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Mathematics and Statistics
Solve the following system of equations by the method of reduction:
x + y + z = 6, y + 3z = 11, x + z = 2y.
Chapter: [2] Matrices
Concept: Application of Matrices
Concept: Application of Matrices
If the vectors `2 hat i - 3 hat j + 4 hat k` and `p hat i + 6 hat j - 8 hat k` are collinear, then find the value of p.
Chapter: [5] Vectors
Concept: Vector Joining Two Points in Algebra
Concept: Vector Joining Two Points in Algebra
Find the volume of the parallelopiped whose vertices are A (3, 2, −1), B (−2, 2, −3) C (3, 5, −2) and D (−2, 5, 4).
Chapter: [5] Vectors
Concept: Scalar Triple Product
Concept: Scalar Triple Product
Find the approximate value of tan−1 (1.002).
[Given: π = 3.1416]
Chapter: [9] Applications of Derivatives
Concept: Approximations
Concept: Approximations
A particle is moving along the X-axis. Its acceleration at time t is proportional to its velocity at that time. Find the differential equation of the motion of the particle.
Chapter: [13] Differential Equations
Concept: Formation of Differential Equations
Concept: Formation of Differential Equations
Solve:
`1 + (dy)/(dx) = cosec (x + y)`; put x + y = u.
Chapter: [13] Differential Equations
Concept: Solution of a Differential Equation
Concept: Solution of a Differential Equation
