Given that \(a = i – 3j\) and \(b = -2i + 5j\) and \(c = 3i – j\), calculate \(|a – b + c|\).
- A. \(\sqrt{13}\)
- B. \(3\sqrt{13}\)
- C. \(6\sqrt{13}\)
- D. \(9\sqrt{13}\)
The marks scored by 4 students in Mathematics and Physics are ranked as shown in the table below
| Mathematics | 3 | 4 | 2 | 1 |
| Physics | 4 | 3 | 1 | 2 |
Calculate the Spearmann’s rank correlation coefficient.
- A. 0.2
- B. 0.5
- C. 0.6
- D. 0.7
Out of 70 schools, 42 of them can be attended by boys and 35 can be attended by girls. If a pupil is selected at random from these schools, find the probability that he/ she is from a mixed school.
- A. \(\frac{1}{11}\)
- B. \(\frac{1}{10}\)
- C. \(\frac{1}{6}\)
- D. \(\frac{1}{5}\)
Evaluate \(\int_{-1}^{1} (x + 1)^{2}\mathrm {d} x\).
- A. \(\frac{8}{3}\)
- B. \(\frac{7}{3}\)
- C. \(\frac{5}{3}\)
- D. 2
Calculate the standard deviation of 30, 29, 25, 28, 32 and 24.
- A. 2.0
- B. 2.8
- C. 3.0
- D. 3.2
Evaluate \(\int_{\frac{1}{2}}^{1} \frac{x^{3} – 4}{x^{3}} \mathrm {d} x\).
- A. -5.5
- B. -2.0
- C. 2.0
- D. 5.5
Find the stationary point of the curve \(y = 3x^{2} – 2x^{3}\).
- A. (1, 0)
- B. (-1, 0)
- C. (1, 1)
- D. (-1, -1)
The midpoint of M(4, -1) and N(x, y) is P(3, -4). Find the coordinates of N.
- A. (2, -3)
- B. (2, -7)
- C. (-1, -3)
- D. (-10, -7)
Given that \(y = x(x + 1)^{2}\), calculate the maximum value of y.
- A. -2
- B. 0
- C. 1
- D. 2
Find the equation to the circle \(x^{2} + y^{2} – 4x – 2y = 0\) at the point (1, 3).
- A. 2y - x -5 = 0
- B. 2y + x - 5 = 0
- C. 2y + x + 5 = 0
- D. 2y - x + 5 = 0
Express \(\frac{13}{4}\pi\) radians in degrees.
- A. 495°
- B. 225°
- C. 585°
- D. 135°
If the determinant of the matrix \(\begin{pmatrix} 2 & x \\ 3 & 5 \end{pmatrix} = 13\), find the value of x.
- A. -2
- B. -1
- C. 1
- D. 2
In how many ways can the letters of the word ‘ELECTIVE’ be arranged?
- A. 336
- B. 1680
- C. 6720
- D. 20160
Find the radius of the circle \(x^{2} + y^{2} – 8x – 2y + 1 = 0\).
- A. 9
- B. 7
- C. 4
- D. 3
If \(\sin\theta = \frac{3}{5}, 0° < \theta < 90°\), evaluate \(\cos(180 – \theta)\).
- A. \(\frac{4}{5}\)
- B. \(\frac{3}{5}\)
- C. \(\frac{-3}{5}\)
- D. \(\frac{-4}{5}\)
The first term of a Geometric Progression (GP) is \(\frac{3}{4}\), If the product of the second and third terms of the sequence is 972, find its common ratio.
- A. 3
- B. 4
- C. 6
- D. 12
How many numbers greater than 150 can be formed from the digits 1, 2, 3, 4, 5 without repetition?
- A. 91
- B. 191
- C. 291
- D. 391
If \(\begin{vmatrix} k & k \\ 4 & k \end{vmatrix} + \begin{vmatrix} 2 & 3 \\ -1 & k \end{vmatrix} = 6\), find the value of the constant k, where k > 0.
- A. 1
- B. 2
- C. 3
- D. 4
The general term of an infinite sequence 9, 4, -1, -6,… is \(u_{r} = ar + b\). Find the values of a and b.
- A. a = 5, b = 14
- B. a = -5, b = 14
- C. a = 5, b = -14
- D. a = -5, b = -14
Find the coefficient of \(x^{3}\) in the binomial expansion of \((x – \frac{3}{x^{2}})^{9}\).
- A. 324
- B. 252
- C. -252
- D. -324
Solve \(\log_{2}(12x – 10) = 1 + \log_{2}(4x + 3)\).
- A. 4.75
- B. 4.00
- C. 1.75
- D. 1.00