10 Questions

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