AP Police SI Mains 2019 Arithmetic and Reasoning

The centroid divides the distance from the orthocentre to the circumcentre in the ratio 2:1. So, they are colinear. 

So, Condition R is true.

But, Condition A doesn't true as they are colinear.So, they can't form any triangle.

So,Option D is correct choice.

Sum of all internal of a polygon is 

$$(n-2)180°.$$

Condition R:

we know that a pentagon has 5 sides.

So, Condition A:

Sum of all internal angles of a pentagon is

$$(5-2)×180°=3×180°=540°.$$

So, both the conditions are correct and A is dependent on R.

So, Option A is correct choice.

If side of an equilateral triangle is 'a' then the height of the triangle is$$=(√3/2)a.$$

Area of the triangle$$=(√3/4)a^2.$$

Condition A:

here ,$$a=5$$

so, Area$$=(√3/4)×5^2=(25/4)√3.$$

Condition R:

we know that sum of all the angle of triangle is 180°.

So, both the conditions are correct but 'A' is not dependent on 'R'.

Option B is correct choice.

We know that sum of squares of first n naturals numbers is $$n(n+1)(2n+1)/6$$.

Condition A:

$$n=49.$$

so,$$1^2+2^2+3^2+......+49^2$$

$$=49×(49+1)(49×2+1)/6$$

$$=49×50×99/6$$

$$=40425.$$

Condition R:

$$n(n+1)(n+2)/6$$

$$=49×50×51/6$$

$$=20825.$$

which doesn't satisfy the given equation.

So,Option C is correct choice.

Earth , Mercury and Venus all are planet except Moon

Awareness, Lore and Cadence is a form of knowledge about a particular subject

Goofy means foolish

Asparagus is a small plant 

Rest all are the different types of fruit

Elevation

-the action or fact of raising or being raised to a higher or more important level, state, or position.

Rest all are synonyms of improvement