[Download PDF] AP Police SI Mains 2019 Arithmetic and Reasoning Paper with Solutions

Instructions

For the Assertion (A) and Reason (R) the correct alternative from the following

Question 161

(A): If D, E and F respectively represent orthocentre, centroid and circumcentre of a triangle $$\triangle ABC$$, then Area of $$\triangle DEF = \frac{1}{4}$$ (Area of $$\triangle ABC$$)
(R) : In any triangle, orthocentre, centroid and circumcentre are collinear:

Video Solution

Solution

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.

Question 162

(A) : The sum of all internal angles in a pentagon is 540°
(R) : A pentagon has 5 sides

Video Solution

Solution

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.

Question 163

(A): The area of an equilateral triangle of side 5 cm is $$\frac{25}{4}\sqrt{3} cm^2$$

(R): Sum of the angles in the triangle is 180°

Video Solution

Solution

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.

Question 164

(A): $$1^2 + 2^2 + 3^2 + ...... +49^2$$ = 40425

(R): Sum of the squares of the first n natural numbers is $$\frac{n(n + 1)(n + 2)}{6}$$

Video Solution

Solution

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.

Instructions

Identify the odd thing from the following options.

Question 165

Video Solution

Solution

Earth , Mercury and Venus all are planet except Moon

Question 166

Video Solution

Solution

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

Goofy means foolish

Question 167

Video Solution

Question 168

Video Solution

Solution

Asparagus is a small plant

Rest all are the different types of fruit

Question 169

Video Solution

Question 170

Video Solution

Solution

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

CAT Content

AP Police SI Mains 2019 Arithmetic and Reasoning

(A): If D, E and F respectively represent orthocentre, centroid and circumcentre of a triangle $$\triangle ABC$$, then Area of $$\triangle DEF = \frac{1}{4}$$ (Area of $$\triangle ABC$$)
(R) : In any triangle, orthocentre, centroid and circumcentre are collinear:

(A) : The sum of all internal angles in a pentagon is 540°
(R) : A pentagon has 5 sides

(A): The area of an equilateral triangle of side 5 cm is $$\frac{25}{4}\sqrt{3} cm^2$$

(R): Sum of the angles in the triangle is 180°

(A): $$1^2 + 2^2 + 3^2 + ...... +49^2$$ = 40425

(R): Sum of the squares of the first n natural numbers is $$\frac{n(n + 1)(n + 2)}{6}$$

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CAT Content

AP Police SI Mains 2019 Arithmetic and Reasoning

(A): If D, E and F respectively represent orthocentre, centroid and circumcentre of a triangle $$\triangle ABC$$, then Area of $$\triangle DEF = \frac{1}{4}$$ (Area of $$\triangle ABC$$)(R) : In any triangle, orthocentre, centroid and circumcentre are collinear:

(A) : The sum of all internal angles in a pentagon is 540°(R) : A pentagon has 5 sides

(A): The area of an equilateral triangle of side 5 cm is $$\frac{25}{4}\sqrt{3} cm^2$$ (R): Sum of the angles in the triangle is 180°

(A): $$1^2 + 2^2 + 3^2 + ...... +49^2$$ = 40425 (R): Sum of the squares of the first n natural numbers is $$\frac{n(n + 1)(n + 2)}{6}$$

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CAT Quant Questions | CAT Quantitative Ability

CAT DILR Questions | LRDI Questions For CAT

CAT Verbal Ability Questions | VARC Questions For CAT

(A): If D, E and F respectively represent orthocentre, centroid and circumcentre of a triangle $$\triangle ABC$$, then Area of $$\triangle DEF = \frac{1}{4}$$ (Area of $$\triangle ABC$$)
(R) : In any triangle, orthocentre, centroid and circumcentre are collinear:

(A) : The sum of all internal angles in a pentagon is 540°
(R) : A pentagon has 5 sides

(A): The area of an equilateral triangle of side 5 cm is $$\frac{25}{4}\sqrt{3} cm^2$$

(R): Sum of the angles in the triangle is 180°

(A): $$1^2 + 2^2 + 3^2 + ...... +49^2$$ = 40425

(R): Sum of the squares of the first n natural numbers is $$\frac{n(n + 1)(n + 2)}{6}$$