What is the locus of the mid-point of all the chords of length 6cm with circle of radius 5cm and with center O?
- A. A circle of radius 4 cm and the center 0
- B. The perpendicular bisector of the chords
- C. A straight line passing through 0
- D. A circle of radius 6 cm and with center 0
Find the locus of a particle which moves in the first quadrant so that it is equidistant from the lines x = 0 and y = 0 (where k is a constant)?
- A. x + y = 0
- B. x - y = 0
- C. x + y + k = 0
- D. x - y - k = 0
Find the radius of a sphere whose surface area is 154 cm\(^2\)?
- A. 7.00 cm
- B. 3.50 cm
- C. 3.00 cm
- D. 1.75 cm
A chord drawn 5 cm away from the center of a circle of radius 13 cm. Calculate the length of the chord?
- A. 7cm
- B. 9cm
- C. 12cm
- D. 24cm
If the hypotenuse of a right-angled isosceles triangle is 2cm. What is the area of the triangle?
- A. 1/√2 cm2
- B. 1 cm2
- C. √2 cm2
- D. 2√2 cm2
In the figure above , TS//XY and XY = TY, ∠STZ = 34°, ∠TXY = 47°, find the angle marked n?
- A. 47o
- B. 52o
- C. 56o
- D. 99o
A regular polygon has 150º as the size of each interior angle. How many sides does it have?
- A. 12
- B. 10
- C. 9
- D. 8
Find the acute angle between the straight lines y = x and y = √3x
- A. 15o
- B. 30o
- C. 45o
- D. 60o
If P \(=\left[\begin{array}{cc}x+3 & x+2\\
x+1 & x-1\end{array}\right]\) evaluate x if |P| = -10
- A. -5
- B. -2
- C. 2
- D. 5
If Q is\( \left[ \begin{array}{cc}
9 & -2 \\
-7 & 4 \\
\end{array} \right]\) , then |Q| is?
- A. -50
- B. -22
- C. 22
- D. 50
A binary operation ⊗ defined on the set of integers is such that m⊗n = m + n + mn for all integers m and n. Find the inverse of -5 under this operation, if the identity element is 0?
- A. -5/4
- B. -5/6
- C. zero
- D. 5
If m * n = n – (m+2) for any real number m and n find the value of 3*(-5)?
- A. -6
- B. -8
- C. -10
- D. -12
Find to infinity, the sum of the sequence \(1, \frac{9}{10}, \left(\frac{9}{10}\right)^2, \left(\frac{9}{10}\right)^3,…..\)
- A. 10
- B. 9
- C. 10/9
- D. 9/10
The sum of the first n terms of the arithmetic progression 5, 11, 17, 23, 29, 35, … is?
- A. n(3n - 0.5)
- B. n(3n + 2)
- C. n(3n + 2.5)
- D. n(3n + 5)
Find the range of values of x for which 3x – 7 \(\leq\) 0 and x + 5 > 0?
- A. -5 < x < \(\frac{7}{3}\)
- B. -5 \(\leq\) x \(\leq\) \(\frac{7}{3}\)
- C. -5 < x \(\leq\) \(\frac{7}{3}\)
- D. -5 \(\leq\) x < \(\frac{7}{3}\)
Determine the value of x for which (x\(^2\) – 1) > 0?
- A. x < -1 or x > 1
- B. -1 < x < 1
- C. x > 0
- D. x < -1
W is directly proportional to U. If W = 5 when U = 3, find U when W = 2/7
- A. 6/35
- B. 10/21
- C. 21/10
- D. 35/6
Which of the following equations represent the graph above?
- A. y = 2+7x+4x2
- B. y = 2-7x+4x2
- C. y = 2+7x-4x2
- D. y = 2-7x-4x2
A polynomial in x whose roots are 4/3 and -3/5 is?
- A. 15x2 - 11x – 12
- B. 15x2 + 11x – 12
- C. 12x2 - x – 12
- D. 12x2 + 11x – 15
If \(p=\sqrt{\frac{rs^3}{t}}\), express r in terms of p, s and t?
- A. \(\frac{p^2 t}{s^3}\)
- B. \(\frac{p^3 t}{s^3}\)
- C. \(\frac{p^3 t}{s^2}\)
- D. \(\frac{p^ t}{s^3}\)
I.S∩T∩W=S II. S ∪ T ∪ W = W
III. T ∩ W = S
If S⊂T⊂W, which of the above statements are true?
- A. I and II
- B. I and III
- C. II and III
- D. I, II and III