Pacesetters Education Centre (Pume Class ) : Mathematics

10 Questions | By Pacesetterseduca | Last updated: Mar 14, 2022 | Total Attempts: 45

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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.

Questions and Answers

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