GATE Numerical Computation Aptitude (Quant) Questions - 1 - Mechanical Engineering MCQ

Correct answer is option C) 1

The odometer reading increases from starting point to end because odometer measures distance not displacement.
So, all the areas should be counted postive only.
Area of the given diagram = Odometer reading
Area of the velocity and time graph per second
1^st sec triangle = 1/2 * 1 * 1= 1/2
2^nd sec square = 1 × 1 = 1
3^rd sec square + triangle = 1 × 1 + 1/2 × 1 × 1 = 3/2
4^th sec triangle =1/2 * 1 * 2 = 1
5^th sec straight line = 0
6^th sec triangle = 1/2 * 1 * 1 = 1/2
7^th sec triangle = 1/2 * 1 * 1 = 1/2
Total Odometer reading at 7 seconds = 1/2 + 1 + 3/2 + 1 + 0 + 1/2 + 1/2 = 5m

As per trigonometric properties

tan θ = cot (90 - θ) and tan θ . cot θ = 1

Thus, tan 89° = cot (90 -89° ) =  cot 1°

Similarly, tan 88° = cot 2°, tan 87° = cot 3° ans so on...

Also from Logarith properties

log m +log n = log (m × n)

Thus, log tan 1° + log tan 89° = log (tan1° × tan89°)

= log (tan1° × cot1°)

= log 1 = 0

similarly, log tan 2° + log tan 88° = log (tan1° × cot1°) = log 1 = 0

Thus, log tan1° +log tan2° +……..+log tan 89° = 0

Concept:

1. (a - b)² = a² - 2ab + b²

2. (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

Where, (a + b + c)² > 0

If a, b & c ∀ 0, then

(a + b + c)²  = 0

Calculation:

Given that,

a² + b² + c² = 1   ----(1)

We know that, (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

⇒ (ab + bc + ca) ≥ -1/2

Again  ( b − c )² + ( c − a )² + ( a − b )² ≥ 0

⇒ bc + ca + ab ≤ a² + b² + c² = 1

Hence  − 1/2 ≤ bc + ca + ab ≤ 1

According to the given Venn diagram number of students who like to read books are.

13 + 12 + 44 + 7 = 76

Number of students who like to play sports are,

44 + 7 + 15 + 17 = 83

But the number of students who like both to read books and play sports are,

44 + 7 = 51

Hence the number of students who like to read books or play sports are,

76 + 83 – 51 = 108.

Here formula used is:

(No. of students Read books ⋃ no. of students play sports) ⋂ No of students read books 2 play sports.

From the logarithmic property, 

when x > y 

ln x > ln y if x and y both greater than 1.

and x > y 

ln x < ln y, if both x and y are less than 1.

but when x > y 

ex > ey  for any value of x and y.

but when x > y, x² > y²

 also cos x < cos y.

Area of Circle= πr² = π.(30)²

Remaining Area = 0.9π(30)² = 810π

If cone is made of some radius 'r'

Then Lateral Surface Area = πrl

Now 810π = π.rl where l = 30cm

810= r x 30

r = 27

h = √171

so r/h = 2.064

From The Question

A tiger is 50 leaps of its own from a deer.

Tiger takes 5 leaps per minute.

Deer takes 4 leaps per minute.

Tiger covers 8 meters per leap.

Deer covers 5 meters per leap.

Therefore, the tiger covers 5 x 8 = 40 meters/minute.
The deer covers 4 x 5 = 20 meters/minute.
Hence, the relative speed is 20 meters/minute.
The tiger is behind the deer by 50 x 8 = 400 meters.
Therefore, the time taken = distance/speed = 400/20 = 20 minutes.
Therefore, in the 20 minutes, the tiger will cover 20 x 40 = 800 meters.

Average only gives the mean value, Standard Deviation gives how close to mean value (consistency) of a sample population distribution.
A standard deviation close to 0 means very close to mean value of a distribution.
Here K has the lowest SD (5.21)