Mathematical Ability Test-1

Result

Mathematical Ability Test-1

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Weekly Quiz Competition

Question 1
1 / -0

The number of terms in the expansion of (1 + 3x + 3x²+ x³)⁶ is:

A
18

B
9

C
19

D
24

Solution

Given:
Question 2
1 / -0

Equation of the circle having diameter 8 and diameters y + 2x - 5 = 0 and 2y + 3x - 8 = 0 is?

A
x²+ y²− 2x − 4y − 25 = 0

B
x²+ y²− 4x − 2y − 11 = 0

C
x²+ y²+ 4x + 2y − 25 = 0

D
x²+ y²− 2x − 4y + 11 = 0

Solution

Given:

Diameter = 8

Radius = 4

Also diameters equations:

y + 2x − 5 = 0 ...(i)

2y + 3x − 8 = 0 ..(ii)

Substracting 2× (i) from (ii)

− x + 2 = 0

x = 2

Putting back in (i):

y + 2 × 2 − 5 = 0

y = 1

So center is (2,1) and radius is 4.

The equation of circle:
Question 3
1 / -0

Three pipes A, B, and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all three pipes are opened. A, B, and C discharge chemical solutions P, Q, and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?

A
6/22

B
6/11

C
3/7

D
7/12

Solution

According to the question,

Three pipes A, B, and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all three pipes are opened. A, B, and C discharge chemical solutions P, Q, and R respectively.

Part filled by A+B+C in 3 minutes
Question 4
1 / -0

Evaluate 2(sec⁡ A − cos ⁡A)²+ 2(cosec A − sin ⁡A)²− 2(cot⁡ A − tan⁡ A)²− 2.

A
0

B
1

C
2

D
3

Solution
Question 5
1 / -0

A can do a piece of work in 5 days and B can do the same work in 5 days. In how many days working together will they do the same work?

A
7

B
14

C
7/4

D
5/2

Solution
Question 6
1 / -0

60% of the employees of a company are college graduates. Of these, 10% are in sales. Of the employees who did not graduate from college, 80% are in sales. The probability that an employee selected at random is in sales is:

A
0.46

B
0.38

C
0.62

D
0.54

Solution

∴ The probability that an employee selected at random is in sales, is 0.38.
Question 7
1 / -0

Shakeel started a software business by investing Rs. 20000. After six months, Neel joined him with a capital of Rs. 30000. After 3 years, they earned a profit of Rs. 13950. What was Shakeel’s share in the profit?

A
Rs. 6200

B
Rs. 6400

C
Rs. 4200

D
Rs. 7750

Solution
Question 8
1 / -0

Find the coefficients of the term independent of x in the expansion of

A
0

B
1

C
32

D
-32

Solution
Question 9
1 / -0

Lines x = ay + b, z = cy + d and x = a'y + b', z = c'y + d' are perpendicular, if:

A
aa' + cc' + 1 = 0

B
aa' + cc' - 1 = 0

C
ac + a'c' -1 = 0

D
ac + a'c' + 1 = 0

Solution

Given,

For line I
Question 10
1 / -0

A person bought two bicycles for Rs. 1600 and sold the first at 10% profit and the second at 20% profit. If he sold the first at 20% profit and the second at 10% profit, he would get ₹ 5 more. The difference in the cost price of the two bicycles was:

A
Rs. 25

B
Rs. 75

C
Rs. 50

D
Rs. 40

Solution