A function \(f\) is defined by \(f :x→\frac{x + 2}{x – 3},x ≠ 3\).Find the inverse of \(f\) .
- A. \(\frac{x + 3}{x - 2},x ≠ 2\)
- B. \(\frac{x - 3}{x + 2},x ≠ -2\)
- C. \(\frac{3x - 2}{x+1},x ≠ -1\)
- D. \(\frac{3x + 2}{x - 1},x ≠ 1\)
If \(X\) and \(Y\) are two independent events such that \(P (X) = \frac{1}{8}\) and \(P (X ⋃ Y) = \frac{5}{8}\), find \(P (Y)\).
- A. \(\frac{1}{6}\)
- B. \(\frac{4}{7}\)
- C. \(\frac{4}{21}\)
- D. \(\frac{3}{7}\)
Given that \(y^2 + xy = 5,find \frac{dy}{dx}\).
- A. \(\frac{y}{2y + x}\)
- B. \(\frac{-y}{2y + x}\)
- C. \(\frac{-y}{2y - x}\)
- D. \(\frac{y}{2y + x}\)
A linear transformation on the oxy plane is defined by \(P : (x, y) → (2x + y, -2y)\). Find \(P^2\)
- A. \(\begin{bmatrix} 4&0\\1&4\end{bmatrix}\)
- B. \(\begin{bmatrix} 4&4\\0&0\end{bmatrix}\)
- C. \(\begin{bmatrix} 4&0\\0&4\end{bmatrix}\)
- D. \(\begin{bmatrix} 4&1\\0&4\end{bmatrix}\)
The velocity of a body of mass 4.56 kg increases from \((10 ms^{-1}, 060^o) to (50 ms ^{-1}, 060^o)\) in 16 seconds . Calculate the magnitude of force acting on it.
- A. 17.1 N
- B. 11.4 N
- C. 36.5 N
- D. 5.7 N
Given that \(\frac{3x + 4}{(x – 2)(x + 3)}≡\frac{P}{x + 3}+\frac{Q}{x – 2}\),find the value of Q.
- A. 2
- B. -2
- C. 1
- D. -1
If \(3x^2 + p x + 12 = 0\) has equal roots, find the values of p .
- A. ±12
- B. ±3
- C. ±4
- D. ±6
If α and β are the roots of \(7×2 +12x – 4 = 0\),find the value of \(\frac{αβ}{(α + β)^2}\)
- A. \( \frac{7}{36}\)
- B. -\( \frac{36}{7}\)
- C. \(\frac{36}{7}\)
- D. -\( \frac{7}{36}\)
Evaluate: \(\int(2x + 1)^3 dx\)
- A. \(8(2x + 1)^2 + k\)
- B. \(6(2x + 1)^2 + k\)
- C. \(\frac{1}{8} (2x + 1)^4 + k\)
- D. \(\frac{1}{6} (2x + 1)^4 + k\)
In how many ways can a committee of 3 women and 2 men be chosen from a group of 7 men and 5 women?
- A. 500
- B. 350
- C. 720
- D. 210
Adu’s scores in five subjects in an examination are 85, 84, 83, 86 and 87. Calculate the standard deviation.
- A. 2.0
- B. 1.4
- C. 1.8
- D. 1.6
An exponential sequence (G.P.) is given by \(\frac{9}{2},\frac{3}{4},\frac{1}{8},\)….Find its sum to infinity.
- A. \(5\frac{2}{5}\)
- B. \(4\frac{1}{5}\)
- C. \(13\frac{1}{2}\)
- D. \(6\frac{3}{4}\)
A uniform beam PQ of length 80 cm and weight 60 N rests on a support at X where | PX | = 30 cm. If the body is kept in equilibrium by a mass m kg which is placed at P , calculate the value of m
[Take g = 10 ms\(^{-2}\)]
- A. 2.0
- B. 3.0
- C. 2.5
- D. 4.0
If \(f : x → 2 tan x\) and \(g : x → √(x^2 + 8), find ( g o f )(45^o)\)
- A. 4
- B. 2√3
- C. 6
- D. 3√2
An exponential sequence (G.P.) is given by 8√2, 16√2, 32√2, … . Find the n\(^{th}\) term of the sequence
- A. \(8\sqrt2^n\)
- B. \(2^{(n+2)}\sqrt2\)
- C. \(\sqrt2^{(n+3)}\)
- D. \(8n\sqrt2\)
Solve 6 sin 2θ tan θ = 4, where 0º < θ < 90º
- A. 18.43º
- B. 30.00º
- C. 35.26º
- D. 19.47º
Given that r = (10 N , 200º) and n = (16 N , 020º), find (3r – 2n).
- A. (62 N , 240º)
- B. (62 N , 200º)
- C. (62 N , 280º)
- D. (62 N , 020º)
\(Simplify: \frac{log √27 – log √8}{log 3 – log 2}\)
- A. \(\frac{3}{2}\)
- B. -\(\frac{1}{4}\)
- C. -\(\frac{3}{2}\)
- D. \(\frac{1}{4}\)
The table shows the mark obtained by students in a test.
| Marks | 1 | 2 | 3 | 4 | 5 |
| Frequency | 2 | k | 1 | 1 | 2 |
If the mean mark is 3, find the value of k.
- A. 4
- B. 1
- C. 2
- D. 3
Express \(\frac{3}{3 – √6}\) in the form \(x + m√y\)
- A. 3 - 3 √6
- B. 3 + 3√6
- C. 3 + √6
- D. 3 - √6
\(Differentiate f (x) = \frac{1}{(1 – x^2)^5}\) with respect to \(x\).
- A. \(\frac{-5x}{(1-x^2)^6}\)
- B. \(\frac{-10x}{(1-x^2)^6}\)
- C. \(\frac{5x}{(1-x^2)^6}\)
- D. \(\frac{10x}{(1-x^2)^6}\)