Mathematics Test

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Mathematics Test - 8

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Weekly Quiz Competition

Question 1
1 / -0

Let S be the focus of the parabola y^2 = 8x and let PQ be the common chord of the circle x^2 + y^2 − 2x − 4y = 0 and the given parabola. The area of the triangle PQS is

A

6

B

5

C

4

D

3
Question 2
1 / -0

A

Option A

B

Option B

C

Option C

D

All of these
Question 3
1 / -0

Four fair dice D1, D2, D3 and D4, each having six faces numbered 1, 2, 3, 4, 5, and 6, are rolledsimultaneously. The probability that D4 shows a number appearing on one of D1, D2 and D3 is

A

91/216

B

125/216

C

108/216

D

127/216
Question 4
1 / -0

If y(x) satisfies the differential equation y′ − ytanx = 2x secx and y(0) = 0, then

A

y'(π/4) = π^2/18

B

y(π/4) = π^2/8√2

C

y(π/3) = π^2/9

D

None of these
Question 5
1 / -0

Let PQR be a triangle of area ∆ with a = 2, b =7/2 and c = 5/2, where a, b, and c are the lengths of the sides of the triangle opposite to the angles at P, Q and R respectively. Then (2sin P - sin 2P)/(2sin + P sin 2P) equals

A

45/4∆

B

3/4∆

C

(3/4∆)^2

D

(45/4∆)^2
Question 6
1 / -0

Consider the statements:P : There exists some x ∈ such that f(x) + 2x = 2(1 + x^2 )Q : There exists some x ∈ such that 2f(x) + 1 = 2x(1 + x) Then

A

P is false and Q is true

B

both P and Q are true

C

P is true and Q is false

D

both P and Q are false
Question 7
1 / -0

A

5

B

7 & -17/2

C

7

D

-17/2
Question 8
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 possible equation of L is

A

x - √3y = 1

B

x - √3y = -1

C

x + √3y = -1

D

x + √3y = 5
Question 9
1 / -0

Let a-n denote the number of all n–digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0. Let b-n = the number of such n–digit integers ending with digit 1 and c-n = the number of such n–digit integers ending with digit 0. The value of b6 is

A

11

B

7

C

9

D

8
Question 10
1 / -0

If the straight lines (x-1)/2 = (y + 1)/k = z/2 and (x+1)/5 = (y + 1)/2 = z/k are coplanar, then the plane(s) containing these two lines is(are)

A

y + 2z = –1

B

y – z = –1

C

y – 2z = –1

D

All of these

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Re-Attempt Weekly Quiz Competition

Mathematics Test - 8

Result

Mathematics Test - 8

Score

-

Rank

-

SHARING IS CARING

Question 1

6

5

4

3

Question 2

Option A

Option B

Option C

All of these

Question 3

91/216

125/216

108/216

127/216

Question 4

y'(π/4) = π^2/18

y(π/4) = π^2/8√2

y(π/3) = π^2/9

None of these

Question 5

45/4∆

3/4∆

(3/4∆)^2

(45/4∆)^2

Question 6

P is false and Q is true

both P and Q are true

P is true and Q is false

both P and Q are false

Question 7

5

7 & -17/2

7

-17/2

Question 8

x - √3y = 1

x - √3y = -1

x + √3y = -1

x + √3y = 5

Question 9

11

7

9

8

Question 10

y + 2z = –1

y – z = –1

y – 2z = –1

All of these

User

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