Find the magnitude of each of two vectors `veca` and `vecb` having the same magnitude such that the angle between them is 60° and their scalar product is `9/2`

Concept: Product of Two Vectors - Scalar (Or Dot) Product of Two Vectors

Find the value of `tan^(-1) sqrt3 - cot^(-1) (-sqrt3)`

Concept: Inverse Trigonometric Functions - Inverse Trigonometric Functions - Principal Value Branch

If a * b denotes the larger of 'a' and 'b' and if a∘b = (a * b) + 3, then write the value of (5)∘(10), where * and ∘ are binary operations.

Concept: Concept of Binary Operations

if the matrix A =`[(0,a,-3),(2,0,-1),(b,1,0)]` is skew symmetric, Find the value of 'a' and 'b'

Concept: Types of Matrices

A black and a red dice are rolled. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

Concept: Conditional Probability

If *θ* is the angle between two vectors `hati - 2hatj + 3hatk and 3hati - 2hatj + hatk` find `sin theta`

Concept: Product of Two Vectors - Vector (Or Cross) Product of Two Vectors

Find the differential equation representing the family of curves `y = ae^(bx + 5)`. where *a* and *b* are arbitrary constants.

Concept: Formation of a Differential Equation Whose General Solution is Given

Evaluate : \[\int\frac{\cos 2x + 2 \sin^2 x}{\cos^2 x}dx\] .

Concept: Indefinite Integral Problems