If y = x sin x, Find \(\frac{d^2 y}{d^2 x}\)

• A. 2 cosx - x sinx
• B. sinx + x cosx
• C. sinx - x cosx
• D. x sinx - 2 cosx

Five people are to be arranged in a row for a group photograph. How many arrangements are there if a married couple in the group insist on sitting next to each other?

• A. 48
• B. 24
• C. 20
• D. 10

Ice forms on a refrigerator ice-box at the rate of (4 - 06t)g per minute after t minutes. If initially there are 2g of ice in the box, find the mass of ice formed in 5 minutes

• A. 19.5
• B. 17.0
• C. 14.5
• D. 12.5

\(\begin{array}{c|c} x & 2 & 4 & 6 & 8\\ \hline f & 4 & y & 6 & 5 \end{array}\)

If the mean of the above frequency distribution is 5.2, find y

• A. 2, 1
• B. 1, 2
• C. 1, 5
• D. 5, 2

Simplify 5\(\sqrt{18}\) - 3\(\sqrt{72}\) + 4\(\sqrt{50}\)

• A. 17\(\sqrt{4}\)
• B. 4\(\sqrt{17}\)
• C. 17\(\sqrt{2}\)
• D. 12\(\sqrt{4}\)

Obtain a maximum value of the function f(x) x³ - 12x + 11

• A. -5
• B. -2
• C. 2
• D. 27

The radius of a circle is given as 5cm subject to an error of 0.1cm. What is the percentage error in the area of the circle?

• A. \(\frac{1}{25}\)
• B. \(\frac{1}{4}\)
• C. 4
• D. 25

Evaluate the integral \(\int^{\frac{\pi}{4}}_{\frac{\pi}{12}} 2 \cos 2x \mathrm {d} x\)

• A. -\(\frac{1}{2}\)
• B. -1
• C. \(\frac{1}{2}\)
• D. 1

X is a point due east of point Y on a coast: Z is another point on the coast but 6√3km due south of y.

If the distance XZ is 12Km. Calculate the bearing of Z from X

• A. 240^o
• B. 210^o
• C. 150^o
• D. 60^o

A student has 5 courses to take from Mathematics and physics. There are 4 courses in Mathematics and 3 in Physics which he can choose his courses so that he takes exactly two courses in Physics?

• A. 48
• B. 12
• C. 10
• D. 7