Competive Exam Math 11

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Q. For three vertices: (x₁​,y₁​), (x₂​,y₂​), (x₃​,y₃​)

Centroid Formula : G(x₁​ + x₂ ​+ x₃/3,  y₁​ + y₂​ + y₃​​/3)

​Trick

Add the three X-coordinates and divide by 3.

Add the three Y-coordinates and divide by 3.

Example: Find the Centroid : A(3,5), B(2,6), C(4,1)

G = (3 + 2 + 4)/3​, (5+6+1​)/3 = (3,4)​

Ans: (3, 4)

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Q. The length of a rectangle is 25 cm and its width is 16 cm. What is its area ?

A) 350 cm²  B) 375 cm²  C) 400 cm²  D) 425 cm²

Solution:

Formula: $$\text{Area of Rectangle }=\text{Length}\times \text{Width}$$ $$=25\times 16$$ = 400 cm²

​Ans: (C) 400 cm²

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Q. If 35% of a number is 140, what is the number ?

A) 350  B) 400  C) 450  D) 500

Solution:

Let the number be x.

$$35\%\text{ of }x=140$$

35​/100 × x = 140

x = 140×100/35

 x = 4 × 100 = 400​

Ans: (B) 400

Trick

Number = Given Value × 100 / Percentage​​ =140 x 100/35 ​= 400

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Q. The HCF of two numbers is 18 and their LCM is 540. If one number is 90, what is the other number ?

A) 96  B) 108  C) 120  D) 135

Solution:

We know:

$$\text{First Number }\times \text{Second Number }=\text{HCF}\times \text{LCM}$$

Therefore,

Second Number = HCF × LCM​ /First Number = 18×540​/90 = 9720​/90 =108​

Ans: (B) 108

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Q. 5/12 ​+ 7​/18 = ?

$Solution:$

LCM of 12 and 18 = 36

5​/12 = 15​/36

7/18 ​= 14/36​

Therefore,

15​/36 + 14/36 ​= 29/36​

Ans: (D) 29/36

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Q. The length of a rectangle is 25 cm and its width is 16 cm. What is its area ?

A) 350 cm²  B) 375 cm²  C) 400 cm²   D) 425 cm²

Solution:

​Formula: Area of Rectangle = Length×Width = 25×16 = 400 cm²

​Ans: (C) 400 cm²

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Q. If 35% of a number is 140, what is the number ?

A) 350  B) 400  C) 450  D) 500

Solution:

Let the number be x.

35% of x = 140

35/100​ × x = 140

x = 140×100​/35

x = 4×100 = 400

Ans: (B) 400

Trick : Number = Given Value × 100​​ / Percentage