Ferromagnetism is the property of materials like iron, cobalt, and nickel to retain permanent magnetic properties due to aligned electron spins.
De Broglie proposed that all matter exhibits wave-particle duality. Both light (photons) and electrons show properties of both waves and particles, confirmed by experiments like double-slit interference and photoelectric effect.
Work done against constant pressure: W = -PΔV. Given W = -500 J and P = 2 atm = 2 × 101325 Pa. ΔV = -W/P = 500/(2 × 101325) ≈ 2.47 × 10⁻³ m³ = 2.47 L.
Linear expansion: ΔL = α × L₀ × ΔT = 1.2 × 10⁻⁵ × 1 × 100 = 1.2 × 10⁻³ m = 1.2 mm.
The lens formula relates object distance, image distance, and focal length for any lens system.
We are given the focal length (f) = 15 cm and image distance (v) = 30 cm. We need to find the object distance (u) using the lens formula.
The lens formula relates these three quantities. Rearranging to solve for object distance:
In the standard sign convention for lenses, the object distance is measured from the lens. Since the object is placed on the side from which light enters (a real object), it is taken as negative.
The object distance is -30 cm (Option D).
The Second Law of Thermodynamics states that for an isolated system, entropy always increases or remains constant, never decreases. This defines the direction of spontaneous processes and the arrow of time.
Each half has resistance R/2. When connected in parallel: 1/R_new = 1/(R/2) + 1/(R/2) = 4/R, so R_new = R/4.
Object at 2f (40 cm = 2 × 20 cm) forms image at 2f. Using mirror equation confirms v = 40 cm, m = -1 (real, inverted, same size as object).
This problem involves using trigonometry to find the height of a ladder against a wall.
The ladder, wall, and ground form a right triangle where the ladder is the hypotenuse, the wall height is the opposite side to the 60° angle, and the ground distance is the adjacent side.
Since we need the height (opposite side) and have the hypotenuse and angle, we use the sine function: sine of the angle equals opposite divided by hypotenuse.
Substitute the value of sin(60°) = √3/2 and solve for height.
Calculate the approximate decimal value: 5√3 ≈ 5 × 1.732 = 8.66 m
The ladder reaches a height of 5√3 m or approximately 8.66 m on the wall.
Answer: (B) 5√3 m or 8.66 m
After 30 years = 3 half-lives: N = N₀ × (1/2)³ = N₀/8. The sample reduces by half three times successively.
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