii) maintenance of introduced DNA in the host and transfer of the DNA to its progeny. Agrobacterium tumifaciens, a pathogen of several dicot plants is able to deliver a piece of DNA known as 'T-DNA' to transform normal plant cells into a tumor and direct these tumor cells to produce the chemicals required by the pathogen. Other molecules can be removed by appropriate treatments and purified DNA ultimately precipitates out after the addition of chilled ethanol. Selection of recombinants due to inactivation of antibiotics is a cumbersome procedure because it requires simultaneous plating on two plates having different antibiotics. Therefore, alternative selectable markers have been developed which differentiate recombinants from non-recombinants on the basis of their ability to produce colour in the presence of a chromogenic substrate. In this, a recombinant DNA is inserted within the coding sequence of an enzyme, ß'-galactosidase. This results into inactivation of the gene for synthesis of this enzyme, which is referred to as insertional inactivation.
Agrobacterium tumefaciens, a pathogen of several dicot plants, is able to deliver a piece of DNA known as:

Which of the following does not affects genetic equilibrium/Hardy Weinberg Equilibrium

Arrange the following in the increasing order of de-Broglie wavelength:
A. A bullet of mass 0.02 kg travelling at speed of 3.3 km s⁻¹
B. A ball of mass 0.0331 kg moving with speed of 2 m s⁻¹
C. A dust particle of mass \( 2 \times 10^{-10} \text{ kg} \) drifting with a speed of 3.3 m s⁻¹
D. A photon having a momentum of \( 6.63 \times 10^{-26} \text{ kg m s}^{-1} \)
E. An electron accelerated through a potential difference of 100 V
Choose the correct answer from the options given below:

For n-type semiconductor, which of the following statements is true?