Read the following statements related to telescopes carefully:
(A) The main considerations of an astronomical telescope are its light gathering power and its resolution.
(B) the ability to observe two objects (very nearly in the same direction) distinctly depends on the diameter of the objective
(C) large-sized lenses which form images that are free from any kind of chromatic aberration and distortions can be made easily
(D) Telescopes with mirror objectives are free from chromatic aberration
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The number densities of electrons and holes in pure silicon at 273 K are equal and their values are \( 1.5 \times 10^{16} \text{ m}^{-3} \). On doping, the hole density increases to \( 4.5 \times 10^{27} \text{ m}^{-3} \). The electron density in the doped silicon will be :

The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability \( \frac{4}{3} \) for this wavelength, will be :

When light travels from one medium to another medium of different refractive index, then the wave will have change in its :

An astronomical telescope has a large aperture to

A polythene piece rubbed with wool is found to have a negative charge of \( 8 \times 10^{-10} \, \text{C} \). What is the number of electrons transferred ?

Equal currents are flowing in four infinitely long wires. The distance between each other is the same and directions of currents are as shown in the figure. The net force on wire 2 is

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Particular solution of the differential equation \(\log \left(\frac{d y}{d x}\right)=x+y\) given that when x = 0 y = 0 is:

Read the passage carefully and answer the given questions.
Recombinant DNA Technology Asexual reproduction preserves the genetic information, while sexual reproduction permits variation. Traditional hybridization procedures used in plants and animals breeding very often lead to inclusion and multiplication of undesirable genes along with the desired genes. The techniques of genetic engineering, which include creation of recombinant DNA, use of gene cloning and gene transfer, overcome this limitation and allow us to isolate and introduce only one or a set of desirable genes without introducing genes into the target organism.
Which one of the following is not used as a vector in recombinant DNA technology?

The radius of a nucleus varies with its mass number A as:

The function \(f(x)=2 x^3-3 x^2-12 x+4\) has:
(A) two points of local maxima.
(B) two points of local minima.
(C) one local maxima and one local minima.
(D) no local maxima or local minima.

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

Let \(f: R \rightarrow R\) defined by \(f(x)=2 x^3-7\) for \(x \in R\). Then :
(A) \(f\) is one-one function
(B) \(f\) is many to one function
(C) \(f\) is bijective function
(D) \(f\) is into function
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