Area- Aptitude Questions and Answers - in Hindi

View in English View in Hindi

One diagonal and perimeter of a rhombus are 24 cm and 52 cm respectively. The area of rhombus will be?

A)
60 cm2

B)
120 cm2

C)
100 cm2

D)
30 cm2


Correct Answer :

120 cm2


Explanation :


Side of roumbus =52/4 = 13 cm

Area of the roumbus = (product of diagonals)/2

Let ABCD is rhombus, in which Side of roumbus =AB=13cm , BD=24cm and AC=? cm
the digonal of rhoumbus bisect each other at right angle

in the right angel AOB
OA2+OB2=AB2
OA2+(BD/2)2=AB2
OA2+(12)2=(13)2
OA2= (13)2 - (12)2
OA = √(169-144) =√25 = 5
Hence the lenght of other dignoal is AC=2*OA= 2*5= 10cm
Thus,Area of the roumbus = (product of diagonals)/2
=> ( 24 * 10 ) /2 => 120 cm2

ABCD is a square of side X cm. Its side is increased by 30%. What is the change in its area?


ABCD एक वर्ग है जिसकी भुजा 'X' सेमी हे। यदि इसकी एक भुजा 30% की वृद्धि कर दे तो इसके क्षेत्र में क्या परिवर्तन होगा?

A)
60%

B)
62.5%

C)
63%

D)
69%


Correct Answer :

69%


Explanation :

Let side = X cm
then Area = length of a side2 ⇒ (X)2 cm2

increased side by 30 then, new side = 130 % of X ⇒ (130/100) *X ⇒ 1.3X cm
And,new area = length of a side2 ⇒ (1.3)2 sq. cm

Increase in area = (1.3*X)2 - (X)2 cm2
= 1.69*X2 - X2
= .69*X2
% Increase = 69

The sides of a triangle a, b, c are such that 2a = 3b = 4c and its perimeter is 208 cm. What is the length of the longest side?

A)
48cm

B)
96cm

C)
64cm

D)
54cm


Correct Answer :

96cm


Explanation :

Let 2a = 3b = 4c = x
So, a = x/2 b = x/3 c = x/4
The L.C.M of 2, 3 and 4 is 12
Therefore, a : b : c = x/2 × 12 : x/3 × 12 : x/4 = 12
= 6x : 4x : 3x
= 6 : 4 : 3
Therefore, a : b : c = 6 : 4 : 3

the perimeter of a triangle is sum of its side
Lets take a variable x for the sides,
hence the sides will be 6x,4x,3x respectively.

Perimeter = 6x+4x+3x
208 = 6x+4x+3x = 13x
13x = 208
=> x = 208/13
x=16

Length of the longest side = 6x = 6 x 16 = 96.

What is the longest side of a rectangle which has a perimeter of 70 units and an area of 276 square units?

A)
12 units

B)
18 units

C)
23 units

D)
36 units


Correct Answer :

23 units


Explanation :

let Length =L and Width=W

Perimeter = 2(L + W) = 70
L + W = 35
L = 35 - W

Area = WL = 276
W(35 - W) = 276
35W - W2 = 276
0 = W2 - 35W + 276
0 = (W - 23)(W - 12)
W = {12, 23}
L = {23, 12}

Therefore, the sides of the rectangle are 23 and 12
The longest side of the rectangle is 23 units.

The length and breadth of a rectangular hall are 40 m and 30 m respectively. What is the distance between two opposite corners of the hall?

A)
20 m

B)
35 m

C)
50 m

D)
40 m


Correct Answer :

50 m


Explanation :

Distance between two corners of hall
= √(Length2 + Breadth2)
= √(402 + 302) = √(1600 + 900) = 50 m

The area of the base of a rectangular tank is 6500 cm2 and volume of water contained in it is 2.6 m3. The depth of water (in metres) in the tank is

A)
2.5

B)
3

C)
4

D)
5.5


Correct Answer :

4


Explanation :

Let the depth of water be x m.Then
(6500/10000) * x = 2.6
x =(2.6*10000)/6500
= 4 m

The ratio of areas of two squares A and B are 4:25. If the side of the square A is 6m. Then, what is the measure of the side of square B?


दो वर्गो A और B के क्षेत्रों का अनुपात 4:25 है। यदि वर्ग A की भुजा 6 मीटर है। फिर, वर्ग B की भुजा का माप क्या होगा?

A)
256m

B)
15m

C)
12m

D)
32m2


Correct Answer :

15m


Explanation :

area of square A= (6)²= 36 m²
let side of square B is x, So area of square B= x² m²

As given 36:x²:: 4:25
36/x² = 4/25
9/x² = 1/25
(3/x)²= (1/5)²
3/x = 1/5
x = 15 m
So side of square B has a length of 15 m

What is the measure of the base angle of an isosceles triangle, if its vertical angle is 70°?


एक समाद्विबाहु त्रिभुज के आधार कोण का माप क्या है, यदि उसका शिर्षकोण 70 डिग्री है?

A)
110°

B)
55°

C)
90°

D)
70°


Correct Answer :

55°


Explanation :

The sum of all the angles of a triangle must equal 180 degrees.
An isosceles triangle has two (Base) angles that are equal. The vertex angle is the odd one. So:

the measure of each base angle x.then
x + x + 70 = 180
2x = 180-70
x = 110/2
x = 55
The base angles measure 55°

If 'x' units are added to the length of the radius of a circle, what is the number of units by which the circumference of the circle is increased?


यदि किसी वृत्त की त्रिज्या की लंबाई में 'X' इकाइयाँ जोड़ी जाती हैं, तो वृत्त की परिधि मे कितनी इकाइयाँ बढ़ जाती है?

A)

X


B)


C)

2πX


D)

X2



Correct Answer :

2πX


Explanation :

Let the radius of the circle be r .
The circumference of the circle will therefore be 2 πr .

If the radius is increased by 'X' units, the new radius will be (r + X) .

The new circumference will be 2 π(r + X) = 2 πr + 2 πX
Hence, the circumference increases by 2 πX units.

The sides of a triangle are 30, 40 and 50 cm. Then this triangle is a?


एक त्रिभुज की भुजाएँ 30, 40 और 50 सेमी हैं। फिर यह त्रिभुज है?

A)

right-angled triangles

/

समकोण त्रिभुज


B)

acute-angled triangle

/

न्यून कोण त्रिभुज


C)

obtuse-angled triangle

/

अधिक कोण त्रिभुज


D)

equilateral triangle

/

समभुज त्रिभुज



Correct Answer :

right-angled triangles


Explanation :

As per Pythagoras Theorem, a triangle with a right angle (an angle of 90°) has a special relationship between the lengths of its three sides.
If the longest side (called the hypotenuse) is c and the other two sides (next to the right angle) are called a and b, then:
a2 + b2 = c2 Pythagoras' Theorem

Therefore, the triangles that follow this rule will be right angled triangles.

The triangle with sides 30, 40, 50 follows the Pythagorean theorem, so it is a right angle
302 + 402 = 900 + 1600 = 2500 = 502

Also 30, 40 and 50 are multiples of 3, 4, and 5 which is a well known "the 3-4-5 triangle"

3-4-5 triangle: there are some right-angled triangles, where all three sides are whole numbers called Pythagorean Triangles. And the three whole number side-lengths are called a Pythagorean triple or triad.

Below the list examples of Pythagorean triples-
3, 4, 5
5, 12, 13
6, 8, 10
7, 24, 25
8, 15, 17
9, 12, 15
9, 40, 41
10, 24, 26
12, 16, 20
12, 35, 37
14, 48, 50
15, 20, 25
15, 36, 39
16, 30, 34
18, 24, 30
20, 21, 29
21, 28, 35
24, 32, 40
27, 36, 45
30, 40, 50

A polygon has 44 diagonals, the number of its sides are?


एक बहुभुज में 44 विकर्ण है, तो उसकी भुजाओं की संख्या होगी?

A)

9


B)

10


C)

11


D)

12



Correct Answer :

11


Explanation :

Polygon: A polygon is a 2-dimensional shape that is formed with straight lines. Triangles, quadrilaterals, pentagons, and hexagons are all examples of polygons.

Let the side is n. because there are n sides, we have to subtract n from total number of line formed by joining two adjacent vertices of polygon.

number of diagonals = nC2 -n = n(n-1)/2 - n
number of diagonals = n(n-3) / 2 = 44
n2 - 3n - 88 = 0
(n+3) (n-11) = 0

n=11 (n can not be negative)
So the number of sides in a shape with 44 diagonals is 11.

If the length and breadth of a rectangular plot were increased by 20 percent; then what would be the percent increase in the area of the plot?


यदि एक आयताकार भूखंड की लंबाई और चौड़ाई में 20 प्रतिशत की वृद्धि हुई थी; तो फिर भूखंड के क्षेत्र में प्रतिशत वृद्धि क्या होगी?

A)

20%


B)

44%


C)

26%


D)

36%



Correct Answer :

44%


Explanation :

Let the length of rectangle be x and breadth be y
So Area= length*breadth= x*y

According to The question
length = x + x*20/100= x *(1 + 1/5)=6x/5
breadth = y + y*20/100=y *(1 + 1/5)= 6y/5

New Area= 6x/5 × 6y/5 = 36*xy/25

Changes in area= 36*xy/25 - xy =xy* (36-25 / 25) =11*xy/25

% change = (11*xy / 25)*100 / xy = 44% area would be increase

Latest Updates

General Knowledge of MP

Under the Madhya Pradesh Ladli Laxmi Yojana, the beneficiary is paid the total amount on attaining the age of ?

Indian Politics

Who appoints the Chairman and the Members of the Union Public Service Commission?

General Knowledge of World

Which country will host the 2022 Football World Cup?

Area

The angles of a triangle are in the ratio 2 : 4 : 3. The smallest angle of the triangle is?

Which one of the following triples does not represent the sides of a triangle?

If the perimeter of a rectangle is 10 cm and the area is 4 cm2, then its length is?

Height and Distance

An aeroplane flying at a height of 300 m above the ground passes vertically above another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 60º and 45º respectively. What is the height of the lower plane from the ground?

From the top of a building 90 m high, the angles of depression of the top and the bottom of a tree are 30º and 45º respectively. What is the height of the tree?

Trigonometry

What is the value of sinx √( 1 /1+cosx + 1 /1-cosx ) ?

What is cos4 A - sin4 A / cos2 A - sin2 A equal to?

If 7sin2 x +3cos2 x = 4, 0 < x < 90º ,then what is the value of tan x?

If x = a cosθ + b sinθ and y = a sinθ - b cosθ then what is x2 + y2 equal to?

Average

The mean of 5 numbers is 15. If one more number is included, the mean of the 6 numbers becomes 17. What is the included number?

The mean marks obtained by 300 students in a subject are 60. The mean of top 100 students was found to be 80 and the mean of last 100 students was found to be 50. The mean marks of the remaining 100 students are?

In an asymmetrical distribution, of the mean and median of the distribution are 270 and 220 respectively, then the mode of the data is?

Let a, b, c, d, e, f, g be consecutive even numbers and j, k, l, m, n be consecutive odd numbers. What is the average of all the numbers?

Alligation or Mixture

25 kg of alloy X is mixed with 125 kg of alloy Y. If the amount of lead and tin in the alloy X is the ratio 1 : 2 and the amount of lead and tin in the alloy Y is in the ratio 2 : 3, then what is the ratio of lead to tin in the mixture?

Simplification

The ratio of two numbers is 1 : 5 and their product is 320. What is the difference between the square of these two numbers?