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\(\frac{1}{\sqrt{3}+2}\) = \(\frac{1}{\sqrt{3}+2}\times \frac{\sqrt{3} - 2}{\sqrt{3} - 2}\) = \(\frac{\sqrt{3}-2}{(\sqrt{3})^{2} -2^{2}}\) = \(\frac{\sqrt{3}-2}{3-4}\) = \(\frac{\sqrt{3}-2}{1}\) = -\(\sqrt{3}+2\) = 2- \(\sqrt{3}\)

5000 : 5000 * 500 5000 : 2500000 5 : 2500 1 : 500

efficiency = (M.A / V.R) x 100/1 => 60/100 = M.A/5 ∴M.A = (60 X 5) / 100 = 3 But M.A = Load/Effort; => 3 = Load/500 ∴Load = 500 x 3 = 1500N

I. Jet aircraft — Expel gases backward → push aircraft forward (thrust). II. Rocket — Expel gases backward → move forward (even in space). III. Gun recoil — Bullet forward → gun moves backward. IV. Walking — Foot pushes ground backward → ground pushes you forward.

Vol. of ice = \(\frac{\text{M}}{\text{D}}\) = \(\frac{450}{900}\) = 0.500m\(^3\) vol. of water = \(\frac{\text{M}}{\text{D}}\) = \(\frac{450}{1000}\) = 0.450m\(^3\) ∴ Difference in vol. = 0.500 - 0.450 = 0.05m\(^3\)

An Electrophorus is a simple manual electrostatic generator used to produce a large number of similar charges through the process of induction.

The company built a DC dynamo (with a commutator) instead of the required AC one (which needs slip rings). The simplest and most direct way to correct this—without rewinding the coil or major redesign—is to replace the commutator with slip rings.

Earthing is used to protect you from an electric shock. It does this by providing a path (a protective conductor) for a fault current to flow to earth. It also causes the protective device (either a circuit-breaker or fuse) to switch off the electric current to the circuit that has the fault.

The extremely short wavelength of X-rays allows them to interact with the atomic-scale structure of crystals via diffraction, revealing details of the crystal lattice, atomic positions, and bond lengths.

Electricity excites the gas atoms inside the tube, causing them to release UV light. This UV light then hits a phosphor coating on the glass, which glows to produce visible light.

In most cases, there are essentially no attractive forces between particles. This means that a gas has nothing to hold a specific shape or volume. It's difficult to achieve an orderly arrangement of gas molecules due to their high kinetic energy, large distances between particles, and lack of intermolecular forces. These factors cause the molecules to move randomly and freely, making it difficult to constrain them into a structured arrangement.

CaCO\(_3\)(s) + 2HCl(aq) → CaCl\(_2\) + H\(_2\)O(l) + CO\(_2\) The relative molecular mass of CaCO\(_3\) = 40 + 12 + (16 x 3) = 52 + 48 = 100 ; Relative molecular mass of CO\(_2\)= 12 + (10 x 2) = 44 From the above equation, 100g of CaCO\(_3\) reacts with 44g of CO\(_2\) at s.t.p. i.e 22.4 dm\(^3\) 2g of CaCO\(_3\) will react with (2 x 22.4)/100 of CO\(_2\) = 0.448 dm\(^3\) 0.448 dm\(^3\) = 0.448 x 1000 = 448cm\(^3\) Alternatively, CaCO\(_3\)(s) + 2HCl(aq) → CaCl\(_2\) + H\(_2\)O(l) + CO\(_2\) 1 : 2 1 The focus is on CaCO\(_3\) and CO\(_2\) and they are in ratio 1 : 1, hence, we can calculate the number of moles of CaCO\(_3\) and substitute the value for the number of moles of CO\(_2\), since their number of moles will also be the same. Molar mass of CaCO\(_3\) = Ca + C + O\(_3\) = 40 + 12 + (16 x 3) = 100g/mol Number of moles of CaCO\(_3\) = \(\frac{mass}{molar mass}\) = \(\frac{2}{100}\) = 0.02 mole Number of moles = \(\frac{Volume}{molar volume}\) 0.02 = \(\frac{volume}{22.4}\) Volume = 0.02 x 22.4 = 0.02 x 22400 = 448 cm\(^3\)

Tan θ = 5√3/5 Tan θ = √3 θ = 60o

Coordinates of the line are (x1 y1)(0,2) respectively and (x2 y2)(2,0) respectively Gradient (m) of the line = (y2 - y1) / (x2 - x1) = (0-6) / (2-0) = -6/2 = -3 Equation of the line y-y1 = m(x-x1) y - 6 = -3(x - 0) y - 6 = -3x y + 3x = 6 inequality; from the y axis, the shaded region is below the line ∴ y + 3x ∠ 6 and line is a broken line

Each interior Angle of the polygon = (n-2)180_n = (6-2)180_6 = 4 x 30 = 120o i.e ∠PQR = 120o ∴ RQD = 120/2 = 60o also ∴ Δ QOR is equilateral Δ ∴ QO = 7cm ∴ PO = QO = RO ...... = 7cm radius of the circumference of the circle = 2πr = 2 x 22/7 x 7/1 = 44 cm