The magnification (m) and focal length (f) of a plane mirror are:

White light is used to illuminate the two slits in a Young's double slit experiment. The separation between the slits is b and the screen is at a distance D from the slits. At a point on a screen directly in front of one of the slits, certain wavelength are missing. Some of these wavelengths are :
(A) \( \lambda = \frac{b^2}{D} \)
(B) \( \lambda = \frac{2b^2}{D} \)
(C) \( \lambda = \frac{b^2}{3D} \)
(D) \( \lambda = \frac{2b^2}{3D} \)
Choose the correct answer from the options given below :

A thin convex lens of refractive index 1.5 has focal length f1. When immersed in a liquid of refractive index 5/3, its focal length is found to be f2. The relationship between f1 and f2 is:

In an AC circuit, the power factor :

By increasing the temperature, resistivity of a conductor and a semiconductor

Which of the following statements is true about electromotive force (emf) of a cell?

A voltmeter of resistance \( 600 \text{ } \Omega \) is used to measure the potential drop across \( 300 \text{ } \Omega \) resistor. The measured value of potential drop will be

Which of the following can be an objective function for a Linear Programming problems in two variables x and y?

Read the following paragraph and answer the given questions.
Cancer detection is based on biopsy and histopathological studies. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs. Do you know why mother's milk is considered very essential for the new-born infant? The yellowish fluid colostrum secreted by mother during the initial days of lactation has abundant antibodies (IgA) to protect the infant. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal. The exaggerated response of the immune system to certain antigens present in the environment is called allergy. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Drugs like barbiturates, amphetamines, benzodiazepines, and other similar drugs, that are normally used as medicines to help patients cope with mental illnesses like depression and insomnia, are often abused. Morphine is a very effective sedative and painkiller, and is very useful in patients who have undergone surgery.
A pregnant female is advised not to discard the yellowish fluid called colostrum, secreted during the initial days of lactation, because it is rich in:

Read the Passage carefully and answer the Questions:
Kinetic studies not only help us to determine the rate of a chemical reaction but also describe the conditions by which the reaction rates can be altered. The factors such as concentration, temperature, pressure and catalyst affect the rate of a reaction.
The speed of a reaction or the rate of a reaction can be defined as the change in concentration of a reactant or product in unit time.
Rate \(=k[A]^{ a }[B]^{ y }\)
Here \(k\) is the rate constant
\(x+y\) gives the overall order of a reaction, whereas \(x\) and \(y\) represent the order with respect to the reactants \(A\) and \(B\), respectively.
The unit of rate constant for first order reaction is:

The focal length of a thin lens in vacuum is f. If the material of the lens has refractive index \( \frac{3}{2} \), its focal length when immersed in water of refractive index \( \frac{4}{3} \) would be :

The particular solution of the differential equation \(e^x \sqrt{1-y^2} d x+\frac{y}{x} d y=0\), given that \(y=1\), when \(x=0\), is:

The area (in sq. units) bounded by the curve y = cos x and x-axis between x = 0 and x = \(\frac{3 \pi}{2}\) is