Maths Mock Test- 1 - Class 9 MCQ

Remainder,

[We have taken individual remainder, which means if 73 is divided by 34 individually, it will give remainder 5, 75 divided 34 gives remainder 7 and so on.]

[We have taken here negative as well as positive remainder at the same time. When 30 divided by 34 it will give either positive remainder 30 or negative remainder -4. We can use any one of negative or positive remainder at any time.]

Required remainder = 32.

Octal to Decimal conversion is obtained by multiplying 8 to the power of base index along with the value at that index position.

(532.2)8 = 5 * 8² + 3 * 8¹ + 2 * 8⁰ + 2 * 8^-1 = (346.25)10

Things which are double of the same things are equal to one another.
Example : 
1. If 2x = 2y then x = y.
2. If a = b, then 2a = 2b

To understand this, let's break down the information given:

1. x-axis: The x-axis is the horizontal line in the coordinate plane. Any point on the x-axis will have a y-coordinate of 0 because it does not move up or down from the axis.

2. Distance of 4 units in the negative direction of x-axis:

   • The x-axis has a positive direction (towards the right) and a negative direction (towards the left).
   • Moving 4 units in the negative direction means moving 4 units to the left from the origin (0,0).

3. Coordinates:

   • When you move 4 units to the left on the x-axis, the x-coordinate becomes -4, and since the point is on the x-axis, the y-coordinate remains 0.

Therefore, the point that lies on the x-axis 4 units in the negative direction is (−4,0)(-4, 0)(−4,0).

This corresponds to option (b) (-4, 0).

To find if ( x = 2, y = -1 ) is a solution for a given equation, substitute these values into each equation:

- A: ( 2(2) + 3(-1) =1 not  5 ) ❌
- B: ( 2 + (-1) = 1 not 5 ) ❌
- C: ( 2 + (-1) = 1 ) ✓
- D: ( 2 - (-1) = 3 not 9 ) ❌

Therefore, option C is the correct answer.

Let
a = 15cm
b = 25cm
c = 14cm

Semi-Perimeter = a + b + c / 2
= 15 + 25 + 14 / 2
= 54 / 2
= 27 cm.


Area Through Heron's Formula

= √s(s-a)(s-b)(s-c)
= √27(27-15)(27-25)(27-14)
= √27 × 12 × 2 × 13
= √3 × 3 × 3 × 2 × 2 × 3 × 13
= 3 × 3 × 2 √13
= 18 √13

A non-terminating, non-repeating decimal is a decimal number that continues endlessly, with no group of digits repeating endlessly.

Decimals of this type cannot be represented as fractions, and as a result, are irrational numbers.

We know that 

∠ABC = 85°  
∠FAE = 24°  
AE is parallel to CD  
AB is produced to F  

Formula Used:  
In a cyclic quadrilateral, opposite angles sum up to 180°.  
The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.  

Calculation:  

We know in a cyclic quadrilateral opposite angles sum up to 180°. So,  
∠ABC + ∠ADC = 180°  
∠ADC = 180° - 85° = 95°  
∠EAD = ∠ADC = 95° [Alternate interior angles of parallel lines CD and AE]  
∠FAD = ∠FAE + ∠EAD  
∠FAD = 24° + 95° = 119°  
∠BCD = ∠FAD = 119° [Exterior angle of a cyclic quadrilateral]  

∴ The correct answer is 119°.
 

Consider a point D on the arc CA and join DC and AD.

We know that the angle subtended by an arc is twice the angle subtended by it on the circumference in the alternate segment.

So we get:
∠2 = 2∠1

By substituting the values:

130° = 2∠1

So we get:
∠1 = 65°

From the figure, we know that the exterior angle of a cyclic quadrilateral = interior opposite angle:
∠PBC = ∠1

So we get:
∠PBC = 65°

Therefore, ∠PBC = 65°.

Degree is the highest exponent of any value in an equation. Here, this highest exponent is 4. Therefore, 4 is the degree of the given equation.