Mathematics Test

Result

Mathematics Test - 15

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
1 / -0

A

4

B

8

C

2

D

0
Question 2
1 / -0

A

4

B

3

C

2

D

9
Question 3
1 / -0

For every pair of continuous functions f, g : [0, 1] → R such that max{ f (x) : x ∈ [0, 1]} = max{g(x) : x ∈ [0, 1]}, the correct statement(s) is(are)

A

(f (c))^2 = (g(c))^2 for some c ∈ [0, 1]

B

(f (c))^2 + 3f (c) = (g(c))^2 + g(c) for some c ∈ [0, 1]

C

(f (c))^2 + f (c) = (g(c))^2 + 3g(c) for some c ∈ [0, 1]

D

None of these
Question 4
1 / -0

Let n1 < n2 < n3 < n4 < n5 be positive integers such that n1 + n2 + n3 + n4 + n5 = 20. Then the number of such distinct arrangements (n1, n2, n3, n4, n5) is _________

A

10

B

8

C

9

D

7
Question 5
1 / -0

A

5

B

3

C

4

D

2
Question 6
1 / -0

Let f : [0, 4π] → [0, π] be defined by f (x) = cos^-1 (cos x). The number of points x ∈ [0, 4π] satisfying the equation f (x) = (10 -x)/10 is ___________

A

3

B

4

C

2

D

5
Question 7
1 / -0

A

Option 1

B

Option 2

C

Option 3

D

Option 4
Question 8
1 / -0

The quadratic equation p(x) = 0 with real coefficients has purely imaginary roots. Then the equation p(p(x)) = 0 has

A

all real roots

B

neither real nor purely imaginary roots

C

two real and two purely imaginary roots

D

only purely imaginary roots
Question 9
1 / -0

A

Option A, C, D

B

Option A, B, D

C

Option B, C

D

Option A, B
Question 10
1 / -0

The variance of first 50 even natural numbers is

A

833/4

B

437/4

C

833

D

437