Q16 of 45 Page 1

By using properties of determinants, prove the following:

Applying C₁→ C₁ + C₂ + C₃

Taking (5x + 4) common from C₁

Apply R₂→ R₂ – R₁ and R₃→ R₃ – R₁

Expanding along C₁, we get

= (5x + 4)[1(4 – x)(4 – x) – 0(0)]

= (5x + 4)(4 – x)²

Solve the following differential equation:

Find the particular solution, satisfying the given condition, for the following differential equation:

y = 0 when x = 1

A die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.

Differentiate the following function w.r.t. x:

x^{sin x} + (sin x)^{cos x} .