Pre-engineering mathematics

cosec 2x − cot 2x is equal to:

• 1 cos x
• 2 sec x
• 3 tan x
• 4 cot x

The limit of (x² − 4) ÷ (x² − 2x) as x tends to 2 is:

• 1 0
• 2 2
• 3 4
• 4 −2

The equation of the normal to the curve y = 5 − x² at the point where x = 2 is:

• 1 4y − x = 2
• 2 y + 4x = 7
• 3 y + 4x = 9
• 4 4y − x = 8

The value of the integral of 3x² from 0 to 2 is:

• 1 8
• 2 12
• 3 4
• 4 6

The dot product of the vectors (2, 3, 1) and (1, −1, 2) is:

• 1 3
• 2 7
• 3 1
• 4 −1

The cross product i × k is equal to:

• 1 −j
• 2 k
• 3 j
• 4 −k

The sum of the first 10 terms of the arithmetic progression 5, 8, 11, … is:

• 1 155
• 2 185
• 3 175
• 4 195

The coefficient of x⁴ in the expansion of (1 + x)⁸ is:

• 1 56
• 2 70
• 3 35
• 4 28

The determinant of the matrix with rows (1, 2, 3), (0, 1, 4) and (5, 6, 0) is:

• 1 24
• 2 0
• 3 1
• 4 −1

The value of i¹⁰, where i = √−1, is:

• 1 1
• 2 −1
• 3 i
• 4 −i

The equation of the tangent to the parabola y = x² at the point (1, 1) is:

• 1 y = x + 1
• 2 y = 2x + 1
• 3 y = 2x − 1
• 4 y = x

The eccentricity of the hyperbola x²/9 − y²/16 = 1 is:

• 1 5/3
• 2 5/4
• 3 4/3
• 4 3/5

The derivative of x eˣ with respect to x is:

• 1 eˣ (x − 1)
• 2 eˣ
• 3 eˣ (1 + x)
• 4 x eˣ

The integral of x eˣ with respect to x is:

• 1 eˣ ÷ x + c
• 2 eˣ (x + 1) + c
• 3 x eˣ + c
• 4 eˣ (x − 1) + c

The number of different arrangements of 5 people in a row is:

• 1 24
• 2 60
• 3 120
• 4 25

Two fair dice are thrown. The probability that the sum is 8 is:

• 1 1/9
• 2 7/36
• 3 5/36
• 4 1/6

The distance of the point (1, 2) from the line 3x + 4y − 10 = 0 is:

• 1 1/5
• 2 1
• 3 3/5
• 4 5

The inverse of the function f(x) = eˣ is:

• 1 ln x
• 2 e⁻ˣ
• 3 1 ÷ eˣ
• 4 x ÷ e

The solution of |2x − 3| < 5 is:

• 1 −1 < x < 4
• 2 x > −1
• 3 x < −1 or x > 4
• 4 x < 4

If cos x = 3/5, then cos 2x is:

• 1 6/5
• 2 −9/25
• 3 −7/25
• 4 7/25

The sum to infinity of the geometric series 9 + 3 + 1 + … is:

• 1 13.5
• 2 27
• 3 10
• 4 12

The limit of (sin 3x) ÷ x as x tends to 0 is:

• 1 1/3
• 2 3
• 3 0
• 4 1

The area between the curve y = x², the x-axis and the line x = 3 is:

• 1 6
• 2 27
• 3 3
• 4 9

The magnitude of the vector 2i − 2j + k is:

• 1 3
• 2 9
• 3 1
• 4 5