Test: Class 9 Math: CBSE Sample Question Paper Term I - 2 - Class 9 MCQ

x² = 2
⇒ x = √2
∴ x³ =  x² . x
= 2√2

• The point (a, -a) means x = a and y = -a.
• For the equation y = x, both x and y should be equal. Since -a is not equal to a, the point does not lie on this line.
• For x + y = 0, substituting gives a - a = 0, so it lies on this line.
• The point lies on x = a and y = -a since they directly represent the coordinates.

In ΔABC
2x + 2y + ∠A = 180° (Angle sum property)
x + y + (∠A/2) = 90°
x + y = 90° – (A/2) ...1
In BOC, we have
x + y + ∠BOC = 180°
90° - (∠A/2) + ∠BOC = 180° [From (1)]
∠BOC = 180° - 90° + (∠A/2)
∠BOC = 90° + (∠A/2)
∠BOC = 90° + 25° = 115°

Area of equilateral triangle = 
= 
= 
= 3 x 1.732 = 5.196 sq. cm

= 
= 6+1-3
= 4
positive and rational

So, the correct options that are not linear equations are 2 and 4. Since the question asks for just one option, and typically in such questions, the first correct match is expected, Option 2 is the correct answer, as it is the one listed in the question.

In ΔABC 
∠ABC + ∠BAC + ∠ACB = 180°  (Angle sum property)
∠ABC = 180° - 90° - 40°
∠ABC = 50°
In ΔBED 
∠BED + ∠EBD + ∠BDE = 180°  (Angle sum property)
∠BDE = 180° - 50° - 100°
∠BDE= 30°

∠OQP = 180° - ∠OQF
= 180° - (30° + 65°)
⇒ ∠OQP = 85° ...(i)
∠APQ = ∠CQF (Corresponding angles)
⇒ 25° + y° = 65°
⇒ y° = 65° - 25°
⇒ y° = 40°
Now in ΔOPQ
∠0 + ∠OPQ + ∠PQO = 180°
⇒ x° + 40° + 85° = 180°
⇒ x° = 180° - 85° -  40° = 55°
⇒ x = 55°, y = 40°

= 
= 
= 
= 

The class width is the difference between the upper or lower class limits of consecutive classes. In this case, class width equals to the difference between the lower limits of the first two classes.
w = 10 - 0
So, the class width is 10

When a pair of parallel lines are cut by a transversal, 8 angles are formed.

4^x - 4^x-1 = 24
⇒ 
⇒ 
⇒ 
⇒ 
4^x = 32
(2²)^x = (2)⁵
2^2x = 2⁵
Comparing, we get

= 
= 
= 

= 
= 
= 
= 

Given that,
l₁ ‖ l₂
Let m and n be two transversal cutting them
∠w + ∠x = 180^o (Consecutive interior angle)
x = 180^o – w (i)
z = y (Alternate angles) (ii)
From (i) and (ii), we get
x + y = 180^o – w + z

y = 5x
at x = 1
y = 5.1 = 5
y = 5
(1,5)
at x = 2
y = 5.2 = 10
y = 10
(2,10)
at x = 3
y = 5.3 = 15
y = 15
(3,15)

A cumulative frequency distribution is the sum of the class and all classes below it in a frequency distribution.
Subtract the previous cumulative frequency (c.f) from the cumulative frequency of the current class.
So frequency of the class interval 20-30 is 14 - 5 = 9

Area of Δ = 1/2 x Base x Height
The smallest side is 11 m
Area = 1/2 x 11 x Height.. (i)
Area by Heron's Formula =  
s =
Area = 
= 330 m²
From eq (i)
330 = 1/2 x 11 x height
Height = 2 x 330/11 = 60 m

A histogram is a display of statistical information that uses rectangles to show the frequency of data items in successive numerical intervals of equal size. In the most common form of histogram, the independent variable is plotted along the horizontal axis and the dependent variable is plotted along the vertical axis.

Since 0 is rational number  it is in the form of p/q , and where q ≠ 0 as 0/1

EA ⊥ AB
∠AEF = 90°
∠AEF = ∠BEF + ∠AEB
∠BEF + ∠AEB = 90°
∠BEF = 55°
55° + ∠AEB = 90°
∠AEB = 90° - 55°
∠AEB = 55°

the linear equation 3x – 2y = 6,   cuts the x-axis
when y co-ordinate is 0
so we put y = 0 in given equation 3x – 2y = 6
3x - 2.0 = 6
3x = 6
∴ x = 2
so the co-ordinates are (2,0)

Area of isosceles right triangle = 8 sq. cm
1/2 x Base  Base = 8    [Since in isosceles right triangle, base and perpendicular are same]
⇒ (Base)² = 16
⇒ Base = 4 cm
Hypotenuse = 

As, the graph of y = 5 is a line parallel to x-axis i.e. y = 0.
⇒ The line represented by the equation y = 5 is parallel to x-axis and intersects y-axis at y = 5.
So, the graph of y = 5 is a line parallel to the x-axis at a distance of 5 units from the origin making an intercept 5 on the y-axis.

Let P be any point whose co-ordinate be P(0, b)
Then, if the value of x-coordinate or abscissa is zero then the point P lies in y-axis.

= 8/9

Let the sides be 3x, 4x and 5x.
Then according to quesiton, 3x + 4x + 5x = 84
⇒ 12x = 84
 ⇒ x = 7
Therefore, the sides are 3 x 7 = 21, cm, 4 x 7 = 28 cm and 5 x 7 = 35 cm
s =  = 42 cm
Area of triangle = 
= 
= 
= 21  7  2 = 294 sq. cm

True, you may have a triangle with two or more acute angles. If a triangle has three acute angles, the triangle is called an Acute Triangle. If a triangle has two acute angles and a single obtuse angle, the triangle is called an Obtuse Triangle.

The sum of two irrational numbers may be a rational number or an irrational number
Eg. a = √2 (which is irrational)
b  = 2√2(which is irrational)
a + b = √2 + 2√2 = 3√2 ( which is irrational)
and Let a = 1+√2  (which is  irrational)
and b= 1- √2 (which is irrational)
Now, a + b = 1+√2 +1- √2
= 2 (which is rational)

 Here,x < 0 (i.e, -ve) and y < 0, (i.e, -ve)
And we know that,co-ordinate of the point in 3rd quadrant is (-,-)i.e, both negative,
So,the given point will lie in 3rd quadrant.

Highest Marks = 100
Lowest Marks = 46
Range of data = 100 - 46 = 54