Mathematical Ability Test-2

Result

Mathematical Ability Test-2

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Weekly Quiz Competition

Question 1
1 / -0

If sin⁴x + 2cos⁴⁡x = 2/3, then what is the value of sec^2⁡x?

A
2

B
3

C
1

D
4

Solution
Question 2
1 / -0

A fair coin is tossed independently four times. The probability of the event "the number of times heads show up is more than the number of times tails show up" is:

A
1/16

B
1/8

C
1/4

D
5/16

Solution
Question 3
1 / -0

The longest chord of a circle is a ___________ of the circle.

A
Line

B
Diameter

C
Tangent

D
None of these

Solution

Diameter is known as the longest chord of the circle.
Question 4
1 / -0

If P and Q be two sets such that P ∪ Q = P, then P ∩ Q will be:

A
P

B
Q

C
ϕ

D
None of these

Solution

Intersection:

Let A and B be two sets. The intersection of A and B is the set of all those elements which are present in both sets A and B.

The intersection of A and B is denoted by A ∩ B

i.e., A ∩ B = {x : x ∈ A and x ∈ B}

The Venn diagram for intersection is as shown below:

Union:

Let A and B be two sets. The union of A and B is the set of all those elements which belong to either A or B or both A and B.

The union of A and B is denoted by A ∪ B.

i.e., A ∪ B = {x : x ∈ A or x ∈ B}

The Venn diagram for the union of any two sets is shown below:

A ∪ B = A + B - A ∩ B

As we know,

P ∪ Q = P + Q - P ∩ Q

Putting the values given in the question,

P = P + Q - P ∩ Q

P ∩ Q = Q

Question 5

1 / -0

The median for the given frequency distribution is:

x	f
1	8
2	10
3	11
4	16
5	20
6	25
7	15
8	9
9	6

20

5

4

65 Solution

x	f	Cf
1	8	8
2	10	18
3	11	29
4	16	45
5	20	65
6	25	90
7	15	105
8	9	114
9	6	120
Total	120

Here total frequency = 120

N = 120 = even

⇒ N/2 = 60

In cumulative frequency (C.f.) we select 65 as it is closer to 60.

∴ Median is 5 because 65 is in line of 5.

Question 6
1 / -0

Find the value of x.

A
70°

B
55°

C
45°

D
35°

Solution

Given:

∠BAC = 40°

∠ ACE = 110°

∠ABC = 2x°

∠ACB + ∠ACE = 180° (linear pair)

⇒ 110° + ∠ACE = 180°

⇒ ∠ACE = 70°

∠ABC + ∠BAC + ∠ACB = 180° (Angle sum property of a triangle)

⇒ 2x + 40° + 70° = 180°

⇒ 2x = 70°

⇒ x = 70/2 = 35°

∴ The value of x is 35°.
Question 7
1 / -0

If 2^n-1+ 2ⁿ⁺¹= 320, find the value of n.

A
6

B
8

C
5

D
7

Solution
Question 8
1 / -0

If the height of a cone is increased by 50% then what is the percentage increase in the volume of cone?

A
25%

B
50%

C
75%

D
100%

Solution

Let h and r be the height and radius of the cone respectively.
Question 9
1 / -0

If f : R → R and g : R → R are two mappings defined as f(x) = 2x and g(x) = x²+2, then the value of (f + g)(2) is:

A
8

B
10

C
12

D
24

Solution
Question 10
1 / -0

A
11/7

B
15/7

C
25/7

D
22/7

Solution