If (0.2)^x = 2 and log₁₀(2) = 0.3010, then what is the value of x to the nearest tenth ?

•  - 10.0

•  - 0.5

• - 0.4

• - 0.2

The total number of 5-digit numbers that can be composed of distinct digits from 0 to 9 is

• 45360

• 30240

• 27216

• 15120

What is the determinant of the matrix 

• (x - y)(y - z)(z - x)

• (x - y)(y - z)

• (y - z)(z - x)

• (z - x)²(x + y + z)

If A, B and C are the angles of a triangle and

• The triangle ABC is isosceles

• The triangle ABC is equilateral

• The triangle ABC is scalene

• No conclusion can be drawn with regard to the nature of the triangle

Consider the following in respect of matrices A and B of same order :

1. A² - B² = (A + B)(A - B)
2. (A - I)(I + A) = O $\iff$ A² = I                            where I is the identity matrix and O is the null matrix.Which of the above is/are correct ?

• 1 only

• 2 only

• both 1 and 2

• neither 1 nor 2

36.

$$\begin{gathered} \mathrm{If} \sec (\mathrm{\theta } - \mathrm{\alpha }), \sec \left(\mathrm{\theta }\right) \mathrm{and} \sec (\mathrm{\theta } + \mathrm{\alpha }) \mathrm{are} \mathrm{in} \mathrm{AP}, \mathrm{where} \cos \left(\mathrm{\alpha }\right) \ne 1, \\ \mathrm{then} \mathrm{what} \mathrm{is} \mathrm{the} \mathrm{value} \mathrm{of} \sin \left(2\mathrm{\theta }\right) + \cos \mathrm{\alpha } ? \end{gathered}$$

• 0

• 1

•  - 1

• $\frac{1}{2}$

What is $\frac{2\tan \left(\mathrm{\theta }\right)}{1 + {\tan }^2\left(\mathrm{\theta }\right)} = ?$

• $\cos \left(2\mathrm{\theta }\right)$

• $\tan \left(2\mathrm{\theta }\right)$

• $\sin \left(2\mathrm{\theta }\right)$

• $\mathrm{cosec}\left(2\mathrm{\theta }\right)$

If A + B + C = 180°, then what is sin(2A) - sin(2B) - sin(2C) equal to ?

• $- 4\sin \left(\mathrm{A}\right)\sin \left(\mathrm{B}\right)\sin \left(\mathrm{C}\right)$

• $- 4\cos \left(\mathrm{A}\right)\sin \left(\mathrm{B}\right)\cos \left(\mathrm{C}\right)$

• $- \cos \left(\mathrm{A}\right)\cos \left(\mathrm{B}\right)\sin \left(\mathrm{C}\right)$

• $- \sin \left(\mathrm{A}\right)\cos \left(\mathrm{B}\right)\cos \left(\mathrm{C}\right)$

A balloon is directly above one end of a bridge. The angle of depression of the other end of the bridge from the balloon is 48°. If the height of the balloon above the bridge is 122 m, then what is the length of the bridge ?

• $122\sin \left(48°\right) \mathrm{m}$

• $122\tan \left(42°\right) \mathrm{m}$

• $122\cos \left(48°\right) \mathrm{m}$

• $122\tan \left(48°\right) \mathrm{m}$

A is an angle in the fourth quadrant. If satisfies the trigonometric equation 3(3 - tan²(A) - cot(A))² = 1.

Which one of the following is a value of A?

• $300°$

• $315°$

• $330°$

• $345°$