Mathematical Ability Test-6

Result

Mathematical Ability Test-6

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Question 1
1 / -0

A subset H of a group (G,∗) is a group if:

A
a,b ∈ H ⇒ a ∗ b ∈ H

B
a ∈ H ⇒ a⁻¹ ∈ H

C
a, b ∈ H ⇒ a ∗ b⁻¹∈ H

D
H contains the identity element

Solution
Question 2
1 / -0

The angle of elevation of the top of the building from the foot of the tower is 30 and the angle of the top of the tower from the foot of the building is 60. If the tower is 50 m high, find the height of the building.

A
16.66m

B
18m

C
18.66m

D
20m

Solution
Question 3
1 / -0

In ΔPQR, side QR is produced to a point S, and exterior angle PRS = 100°. If RP = RQ, then measure of ∠PQR is:

A
50°

B
70°

C
75°

D
80°

Solution

Given:

PRS = 100°

RP = RQ

Let ∠PQR, ∠QPR (the equal angles) be x.

Sum of angles on a straight line = ∠PRS + ∠PRQ

⇒ 100° + ∠PRQ = 180°

⇒ ∠PRQ = 80°

Sum of angles of the ΔPQR = ∠PRQ + ∠PQR + ∠QPR

⇒ 80° + x + x = 180°

⇒ 2x = 100°

⇒ x = 50°

⇒ ∠PQR = 50°

∴ The value of ∠PQR is 50°.
Question 4
1 / -0

Find the centre and radius of x²+ y²+ 6y = 0.

A
(0, 3), 3

B
(−3, 0), 3

C
(3, 0), 3

D
(0, −3), 3

Solution
Question 5
1 / -0

Find the number of terms in the expansion of (2x + 3y + z)⁷.

A
34

B
33

C
35

D
36

Solution
Question 6
1 / -0

If the numerator and denominator of a fraction are decreased by 2 then the ratio becomes 2:1 and if the numerator is increased by 4 and the denominator by 3 then the ratio becomes 5:3 then what is the original fraction?

A
256 : 81

B
16 : 9

C
4 : 3

D
2 : 1

Solution
Question 7
1 / -0

A dice is tossed thrice. Find the probability of getting an odd number at least once:

A
4/9

B
7/9

C
7/8

D
3/4

Solution

Given,

A dice is tossed thrice

Then the sample space S = {1, 2, 3, 4, 5, 6}

Let P (A) = probability of getting an odd number in the first throw.
Question 8
1 / -0

The shadow of a tower standing on a level plane is found to be 50 m longer when Sun’s elevation is 30° than when it is 60°. Find the height of the tower.

A
20√3

B
25√3

C
10√3

D
30√3

Solution

Let SQ = h be the height of tower.

∠SPQ = 30^∘ and ∠SRQ = 60^∘

According to the question, the length of shadow is 50m long hen angle of elevation of the sun is 30^∘ than when it was 60^∘. So,

PR = 50m and RQ = xm
Question 9
1 / -0

If b_yx= 0.5, b_xy= 0.46, then the value of r is:

A
0.48

B
0.39

C
0.25

D
0.23

Solution
Question 10
1 / -0

A

B

C

D

Solution