Class 12th

If the function f(x) = (cos(sin x) - cos x) / x⁴ is continuous at each point in its domain and f(0) = 1/k, then k is .

Consider the above reaction. The percentage yield of amide product is ______.
Benzoyl chloride (0.140 g) + Diphenylamine (0.388 g) → N,N-Diphenylbenzamide (0.210 g)
(Round off to the nearest integer).
(Given: Atomic mass: C: 12.0 u, H:1.0 u, N: 14.0 u, O: 16.0 u, Cl: 35.5 u)

If [.] represents the greatest integer function, then the value of ∫[from 1 to 5] ([x²] - cos x) dx is.

If the equation of the plane passing through the line of intersection of the planes 2x - 7y + 4z - 3 = 0, 3x – 5y + 4z + 11 = 0 and the point (-2, 1, 3) is ax + by + cz - 7 = 0, then the value of 2a + b + c - 7 is.

The maximum value of z in the following equation z = 6xy + y², where 3x + 4y ≤ 100 and 4x + 3y ≤ 75 for x ≥ 0 and y ≥ 0 is.

If a = αi + βj + 3k, b = -βi - αj - k and c = i - 2j - k such that a ⋅ b = 1 and b ⋅ c = -3, then (1/3)((a * b) ⋅ c) is equal to.

If A = [, [0, -1]], then the value of det(A⁴) + det(A¹⁰ - (Adj(2A))¹⁰) is equal to.

The voltage across the 10Ω resistor in the given circuit is x volt. The value of 'x' to the nearest integer is ----------.

If f(x) = sin(cos⁻¹((1 - 2²ˣ) / (1 + 2²ˣ))) and its first derivative with respect to x is -(a/b)logₑ2 when x = 1, where a and b are integers, then the minimum value of |a² - b²| is.

If A = [[0, sin α], [sin α, 0]] and det(A² - (1/2)I) = 0, then a possible value of α is: