Mathematical Ability Test-6

Result

Mathematical Ability Test-6

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Question 1
1 / -0

A metallic sphere of radius 10.5 cm is melted and thus recast into small cones, each of radius 3.5 cm and height 3 cm. Find how many cones are obtained.

A
123

B
124

C
125

D
126

Solution

Therefore, 126 smaller cones are obtained from the melted metallic sphere.
Question 2
1 / -0

The angle of intersection of the curves y = 4 − x² and y = x² is:

A

B

C

D
π/2

Solution
Question 3
1 / -0

If P and Q are two sets, then (P − Q) ∪ (Q − P) ∪ (P ∩ Q) will be:

A
P

B
Q

C
P ∩ Q

D
P ∪ Q

Solution

P - Q = The set of elements which belong to P but not to Q.

P U Q = The set which consists of all elements of P and all elements of Q, the common elements being taken only once.

P ∩ Q = The set of all elements which are common to both P and Q.

let us suppose P = {1, 2, 3, 4} and Q = {3, 4, 5, 6}

⇒ P - Q = {1, 2}

⇒ Q - P = {5, 6}

⇒ P U Q = {1, 2, 3, 4, 5, 6}

⇒ P ∩ Q = {3, 4}

⇒ (P - Q) ∪ (Q - P) ∪ (P ∩ Q) = {1, 2} U {5, 6} U {3, 4} = {1, 2, 3, 4, 5, 6} = P U Q
Question 4
1 / -0

A
2

B
1

C
-2

D
-1

Solution
Question 5
1 / -0

A TV set is being sold for Rs. X in Delhi. A dealer went to Chandigarh and bought the TV at 20% discount (from the price of Delhi). He spends Rs. 600 on transport. Thus, he sold the set in Delhi for Rs. X making (100/7) % profit what is the value of X?

A
Rs. 7200

B
Rs. 8000

C
Rs. 8800

D
Rs. 9600

Solution
Question 6
1 / -0

From the top of a cliff 25 m high the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. The height of the tower is:

A
25 m

B
50 m

C
75 m

D
100 m

Solution

Let AB be the tower and CD be the cliff Angle of elevation of A is equal to the angle of depression of B at C.

Let angle be Q and CD is 25 m.
Question 7
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Which of the following option is correct?

A
A > B

B
A = B = 1

C
A < B

D
A + B = 3

Solution
Question 8
1 / -0

If A = { x : x ∈ N, 0 < x < 6} and B = {x : x is a prime natural number, 0 < x < 10} Find A - B ?

A
{2, 3, 5}

B
{1, 4}

C
{2, 3}

D
{2, 3, 4}

Solution

Given:

A = { x : x ∈ N, 0 < x < 6}

B = {x : x is a prime natural number, 0 < x < 10}

A = { x : x ∈ N, 0 < x < 6}

A = {1, 2, 3, 4, 5}

B = {x : x is a prime natural number, 0 < x < 10}

B = {2, 3, 5, 7}

A - B = {1, 2, 3, 4, 5} - {2, 3, 5, 7}

= {1, 4}

∴ The value A - B is {1, 4}.
Question 9
1 / -0

A
π/2

B
π/4

C
π/6

D
π/8

Solution
Question 10
1 / -0

A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60^∘ with the wall, then the height of the wall is:

A
15√3 m

B

C
15/2 m

D
15 m

Solution

Let AB is a wall and AC is the ladder 15 m long which makes an angle of 60° with the ground.