Pacesetters Education Centre (Pume Class ) : Mathematics
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Mathematics can be a rather hard subject for many people. However, most of it is well aided by practice. The Pacesetters Education Centre (pume class) : Mathematics quiz below tests on among other concepts, measures of central tendency. All the best.
- 1.(1) A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P (A ∪ B) is
- A.
3/5
- B.
0
- C.
1
- D.
5/2
- 2.A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at
- A.
0, 2)
- B.
(0, 1)
- C.
(1, 0)
- D.
(2, 0)
- 3.The point diametrically opposite to the point P (1, 0) on the circle x2 + y2 + 2x + 4y − 3 = 0 is
- A.
(− 3, − 4)
- B.
(-3, 4)
- C.
(3, 4)
- D.
(-4, -1)
- 4.The perpendicular bisector of the line segment joining P (1, 4) and Q (k, 3) has y−intercept − 4. Then a possible value of k is
- A.
1
- B.
-4
- C.
3
- D.
2
- 5.Let A be a 2 × 2 matrix with real entries. Let I be the 2 × 2 identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that A2 = I. Statement −1: If A ≠ I and A ≠ − I, then det A = − 1. Statement −2: If A ≠ I and A ≠ − I, then tr (A) ≠ 0.
- A.
Statement −1 is false, Statement −2 is true
- B.
Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1
- C.
Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.
- D.
Statement − 1 is true, Statement − 2 is false.
- 6.Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12} be a relation on the set A = {3, 6, 9, 12}. The relation is
- A.
Reflexive and transitive only
- B.
Reflexive only
- C.
An equivalence relation
- D.
Reflexive and symmetric only
- 7.If in a frequently distribution, the mean and median are 21 and 22 respectively, then its mode is approximately
- A.
22.0
- B.
20.5
- C.
25.5
- D.
24.0
- 8.Here 2 is read as square Let P be the point (1, 0) and Q a point on the locus y2 = 8x. The locus of mid point of PQ is
- A.
y2 – 4x + 2 = 0
- B.
y2 + 4x + 2 = 0
- C.
x2 + 4y + 2 = 0
- D.
X2 – 4y + 2 = 0
- 9.The system of equations αx + y + z = α - 1, x + αy + z = α - 1, x + y + αz = α - 1 has no solution, if α is
- A.
-2
- B.
Either – 2 or 1
- C.
Not -2
- D.
1
- 10.The value of α for which the sum of the squares of the roots of the equation x2 – (a – 2)x – a – 1 = 0 assume the least value is
- A.
1
- B.
0
- C.
3
- D.
2
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