Archives

Is bleach acid or alkali?

Bleach is any chemical that is used in the whitening of the fabrics or other materials. The bleach can be either an acid or alkali. The most... View Article

Are glucose and fructose structural isomers

Glucose and fructose have the same chemical formula C6H12O6 but their atoms are organised differently making them isomers of each other. Glucose... View Article

Why can fusion and fission both produce energy

Nuclear fission is the splitting of the atomic nuclei. Fusion is the fusing of the nuclei. Both the fission and fusion process releases a... View Article

What is the difference between sulphur and sulphate?

Sulphur is a chemical element that has only sulphur and does not have a charge. Sulphur is a very essential element in life. Sulphate is made... View Article

Why is sulfur so important?

Sulphur is very important for life. Sulphur is the key component in amino acids like methionine and cysteine which is used to make proteins. It... View Article

If tan^-1 2 and tan^-1 3 are two angles of a triangle, then the third angle is

1) π/2 2) π/3 3) π/4 4) π/6 Solution: (3) π/4 Let the third angle be θ, then, tan-1 2 + tan-1 3 + θ = 180o ⇒ tan-1 (2 + 3) / [1... View Article

If 0 < x < 1, then √1 + x² [{x cos (cot^-1 x) + sin (cot^-1 x)}² – 1]^½ =

1) x / √1 + x2 2) x 3) x √1 + x2 4) √1 + x2 Solution: (3) x √1 + x2 0 < x < 1 Let cot-1 x = θ ⇒ cot θ = x ⇒ sin θ = 1 /... View Article

If cos^-1 x + cos^-1 y + cos^-1 z = π, then the value of x² + y² + z² + 2xyz is

1) xy + yz + zx 2) 1 - 2xyz 3) 1 4) 6 Solution: (3) 1 cos-1 x + cos-1 y + cos-1 z = π cos-1 x + cos-1 y = π - [cos-1 z] cos-1... View Article

The value of cos (2 cos^-1 0.8) is

1) 0.48 2) 0.96 3) 0.6 4) None of these Solution: (4) None of these 2 cos-1 x = cos-1 (2x2 - 1) (2 cos-1 0.8) = cos-1 [2 * 0.64 -... View Article

The value of tan^-1 (1 / 2) + tan^-1 (1 / 3) + tan^-1 (7 / 8) =

1) tan-1 7/8 2) cot-1 15 3) tan-1 15 4) tan-1 25/24 Solution: (3) tan-1 15 tan-1 (1 / 2) + tan-1 (1 / 3) + tan-1 (7 / 8) = tan-1... View Article

Number of solutions of the equations tan^-1 (1 / (2x + 1)) + tan^-1 1 / [4x + 1] = tan^-1 (2 / x²) =

1) 1 2) 2 3) 3 4) 4 Solution: (2) 2 tan-1 (1 / (2x + 1)) + tan-1 1 / [4x + 1] = tan-1 (2 / x2) ⇒ tan-1{[1 / (2x + 1) + 1 / (4x +... View Article

If cot (cos^-1 x) = sec [tan^-1 (a) / (√b² – a²)], then x =

1) b / √b2 - a2 2) a / √2b2 - a2 3) √2b2 - a2 / a 4) √2b2 - a2 / b Solution: (1) b / √b2 - a2 cot (cos-1 x) = sec [tan-1 (a) /... View Article

tan [(π / 4) + (1 / 2) cos^-1 (a / b) + tan [(π / 4) – (1 / 2) cos^-1 (a / b)]] is

1) 2a/b 2) 2b/a 3) a/b 4) b/a Solution: (2) 2b/a tan [(π / 4) + (1 / 2) cos-1 (a / b) + tan [(π / 4) - (1 / 2) cos-1 (a / b)]] =... View Article

If (π / 2) < sin^-1 x < (π / 2), then tan (sin^-1 x) =

1) x / [1 - x2] 2) x / [1 + x2] 3) x / √1 - x2 4) 1 / √1 - x2 5) x / √x2 - 1 Solution: (3) x / √1 - x2 tan θ = sin θ / cos θ =... View Article

The value of x for which sin (cot^-1 (1 + x)) = cos (tan^-1 x) is

1) 1/2 2) 1 3) 0 4) -1/2 Solution: (4) -1/2 sin (cot-1 (1 + x)) = cos (tan-1 x) cos (π / 2) - cot-1 (x + 1 = cos [tan-1 x] (π /... View Article

If x takes a negative permissible value, then sin^-1 x is equal to

1) - cos-1 √1 - x2 2) cos-1 √x2 - 1 3) π - cos-1 √1 - x2 4) cos-1 √1 - x2 Solution: (1) - cos-1 √1 - x2 -1 ≤ x ≤ 0 sin-1 x is a... View Article

cot^-1 (2.1²) + cot^-1 (2.2²) + cot^-1 (2.3²) + … upto ∞ is equal to

1) π/4 2) π/3 3) π/2 4) π/5 Solution: (1) π/4 cot-1 (2.12) + cot-1 (2.22) + cot-1 (2.32) + … The nth term is = cot-1 2n2 =... View Article

If sin^-1 1 / 3 + sin^-1 2 / 3 = sin^-1 x, then the value of x is

1) 0 2) [√5 - 4√2] / 9 3) [√5 + 4√2] / 9 4) π/2 Solution: (3) [√5 + 4√2] / 9 sin-1 1 / 3 + sin-1 2 / 3 = sin-1 [(1 / 3) √1 - (4 /... View Article

The value of tan^-1 [sin 2θ – 1] / [cos 2θ] is

1) π/2 - θ 2) θ - (π/4) 3) 2θ - (π/2) 4) π/4 - θ Solution: (2) θ - (π/4) tan-1 [sin 2θ - 1] / [cos 2θ] = [1 - sin 2θ] / cos 2θ =... View Article

If sin^-1 [x – (x² / 2) + (x³ / 4) – ….. ] + cos^-1 [x² – (x⁴ / 2) + (x⁶ / 4) – ….] = π / 2 for 0 < |x| < √2, then x equals

1) 1/2 2) 1 3) -1/2 4) -1 Solution: (2) 1 sin-1 ɑ + cos-1 ɑ = π / 2 x - (x2 / 2) + (x3 / 4) - …. = x2 - (x4 / 2) + (x6 / 4) - …..... View Article

M	T	W	T	F	S	S
1	2	3	4	5	6	7
8	9	10	11	12	13	14
15	16	17	18	19	20	21
22	23	24	25	26	27	28