Using the distance formula: d = √[(1 - 5)² + (1 - 5)²] = √[16 + 16] = √32 = 4√2.

Adding a base to hydrochloric acid will neutralize it, resulting in an increase in pH.

Adding a base to an acidic solution increases the pH, making it less acidic.

The electron configuration of chlorine is 1s² 2s² 2p⁶ 3s² 3p⁵, filling up to the 3p subshell.

Oxygen has 8 electrons, and its electron configuration is 1s² 2s² 2p⁴.

The standard form of a circle's equation is (x-h)² + (y-k)² = r². Here, h=3, k=-2, r=5, so (x-3)² + (y+2)² = 25.

Standard form of a circle: (x-h)² + (y-k)² = r². Here, h=2, k=-3, r=5.

Parallel lines have the same slope. Using point-slope form: y - 2 = 3(x - 1) gives y = 3x - 1.

The equation of a line through the origin with slope m is y = mx. Thus, y = -3x.

Using the slope-intercept form y = mx + b, with m = -4 and b = 0, the equation is y = -4x.

In series, the equivalent resistance is the sum: R_eq = R1 + R2 = 4 Ω + 6 Ω = 10 Ω.

In series, the equivalent resistance is the sum: R_eq = R1 + R2 = 4 Ω + 6 Ω = 10 Ω.

Using the lens formula 1/f = 1/v - 1/u, we find f = -20 cm.

The capacitance (C) of a parallel plate capacitor is given by C = εA/d, where ε is the permittivity, A is the area of the plates, and d is the distance between them.

Chlorophyll is the pigment in plants that absorbs sunlight, which is essential for photosynthesis.

Mitochondria are known as the powerhouses of the cell, generating ATP through cellular respiration.

The GDP growth rate of India is projected to be around 6.8% for 2023.

Kangchenjunga is the highest peak in India, standing at 8,586 meters.

The IUPAC name for CH3-CH2-COOH is propanoic acid, as it has three carbon atoms in the longest chain.

Latent heat of fusion (L) = Q/m = 2400 J / 80 g = 30 J/g.

The latus rectum of a parabola y^2 = 4px is given by 4p. Here, 4p = 12, so p = 3, and the latus rectum is 4p = 12.

LCM of 4 and 6 is 12.

The length of the diagonal d of a rectangle can be found using the Pythagorean theorem: d = √(length² + width²) = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.

Diagonal = √(length² + width²) = √(6² + 8²) = √(36 + 64) = √100 = 10 cm

Area = πr². Given area = 50π, r² = 50, r = √50 = 5√2. Diameter = 2r = 10√2 units.

In an equilateral triangle, the median is equal to the side length, so it is 10 cm.

Using the Taylor series expansion for cos(x), we find that lim (x -> 0) (cos(x) - 1)/x^2 = -1/2.

Using the derivative of e^x at x = 0, we find that lim (x -> 0) (e^x - 1)/x = 1.

45°E corresponds to 45 / 15 = 3 hours ahead of GMT, so it will be 12:00 noon + 3 hours = 3:00 PM.

90 degrees East is 6 hours ahead of GMT, so 6:00 AM + 6 hours = 12:00 PM.