Mathematics Test

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Mathematics Test - 7

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Weekly Quiz Competition

Question 1
1 / -0

Find the area and the circumference of a circle whose radius is 10 cm. (Take the value of π = 3.14)

A

125.6 cm

B

48 cm

C

52.8 cm

D

62.8 cm

Solution

Radius = 10 cm.

Area =πr²

= 3.14 × 102

A= 314 cm²

Circumference,C = 2πr

C= 2 × 3.14 × 10

Circumference= 62.8 cm
Question 2
1 / -0

A

4

B

0

C

8

D

3
Question 3
1 / -0

Let ω be a complex cube root of unity with ω ≠ 1 and P = [p-ij] be a n x n matrix with p-ij = ω^(i+j). Then P^2 ≠ 0, when n =

A

58

B

55

C

56

D

All of these
Question 4
1 / -0

Let a1, a2, a3, ….. be in harmonic progression with a1 = 5 and a20 = 25. The least positive integer n for which an < 0

A

25

B

23

C

22

D

24
Question 5
1 / -0

Let S be the area of the region enclosed by y = e^−x^2 , y = 0, x = 0 and x = 1. Then

A

S ≥ 1/e

B

S ≥ 1 - 1/e

C

S ≤ 1/√2 + 1/√e[1 - 1/√2]

D

All of these
Question 6
1 / -0

A

Option (C, D)

B

Option (B, C)

C

Option (A, B)

D

Option (A, D)
Question 7
1 / -0

Let p(x) be a real polynomial of least degree which has a local maximum at x = 1 and a local minimum at x = 3. If p(1) = 6 and p(3) = 2, then p′(0) is

A

8

B

10

C

9

D

7
Question 8
1 / -0

Which of the following is true?

A

g is decreasing on (1, 2) and increasing on (2, ∞)

B

g is decreasing on (1, ∞)

C

g is increasing on (1, 2) and decreasing on (2, ∞)

D

g is increasing on (1, ∞)
Question 9
1 / -0

A
$\pm 2$

B
$\pm 1$

C
$\pm 3$

D
0

Solution

$A d j . P = |\begin{matrix} 1 & 4 & 4 \\ 2 & 1 & 7 \\ 1 & 1 & 3 \end{matrix}|$

$| A d j . P | = - 4 + 4 + 4$

$= 4$

$| A d j . P | = | P^{2} |$ [ $A d j . P = | P |^{n - 1}$ ]

$| P |^{2} = 4$

$P = \pm 2$
Question 10
1 / -0

A ship is fitted with three engines E1, E2 and E3. The engines function independently of each other with respective probabilities 1/2 1/4, and 1/4. For the ship to be operational at least two of its engines must function. Let X denote the event that the ship is operational and let X1, X2 and X3 denote respectively the events that the engines E1, E2 and E3 are functioning. Which of the following is(are) true ?

A

P [Exactly two engines of the ship are functioning | X] = 7/8 and P[X|X1] = 7/16 both.

B

P[X|X2] = 5/16.

C

P[X|X1] = 7/16.

D

P [Exactly two engines of the ship are functioning | X] = 7/8.

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Re-Attempt Weekly Quiz Competition

Mathematics Test - 7

Result

Mathematics Test - 7

Score

-

Rank

-

SHARING IS CARING

Question 1

125.6 cm

48 cm

52.8 cm

62.8 cm

Solution

Question 2

4

0

8

3

Question 3

58

55

56

All of these

Question 4

25

23

22

24

Question 5

S ≥ 1/e

S ≥ 1 - 1/e

S ≤ 1/√2 + 1/√e[1 - 1/√2]

All of these

Question 6

Option (C, D)

Option (B, C)

Option (A, B)

Option (A, D)

Question 7

8

10

9

7

Question 8

g is decreasing on (1, 2) and increasing on (2, ∞)

g is decreasing on (1, ∞)

g is increasing on (1, 2) and decreasing on (2, ∞)

g is increasing on (1, ∞)

Question 9

±2

±1

±3

0

Solution

Question 10

P [Exactly two engines of the ship are functioning | X] = 7/8 and P[X|X1] = 7/16 both.

P[X|X2] = 5/16.

P[X|X1] = 7/16.

P [Exactly two engines of the ship are functioning | X] = 7/8.

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