RRB NTPC GK Questions 2026

The Treaty of Frankfurt ended the Franco-Prussian War in 1871 and transferred the industrial border provinces of Alsace and most of Lorraine to the new German Empire, along with a heavy war indemnity.

The parliament elected in May 1848 met in the Church of St Paul at Frankfurt, drafted a constitution for a German nation headed by a monarch answerable to a parliament, and offered that crown to the Prussian king.

Cavour judged that Sardinia-Piedmont could not defeat Austria alone, and at Plombieres in July 1858 he reached a secret understanding with Napoleon III for French military help in a war against Austria.

On 17 March 1861 Victor Emmanuel II of Sardinia-Piedmont was proclaimed King of Italy by the first Italian parliament, after the war of 1859 had taken Lombardy and Garibaldi's campaign of 1860 had added the south.

The Austro-Prussian War of 1866, often called the Seven Weeks War, was decided at Sadowa, also known as Koniggratz, where the Prussian army defeated Austria.

In May 1860 Garibaldi sailed from Genoa with roughly a thousand volunteers, known from their uniform as the Red Shirts, landed in Sicily and then crossed to the mainland and took Naples from the Bourbon rulers of the Kingdom of the Two Sicilies.

The Zollverein was formed in 1834 under Prussian leadership. It removed the internal customs duties that had made trade between the German states slow and costly and reduced the number of currencies in circulation, so a single economic space existed long before a single political one.

As the Franco-Prussian War ended, the German princes assembled in the Hall of Mirrors of the French royal palace at Versailles and proclaimed Wilhelm I of Prussia as German Emperor on 18 January 1871.

Mazzini, a member of the Carbonari who had been sent into exile, founded Young Italy at Marseilles in 1831 and a wider society, Young Europe, at Berne in 1834.

Thomas Young passed light from one source through two narrow slits placed close together and obtained alternate bright and dark bands on a screen.

Polarisation means restricting the vibrations of a wave to one plane, which is only possible if the vibrations are perpendicular to the direction of travel.

The smallest angular separation a telescope can resolve is 1.22 times the wavelength divided by the diameter of the objective, so a larger aperture means a smaller limit of resolution and a greater resolving power.

Diffraction, the bending of a wave round an edge, is appreciable only when the obstacle or opening is of the same order of size as the wavelength.

By Malus's law the intensity transmitted by the second Polaroid is the intensity falling on it multiplied by the square of the cosine of the angle between the two transmission planes.

The fringe width equals the wavelength multiplied by the distance of the screen and divided by the separation of the two slits.

The light reflected from the upper surface of the thin film and the light reflected from the lower surface travel slightly different distances and interfere.

Only a transverse wave, in which the vibrations are at right angles to the direction of travel, can have those vibrations restricted to a single plane by a Polaroid.

Inserting a plate of thickness t in one arm makes the light cross it twice, so the extra path introduced is twice the thickness times the quantity refractive index minus one.

By the Rayleigh criterion the smallest angle the eye can resolve is 1.22 times the wavelength divided by the diameter of the pupil, that is 1.22 multiplied by 500 nanometres and divided by 3 millimetres, which comes to about 2.03 times ten to the power minus four radian.

Brewster found that when unpolarised light falls on a transparent surface at one particular angle of incidence, called the polarising angle, the reflected light is completely plane polarised, and at that angle the refractive index of the surface equals the tangent of the polarising angle.