Class 12th
Get insights from 12k questions on Class 12th, answered by students, alumni, and experts. You may also ask and answer any question you like about Class 12th
Follow Ask QuestionQuestions
Discussions
Active Users
Followers
New answer posted
a year agoContributor-Level 10
Solve sin? ¹ (3x/5) + sin? ¹ (4x/5) = sin? ¹x.
Using the formula sin? ¹a + sin? ¹b = sin? ¹ (a√ (1-b²) + b√ (1-a²):
sin? ¹ ( (3x/5)√ (1 - (4x/5)²) + (4x/5)√ (1 - (3x/5)²) ) = sin? ¹x
(3x/5) * √ (1 - 16x²/25) + (4x/5) * √ (1 - 9x²/25) = x
x * [ (3/5) * √ (25-16x²)/5 + (4/5) * √ (25-9x²)/5 - 1 ] = 0
So, x = 0 is one solution.
For the other part:
3√ (25-16x²) + 4√ (25-9x²) = 25
Let's check integer solutions. If x = 1:
3√ (9) + 4√ (16) = 33 + 44 = 9 + 16 = 25. So x = 1 is a solution.
If x = -1:
3√ (9) + 4√ (16) = 25. So x = -1 is a solution.
The solutions are x = 0, 1, -1.
New answer posted
a year agoContributor-Level 9
Edge length in bcc, a? = 27 Å
Let, Edge length in fcc be a? Å
Now, the same element crystallises in bcc as well as fcc.
For bcc: 4r = √3 a? ⇒ r = (√3 / 4) a?
For fcc: 4r = √2 a? ⇒ r = a? / (2√2)
So, (√3 / 4) a? = a? / (2√2)
(√3 / 4) * 27 = a? / (2√2)
a? = 33.13 Å
The nearest integer is 33.
New answer posted
a year agoContributor-Level 9
Roasting is a process in which sulphur is removed as SO? gas from sulphide ores on heating in excess of oxygen.
New answer posted
a year ago
Contributor-Level 9
R-CONH? + Br? + 4NaOH → R-NH? + 2NaBr + Na? CO? + 2H? O
This reaction is the Hoffmann bromamide degradation, in which an amide is converted to a 1° amine.
New answer posted
a year agoContributor-Level 10
The shortest distance D between two skew lines is given by the formula:
D = | (a? - a? ) ⋅ (b? x b? )| / |b? x b? |
Line L? : (x-1)/2 = (y-2)/3 = (z-4)/4
Line L? : (x-2)/3 = (y-4)/4 = (z-5)/5
Here, a? = I + 2j + 4k, b? = 2i + 3j + 4k
a? = 2i + 4j + 5k, b? = 3i + 4j + 5k
a? - a? = I + 2j + k
b? x b? = | I j k |
| 2 3 4 |
| 3 4 5 |
= I (15-16) - j (10-12) + k (8-9) = -i + 2j - k
D = | (i + 2j + k) ⋅ (-i + 2j - k)| / √ (-1)² + 2² + (-1)²)
= |-1 + 4 - 1| / √ (1 + 4 + 1)
= 2 / √6
New answer posted
a year agoContributor-Level 10
The equation of the plane is given as x + y + z = 42. It is also mentioned that x³ + y³ + z³ = 3xyz.
From the identity, if x³ + y³ + z³ - 3xyz = 0, then x + y + z = 0 or x = y = z.
Given the expression:
3 + (x³ + y³ + z³ - 3xyz) / (xyz)²
Since x³ + y³ + z³ = 3xyz, the expression simplifies to:
3 + 0 = 3
New answer posted
a year agoContributor-Level 10
The problem involves a function f (x) defined by a determinant:
f (x) = | sin²x 1+cos²x cos2x |
| 1+sin²x cos²x cos2x |
| sin²x cos²x sin2x |
Applying the row operation R? → R? - R? , we get:
f (x) = | -1 0 |
| 1+sin²x cos²x cos2x |
| sin²x cos²x sin2x |
Expanding the determinant along the first row:
f (x) = -1 (cos²x * sin2x - cos2x * cos²x) - 1 (1+sin²x)sin2x - sin²x * cos2x)
= -cos²x * sin2x + cos2x * cos²x - sin2x - sin²x * sin2x + sin²x * cos2x
= -sin2x (cos²x + sin²x) + cos2x (cos²x + sin²x) - sin2x
= -sin2x + cos2x - sin2x
= cos2x - 2sin2x
To find the maximum value of f (x), we use the form acosθ + bsinθ, where the m
Taking an Exam? Selecting a College?
Get authentic answers from experts, students and alumni that you won't find anywhere else
Sign Up on ShikshaOn Shiksha, get access to
- 67k Colleges
- 1.2k Exams
- 716k Reviews
- 1850k Answers