Mathematics Test

Result

Mathematics Test - 13

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
1 / -0

A
1

B

8

C

2

D

9
Question 2
1 / -0

The common tangents to the circle x^2 + y^2 = 2 and the parabola y^2 = 8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQRS is

A

6

B

15

C

9

D

3
Question 3
1 / -0

For a point P in the plane, let d1(P) and d2(P) be the distances of the point P from the lines x -y = 0 and x + y = 0 respectively. The area of the region R consisting of all points P lying in the first quadrant of the plane and satisfying 2 ≤ d1(P) + d2(P) ≤ 4, is ________

A

6

B

5

C

7

D

4
Question 4
1 / -0

Three boys and two girls stand in a queue. The probability, that the number of boys ahead of every girl is at least one more than the number of girls ahead of her, is

A

1/3

B

2/3

C

1/2

D

3/4
Question 5
1 / -0

A

g(x) is continuous but not differentiable at a

B

g(x) is differentiable on R

C

g(x) is continuous and differentiable at either a or b but not both

D

None of these
Question 6
1 / -0

A

2

B

4

C

8

D

0
Question 7
1 / -0

A

4

B

2

C

1

D

3
Question 8
1 / -0

Box 1 contains three cards bearing numbers 1, 2, 3 ; box 2 contains five cards bearing numbers 1, 2, 3, 4, 5 ; and box 3 contains seven cards bearing numbers 1, 2, 3, 4, 5, 6, 7. A card is drawn from each of the boxes. Let xi be the number on the card drawn from the i th box, i = 1, 2, 3.The probability that x1 , x2 , x3 are in an arithmetic progression, is

A

9/105

B

11/105

C

10/105

D

7/105
Question 9
1 / -0

The value of g' (1/2) is

A

0

B

π

C

π/2

D

- π/2
Question 10
1 / -0

Let M and N be two 3  3 matrices such that MN = NM. Further, if M ≠ N^2 and M^2 = N^4, then

A

determinant of (M^2 + MN^2 ) is 0 and there is a 3 x 3 non-zero matrix U such that (M^2 + MN^2 )U is the zero matrix both

B

there is a 3 x 3 non-zero matrix U such that (M^2 + MN^2 )U is the zero matrix.

C

determinant of (M^2 + MN^2 ) >= 1.

D

determinant of (M^2 + MN^2 ) is 0.