Which of the following is a point on the curve y = x² - 4x + 7?

• A. (0,6)
• B. (1,4)
• C. (2,0)
• D. (7,0)

A ladder 6m long leans against a vertical wall so that it makes an angle of 60^o with the wall. Calculate the distance of the foot of the ladder from the wall

• A. 3m
• B. 6m
• C. 2√3m
• D. 3√3m

\(\begin{array}{c|c} Class Intervals & 0 - 2 & 3 - 5 & 6 - 8 & 9 - 11 & \\ \hline Frequency & 3 & 2 & 5 & 3 &\end{array}\)

Find the mode of the above distribution

• A. 9
• B. 8
• C. 10
• D. 7

Two angles (a + 31) and (b - 49°) are adjacent angles on a straight line. Which of the following is true

• A. a + b = 198°
• B. a + b = 180°
• C. a + b = 162°
• D. a + b = 100°

Find the determinant of the matrix A = \(\begin{pmatrix} 2 & 3 \\ 1 & 3 \end{pmatrix}\)

• A. 4
• B. 2
• C. 5
• D. 3

(a) Two places X and Y on the equator are on longitudes 67°E and 123°E respectively. (i) What is the distance between them along the equator? (ii) How far from the North pole is X? [Take \(\pi = \frac{22}{7}\) and radius of earth = 6400km].

(b) In the diagram, PQR is a circle centre O. N is the mid-point of chord PQ. |PQ| = 8cm, |ON| = 3cm and < ONR = 20°. Calculate the size of < ORN to the nearest degree.

Five digit numbers are formed from digits 4, 5, 6, 7 and 8.

(a)How many such numbers can be formed if repitition of digits is (i) allowed (ii) not allowed?

(b) How many of the numbers are odd, if repetition of digits is not allowed?

A boy 14 m tall, stood 10m away from a tree of height 12 m. Calculate, correct to the nearest degree, the angle of elevation of the top of the tree from the boy's eyes.

• A. 70°
• B. 47°
• C. 19°
• D. 8°

If y = 4x³ - 2x² + x, find \(\frac{\delta y}{\delta x}\)

• A. 8x² - 2x + 1
• B. 8x² - 4x + 1
• C. 12x² - 2x + 1
• D. 12x² - 4x + 1

Which of the following statements is/are true when two straight lines intersect? I. Adjacent angles are equal II. Vertically opposite angles are equal III. Adjacent angles are supplementary

• A. II only
• B. I and III only
• C. II and III only
• D. I, II and III