GATE Numerical Ability Questions (Quant & Analytical) -1 - Mechanical Engineering MCQ

In Farm P:

Hens = 65, Ducks = 91 and Goats = 169

In Farm Q:

Total number of Hens, Ducks, and Goats = 416

The ratio of Hens : Ducks : Goats = 5 : 14 : 13

Total number of Hens = 5/32 × 416 = 65
Total number of Ducks = 14/32 × 416 = 182
Total numbers of Goats = 13/32 × 416=169

From Farm P, all the Hens, Ducks and Goats are sent to Farm Q. 

Total Hens in farm Q = 65 + 65 = 130

Total Ducks in farm Q = 91 + 182 = 273

Total Goats in farm Q = 169 + 169 = 338

New Ratio = 130 : 273 : 338 = 10 : 21 : 26

The series formed is as follows,

Draw a rectangle and carved out the remaining position.

After the carved-out portion is out, make a mirror image of it.

Concept:

Replace the symbol as per their standard sign and solve using BODMAS.

Calculation:

Given:

Δ 2 ⊕ 3 Δ ((4 ⊗ 2) ∇ 4) = + 2 - 3 + ((4 ÷ 2) × 4)

∴ + 2 - 3 + (2 × 4)

∴ + 2 - 3 + 8

∴ 10 - 3 = 7

Concept:

From pie-chart, we can get the total number of executives in each company.

From the ratio table, we can get the numbers of executives with and without a management degree.

Calculation:

Given:

Total executives = 10,000

Percentage of executives in C2 = 5%, C5 = 20%

Ratio of executives with and without management degree C2 = 1 : 4, and C5 = 9 : 1.

Executives in C2 = 5/100 × 10000 = 500

Executives in C5 = 20/100 × 10000 = 2000

Executives with Management degree holders in C2 = 1/5 × 500 = 100

Executives with Management degree holders in C5 = 9/10 × 2000=1800

∴ total executives with management degree holders in C2 and C5 = 100 + 1800 = 1900.

Concept:

The Watched will beep together at the time of their Least Common Multiple (LCM).

Calculation:

Given:

Watch X beeps at = 30 sec

Watch Y beeps at = 32 sec

They beep together at = 10.00 AM

LCM of (30 & 32) = 480 sec

And X and Y will beep together after 480 sec or 8 minutes.

So Next beep time = 10.08 AM

Tracing path followed by Mr. X,

Hence Mr. X will be in North-West direction from the starting point.

The Venn diagram according to the given statements is as follows:

Conclusions:

All risk seekers are wealthy. → False (All wealthy are risk seekers but can't say vice versa is also true)

Only some entrepreneurs are risk seekers → False (All entrepreneurs are wealthy and All wealthy are risk seekers so all entrepreneurs will be risk seekers)

Hence neither conclusion I nor II is correct.

Let the radius of the circumscribed circle is R, and the radius of the inscribed circle is r.

Then area of circumscribed circle = πR²

Then the area of the inscribed circle = πr²

We know the angle between two adjacent sides in an equilateral triangle is 60°.

ΔOAB, Sin30 = r / R

R = 2r

The ratio of the area of the inscribed circle to the area of the circumscribed circle 

Concept:

P(E) = Number of favorable outcomes / Total number of outcomes

Calculation:

Given:

Number of blue balls = 15, Number of black balls = 45

Total number of balls = 15 + 45 = 60 balls

Balls are drawn from the box at random without replacement.

The probability of drawing first blue ball and second black ball is;