Mathematics Test

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Mathematics Test - 10

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Weekly Quiz Competition

Question 1
1 / -0

The function f(x) = 2 |x| + |x + 2| - ||x + 2| - 2 |x|| has a local minimum or a local maximum at x =

A

-2

B

2

C

2/3

D

1/3
Question 2
1 / -0

A

Option A

B

Option B

C

Option D

D

Option C
Question 3
1 / -0

Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length 2√7 on y-axis is (are)

A

x^2 + y^2 - 6x - 7y + 9 = 0

B

None of these

C

x^2 + y^2 - 6x + 7y + 9 = 0

D

x^2 + y^2 - 6x + 8y + 9 = 0
Question 4
1 / -0

A tangent PT is drawn to the circle x^2 + y^2 = 4 at the point P( √3,1). A straight line L, perpendicular to PT is a tangent to the circle (x - 3)^2 + y^2 = 1.A common tangent of the two circles is

A

x + 2√2y = 6

B

x + √3y = 4

C

x = 4

D

y = 2
Question 5
1 / -0

Let z be a complex number such that the imaginary part of z is nonzero and a = z^2 + z + 1 is real. Then a cannot take the value

A

-1

B

1/3

C

3/4

D

1/2
Question 6
1 / -0

A

4

B

5

C

6

D

3
Question 7
1 / -0

A

- 9/2 and 3

B

- 1/2 and -1

C

- 7/2 and 2

D

- 5/2 and 1
Question 8
1 / -0

Let X and Y be two events such that P(X|Y) = 1/2, P(Y|X) = 1/3 , P(Y ∩ X) = 1/6 . Which of thefollowing is (are) correct?

A

X and Y are independent

B

P(X ∪ Y) = 1/3.

C

X and Y are not independent

D

All of these
Question 9
1 / -0

Tangents are drawn to the hyperbola x^2 /9 - y^2 /4 = 1, parallel to the straight line 2x − y = 1. The points of contact of the tangents on the hyperbola are

A

(3√3, - 2√2)

B

(9/2√2, - 1/√2)

C

(9/2√2, 1/√2)

D

(- 3√3, 2√2)
Question 10
1 / -0

Let PQ be a focal chord of the parabola y^2 = 4ax. The tangents to the parabola at P and Q meet at a point lying on the line y = 2x + a, a > 0.If chord PQ subtends an angle θ at the vertex of y^2 = 4ax, then tanθ =

A

-2√5/3

B

-2√7/3

C

2√7/3

D

2√5/3

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Mathematics Test - 10

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Mathematics Test - 10

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SHARING IS CARING

Question 1

-2

2

2/3

1/3

Question 2

Option A

Option B

Option D

Option C

Question 3

x^2 + y^2 - 6x - 7y + 9 = 0

None of these

x^2 + y^2 - 6x + 7y + 9 = 0

x^2 + y^2 - 6x + 8y + 9 = 0

Question 4

x + 2√2y = 6

x + √3y = 4

x = 4

y = 2

Question 5

-1

1/3

3/4

1/2

Question 6

4

5

6

3

Question 7

- 9/2 and 3

- 1/2 and -1

- 7/2 and 2

- 5/2 and 1

Question 8

X and Y are independent

P(X ∪ Y) = 1/3.

X and Y are not independent

All of these

Question 9

(3√3, - 2√2)

(9/2√2, - 1/√2)

(9/2√2, 1/√2)

(- 3√3, 2√2)

Question 10

-2√5/3

-2√7/3

2√7/3

2√5/3

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