Test Preparation on NDA Model Paper Set-3

Consider the following expressions:

Which of the above are rational expressions?

For a square matrix A, which of the following properties hold?

1. (A^-1)^-1 = A

2. det (A^-1) = 1/det A

3. (λA)^-1 = λA^-1 Where λ is a scalar

Select the correct answer using the code given below:

What is the Adjoint of the matrix?

The perpendiculars that fall from any point or the straight line 2x + 11y = 5 upon the two straight lines 24x + 7y = 20 and 4x - 3y = 2 are

(a) e^π + 1/2

(b) e^π - 1/2

(c) e^π + 1

(d) e^π + ¼

The coordinates of the vertices P, Q and R of a triangle PQR are (1, -1, 1), (3, -2, 2) and (0, 2, 6) respectively. If ∠RQP = θ, then what is ∠PRQ equal to?

Consider the following statements:

1. The length p of the perpendicular from the origin to the line ax + by = c satisfies the relation p² = c²/a² + b².

2. The length p of the perpendicular from the origin to the line x/a + y/b = 1 satisfies the relation 1/p² = 1/a² + 1/b².

3. The length p of the perpendicular from the origin to the line y = mx + c satisfies the relation 1/p² = 1 + m² + c²/c².

Which of the above is/are correct?

Which one of the following is the major
cause of depletion of ozone strata of the
atmosphere