A small telescope has an objective lens of focal length 120 cm and an eyepiece of focal length of 5.0 cm. The magnifying power of telescope for viewing distant objects in normal adjustment is

A solenoid with an iron core and a bulb are connected to an a.c. source. The bulb is glowing with certain brightness. When the iron core is removed from the solenoid, the brightness of the bulb

A point charge – 5 µC is at a distance 5 cm directly above the centre of a square of side 10 cm.
The magnitude of electric flux through this square is:

Choose the incorrect statements from the options given below:
(A) S I unit of inductive reactance and capacitive reactance is Ohm
(B) Inductive reactance acting like resistance, stops the dc and ac both
(C) Inductive reactance and capacitive reactance both are proportional to frequency of ac supply,
(D) There is no power consumption in pure capacitive reactance.
Choose the correct answer from the options given below:

Identify the important features of the semiconductor devices from the following
1. Semiconductor devices require cathode heating for the production of charge carriers.
2. They have long life and high reliability.
3. They are small in size and consume low power.
4. They operate at high voltage.
Choose the correct answer from the options given below:

A plane electromagnetic wave of frequency 50 MHz travels in free space along the z-direction. If at a particular point in space and time, \( \vec{E} = (9.3\hat{j}) \text{ V m}^{-1} \), what is \( \vec{B} \) at this point?

Light of frequency \( \nu \) falls on a metal whose work function is \( h\nu_0 \). Choose the most appropriate condition from the following under which the photoelectric effect will take place.

The differential equation representing the family of curves \(y=A x+\frac{B}{x}, x \neq 0\), where A and B are arbitrary constants, is given by

The general solution of the differential equation \(x\frac{d y}{d x}+2 y=x^2,x\neq 0\) is:

The interval, on which the function \(f(x)=x^2 e^{-x}\) is increasing, is equal to:

Answer the question on the basis of passage given below :
Aldehydes and ketones represent two essential classes of organic compounds
which are extensively used in the synthesis of a wide variety of other organic molecules.
Due to the inherent polarity of the central carbonyl group, these substances readily undergo nucleophilic addition reactions.
Broadly speaking, these addition reactions can be categorized into two types:
one in which simple addition of the nucleophilic reagent occurs across the \(> C = O\) bond, and the second type where the initial addition is subsequently followed by the elimination of a water molecule.
A variety of ammonia derivatives, including hydroxylamine, hydrazine, phenylhydrazine,
2, 4-dinitroplhenylhdrasine, and semicarbaside, all belong to this second category of reactions.
These specific derivatives are fundamentally used for the identification and definitive characterization of aldehydes and ketones. Significantly, both types of nucleophilic addition reactions are strongly influenced by both steric and electronic factors.
As a general rule, aliphatic aldehydes exhibit higher reactivity compared to aromatic aldehydes.
The aliphatic aldehydes demonstrate the ability to reduce both Fehling's solution and Tollen's reagent, whereas aromatic aldehydes are limited to reducing only Tollen's reagent.
In a similar manner to aldehydes, aromatic ketones are observed to be less reactive than aliphatic ketones towards all nucleophilic addition reactions.
In a separate context, phenols and carborylic acids both exhibit acidic properties in nature.
Both classes of compounds readily dissolve in NaOH solution and cause blue litmus to turn red.
However, carboxylic acids stand out as much stronger acids than phenols and thus can decompose sodium bicarbonate \(\left( NaHCO _3\right)\) with the distinct evolution of \(CO _2\) gas, a reaction which phenols do not undergo.
It is important to note that both electron- donating and electron- withdrawing substituents significantly influence the acid strength of both aliphatic as well as aromatic carborylic acids.
Furthermore, unlike all other common aliphatic acids, formic acid uniquely possesses reducing properties and simultaneously does not display the typical reactions characteristic of the alkyl group.
Which of the following compound most readily undergoes nucleophilic addition reaction?

Using integration the area enclosed by the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) is equal to :

For Z = 3x + 4y, subject to the constraints \(x+y \leq 5, x \geq 0, y \geq 0\), the shaded region shown in the figure as OAB is bounded and the coordinates of the corner points O, A, B are (0, 0), (5, 0) and (0, 5) respectively. The maximum value of Z is: