The equation of a circle is given as 2x\(^2\) + 2y\(^2\) – x – 3y – 41 = 0. Find the coordinates of its centre.
- A. (\(\frac{-1}{4}\), \(\frac{3}{4}\))
- B. (\(\frac{1}{4}\), \(\frac{3}{4}\))
- C. (\(\frac{-1}{2}\), \(\frac{3}{2}\))
- D. (\(\frac{-1}{2}\), \(\frac{-3}{2}\))
The probability that a student will graduate from college is 0.4. If 3 students are selected from the college, what is the probability that at least one student will graduate?
- A. 0.06
- B. 0.22
- C. 0.78
- D. 0.80
Find the range of values of x for which 2x\(^2\) + 7x – 15 ≥ 0.
- A. x ≤ -5 or x ≥ \(\frac{3}{2}\)
- B. x ≥ -5 or x ≤\(\frac{3}{2}\)
- C. -5 ≤ x ≤ \(\frac{3}{5}\)
- D. \(\frac{3}{5}\) ≤ x ≤ -5
Solve: 4sin\(^2\)θ + 1 = 2, where 0º < θ < 180º
- A. 60º 0r 120º
- B. 30º 0r 150º
- C. 30º 0r 120º
- D. 60º 0r 150º
Find correct to the nearest degree, the acute angle formed by the lines y = 2x + 5 and 2y = x – 6
- A. 76\(^∘\)
- B. 53\(^∘\)
- C. 37\(^∘\)
- D. 14\(^∘\)
The mean heights of three groups of students consisting of 20, 16 and 14 students each are 1.67m, 1.50m and 1.40m respectively. Find the mean height of all the students.
- A. 1.63m
- B. 1.54m
- C. 1.52m
- D. 1.42m
A body of mass 18kg moving with velocity 4ms-1 collides with another body of mass 6kg moving in the opposite direction with velocity 10ms-1. If they stick together after the collision, find their common velocity.
- A. \(\frac{1}{2}\) m/s
- B. \(\frac{1}{3}\) m/s
- C. 2m/s
- D. 3m/s
The first, second and third terms of an exponential sequence (G.P) are (x – 4), (x + 2), and (3x + 1) respectively. Find the values of x.
- A. \(\frac{-1}{2}, 8\)
- B. \(\frac{1}{2}, -8\)
- C. \(\frac{-1}{2}, -8\)
- D. \(\frac{1}{2}, 8\)
Find the coefficient of x\(^3\)y\(^2\) in the binomial expansion of (x-2y)\(^5\)
- A. -80
- B. 10
- C. 40
- D. 80
If g(x) = √(1-x\(^2\)), find the domain of g(x)
- A. x < -1 or x > 1
- B. x ≤ -1 or x ≥1
- C. -1 ≤ x ≤ 1
- D. -1 < x < 1
The table shows the distribution of the distance (in km) covered by 40 hunters while hunting.
What is the mode of the distribution?
| Distance(km) | 3 | 4 | 5 | 6 | 7 | 8 |
| Frequency | 5 | 4 | x | 9 | 2x | 1 |
- A. 5
- B. 6
- C. 7
- D. 8
The table shows the distribution of the distance (in km) covered by 40 hunters while hunting.
| Distance(km) | 3 | 4 | 5 | 6 | 7 | 8 |
| Frequency | 5 | 4 | x | 9 | 2x | 1 |
If a hunter is selected at random, find the probability that the hunter covered at least 6km.
- A. \(\frac{3}{5}\)
- B. \(\frac{2}{5}\)
- C. \(\frac{3}{8}\)
- D. \(\frac{9}{40}\)
If →PQ = -2i + 5j and →RQ = -i – 7j, find →PR
- A. -3i + 12j
- B. -3i - 12j
- C. -i + 12j
- D. i - 12j
Given that P = (-4, -5) and Q = (2,3), express →PQ in the form (k,θ). where k is the magnitude and θ the bearing.
- A. (10 units, 053º)
- B. (9 units, 049º)
- C. (10 units, 037º)
- D. (9 units, 027º)
Solve: \(3^{2x-2} – 28(3^{x-2}) + 3 = 0\)
- A. x = -2 or x = 1
- B. x = 0 or x = -3
- C. x = 2 or x = 1
- D. x = 0 or x = 3
If Un = kn\(^2\) + pn, U\(_1\) = -1, U\(_5\) = 15, find the values of k and p.
- A. k = -1, p = 2
- B. k = -1, p = -2
- C. k = 1, p = -2
- D. k = 1, p = 2
A particle moving with a velocity of 5m/s accelerates at 2m/s\(^2\). Find the distance it covers in 4 seconds.
- A. 16m
- B. 26m
- C. 36m
- D. 46m
Given that P = {x: x is a multiple of 5}, Q = {x: x is a multiple of 3} and R = {x: x is an odd number} are subsets of μ = {x: 20 ≤ x ≤ 35}, (P⋃Q)∩R.
- A. {20, 21, 25, 30, 33}
- B. {21, 25, 27, 33, 35}
- C. {20, 21, 25, 27, 33, 35}
- D. {21, 25, 27, 30, 33, 35}
Find the coefficient of x\(^2\)in the binomial expansion of \((x + \frac{2}{x^2})^5\)
- A. 10
- B. 40
- C. 32
- D. 80