Mathematics Test

Result

Mathematics Test - 9

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Weekly Quiz Competition

Question 1
1 / -0

A

f is decreasing on (2, 3)

B

f has a local maximum at x = 2

C

there exists some c ∈ (0, ∞) such that f″(c) = 0

D

All of these
Question 2
1 / -0

The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is

A

243

B

150

C

210

D

75
Question 3
1 / -0

The ellipse E1 : x^2 /9 +y^ 2 /4 =1 is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse E2 passing through the point (0, 4) circumscribes the rectangle R. The eccentricity of the ellipse E2 is

A

√2/2

B

3/4

C

1/2

D

√3/2
Question 4
1 / -0

A

5

B

6

C

7

D

4
Question 5
1 / -0

Two lines L1 : x = 5, y/3-α = z/-2 and L2 : x = α, y/-1 = z/2-α are coplanar. Then α can take value(s)

A

2

B

1

C

3

D

0
Question 6
1 / -0

A

5π/3

B

π/2

C

π/6

D

2π/3
Question 7
1 / -0

Let f : [0, 1] → R (the set of all real numbers) be a function. Suppose the function f is twice differentiable, f(0) = f(1) = 0 and satisfies f "(x) - 2f '(x) + f(x) >= e^x, x ∈ [0, 1].If the function e^-x f(x) assumes its minimum in the interval [0, 1] at x = 1/4, which of the following is true ?

A

f'(x)

B

f'(x)

C

f'(x)>f(x), 0

D

f'(x)
Question 8
1 / -0

A

PX = X

B

PX = – X

C

PX = 2X

D

PX = - 2X
Question 9
1 / -0

A

differentiable at x = 0 but not differentiable at x = 2

B

differentiable both at x = 0 and at x = 2

C

not differentiable at x = 0 but differentiable at x = 2

D

differentiable neither at x = 0 nor at x = 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.Length of chord PQ is

A

5a

B

3a

C

7a

D

2a